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Sample records for nonlinear geostatistical inverse

  1. Monte Carlo full-waveform inversion of crosshole GPR data using multiple-point geostatistical a priori information

    DEFF Research Database (Denmark)

    Cordua, Knud Skou; Hansen, Thomas Mejer; Mosegaard, Klaus

    2012-01-01

    We present a general Monte Carlo full-waveform inversion strategy that integrates a priori information described by geostatistical algorithms with Bayesian inverse problem theory. The extended Metropolis algorithm can be used to sample the a posteriori probability density of highly nonlinear...... inverse problems, such as full-waveform inversion. Sequential Gibbs sampling is a method that allows efficient sampling of a priori probability densities described by geostatistical algorithms based on either two-point (e.g., Gaussian) or multiple-point statistics. We outline the theoretical framework......) Based on a posteriori realizations, complicated statistical questions can be answered, such as the probability of connectivity across a layer. (3) Complex a priori information can be included through geostatistical algorithms. These benefits, however, require more computing resources than traditional...

  2. Geostatistical regularization operators for geophysical inverse problems on irregular meshes

    Science.gov (United States)

    Jordi, C.; Doetsch, J.; Günther, T.; Schmelzbach, C.; Robertsson, J. OA

    2018-05-01

    Irregular meshes allow to include complicated subsurface structures into geophysical modelling and inverse problems. The non-uniqueness of these inverse problems requires appropriate regularization that can incorporate a priori information. However, defining regularization operators for irregular discretizations is not trivial. Different schemes for calculating smoothness operators on irregular meshes have been proposed. In contrast to classical regularization constraints that are only defined using the nearest neighbours of a cell, geostatistical operators include a larger neighbourhood around a particular cell. A correlation model defines the extent of the neighbourhood and allows to incorporate information about geological structures. We propose an approach to calculate geostatistical operators for inverse problems on irregular meshes by eigendecomposition of a covariance matrix that contains the a priori geological information. Using our approach, the calculation of the operator matrix becomes tractable for 3-D inverse problems on irregular meshes. We tested the performance of the geostatistical regularization operators and compared them against the results of anisotropic smoothing in inversions of 2-D surface synthetic electrical resistivity tomography (ERT) data as well as in the inversion of a realistic 3-D cross-well synthetic ERT scenario. The inversions of 2-D ERT and seismic traveltime field data with geostatistical regularization provide results that are in good accordance with the expected geology and thus facilitate their interpretation. In particular, for layered structures the geostatistical regularization provides geologically more plausible results compared to the anisotropic smoothness constraints.

  3. Approaches in highly parameterized inversion: bgaPEST, a Bayesian geostatistical approach implementation with PEST: documentation and instructions

    Science.gov (United States)

    Fienen, Michael N.; D'Oria, Marco; Doherty, John E.; Hunt, Randall J.

    2013-01-01

    The application bgaPEST is a highly parameterized inversion software package implementing the Bayesian Geostatistical Approach in a framework compatible with the parameter estimation suite PEST. Highly parameterized inversion refers to cases in which parameters are distributed in space or time and are correlated with one another. The Bayesian aspect of bgaPEST is related to Bayesian probability theory in which prior information about parameters is formally revised on the basis of the calibration dataset used for the inversion. Conceptually, this approach formalizes the conditionality of estimated parameters on the specific data and model available. The geostatistical component of the method refers to the way in which prior information about the parameters is used. A geostatistical autocorrelation function is used to enforce structure on the parameters to avoid overfitting and unrealistic results. Bayesian Geostatistical Approach is designed to provide the smoothest solution that is consistent with the data. Optionally, users can specify a level of fit or estimate a balance between fit and model complexity informed by the data. Groundwater and surface-water applications are used as examples in this text, but the possible uses of bgaPEST extend to any distributed parameter applications.

  4. Reservoir Modeling Combining Geostatistics with Markov Chain Monte Carlo Inversion

    DEFF Research Database (Denmark)

    Zunino, Andrea; Lange, Katrine; Melnikova, Yulia

    2014-01-01

    We present a study on the inversion of seismic reflection data generated from a synthetic reservoir model. Our aim is to invert directly for rock facies and porosity of the target reservoir zone. We solve this inverse problem using a Markov chain Monte Carlo (McMC) method to handle the nonlinear...

  5. Nonlinear problems in fluid dynamics and inverse scattering: Nonlinear waves and inverse scattering

    Science.gov (United States)

    Ablowitz, Mark J.

    1994-12-01

    Research investigations involving the fundamental understanding and applications of nonlinear wave motion and related studies of inverse scattering and numerical computation have been carried out and a number of significant results have been obtained. A class of nonlinear wave equations which can be solved by the inverse scattering transform (IST) have been studied, including the Kadaomtsev-Petviashvili (KP) equation, the Davey-Stewartson equation, and the 2+1 Toda system. The solutions obtained by IST correspond to the Cauchy initial value problem with decaying initial data. We have also solved two important systems via the IST method: a 'Volterra' system in 2+1 dimensions and a new one dimensional nonlinear equation which we refer to as the Toda differential-delay equation. Research in computational chaos in moderate to long time numerical simulations continues.

  6. Limits to Nonlinear Inversion

    DEFF Research Database (Denmark)

    Mosegaard, Klaus

    2012-01-01

    For non-linear inverse problems, the mathematical structure of the mapping from model parameters to data is usually unknown or partly unknown. Absence of information about the mathematical structure of this function prevents us from presenting an analytical solution, so our solution depends on our......-heuristics are inefficient for large-scale, non-linear inverse problems, and that the 'no-free-lunch' theorem holds. We discuss typical objections to the relevance of this theorem. A consequence of the no-free-lunch theorem is that algorithms adapted to the mathematical structure of the problem perform more efficiently than...... pure meta-heuristics. We study problem-adapted inversion algorithms that exploit the knowledge of the smoothness of the misfit function of the problem. Optimal sampling strategies exist for such problems, but many of these problems remain hard. © 2012 Springer-Verlag....

  7. Training-Image Based Geostatistical Inversion Using a Spatial Generative Adversarial Neural Network

    Science.gov (United States)

    Laloy, Eric; Hérault, Romain; Jacques, Diederik; Linde, Niklas

    2018-01-01

    Probabilistic inversion within a multiple-point statistics framework is often computationally prohibitive for high-dimensional problems. To partly address this, we introduce and evaluate a new training-image based inversion approach for complex geologic media. Our approach relies on a deep neural network of the generative adversarial network (GAN) type. After training using a training image (TI), our proposed spatial GAN (SGAN) can quickly generate 2-D and 3-D unconditional realizations. A key characteristic of our SGAN is that it defines a (very) low-dimensional parameterization, thereby allowing for efficient probabilistic inversion using state-of-the-art Markov chain Monte Carlo (MCMC) methods. In addition, available direct conditioning data can be incorporated within the inversion. Several 2-D and 3-D categorical TIs are first used to analyze the performance of our SGAN for unconditional geostatistical simulation. Training our deep network can take several hours. After training, realizations containing a few millions of pixels/voxels can be produced in a matter of seconds. This makes it especially useful for simulating many thousands of realizations (e.g., for MCMC inversion) as the relative cost of the training per realization diminishes with the considered number of realizations. Synthetic inversion case studies involving 2-D steady state flow and 3-D transient hydraulic tomography with and without direct conditioning data are used to illustrate the effectiveness of our proposed SGAN-based inversion. For the 2-D case, the inversion rapidly explores the posterior model distribution. For the 3-D case, the inversion recovers model realizations that fit the data close to the target level and visually resemble the true model well.

  8. Optimization for nonlinear inverse problem

    International Nuclear Information System (INIS)

    Boyadzhiev, G.; Brandmayr, E.; Pinat, T.; Panza, G.F.

    2007-06-01

    The nonlinear inversion of geophysical data in general does not yield a unique solution, but a single model, representing the investigated field, is preferred for an easy geological interpretation of the observations. The analyzed region is constituted by a number of sub-regions where the multi-valued nonlinear inversion is applied, which leads to a multi-valued solution. Therefore, combining the values of the solution in each sub-region, many acceptable models are obtained for the entire region and this complicates the geological interpretation of geophysical investigations. In this paper are presented new methodologies, capable to select one model, among all acceptable ones, that satisfies different criteria of smoothness in the explored space of solutions. In this work we focus on the non-linear inversion of surface waves dispersion curves, which gives structural models of shear-wave velocity versus depth, but the basic concepts have a general validity. (author)

  9. Inverse Higgs effect in nonlinear realizations

    International Nuclear Information System (INIS)

    Ivanov, E.A.; Ogievetskij, V.I.

    1975-01-01

    In theories with nonlinearly realized symmetry it is possible in a number of cases to eliminate some initial Goldstone and gauge fields by means of putting appropriate Cartan forms equal to zero. This is called the inverse Higgs phenomenon. We give a general treatment of the inverse Higgs phenomenon for gauge and space-time symmetries and consider four instructive examples which are the elimination of unessential gauge fields in chiral symmetry and in non-linearly realized supersymmetry and also the elimination of unessential Goldstone fields in the spontaneously broken conformal and projective symmetries

  10. Discrete-time inverse optimal control for nonlinear systems

    CERN Document Server

    Sanchez, Edgar N

    2013-01-01

    Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). Th

  11. Robust flight control using incremental nonlinear dynamic inversion and angular acceleration prediction

    NARCIS (Netherlands)

    Sieberling, S.; Chu, Q.P.; Mulder, J.A.

    2010-01-01

    This paper presents a flight control strategy based on nonlinear dynamic inversion. The approach presented, called incremental nonlinear dynamic inversion, uses properties of general mechanical systems and nonlinear dynamic inversion by feeding back angular accelerations. Theoretically, feedback of

  12. Nonlinear adaptive inverse control via the unified model neural network

    Science.gov (United States)

    Jeng, Jin-Tsong; Lee, Tsu-Tian

    1999-03-01

    In this paper, we propose a new nonlinear adaptive inverse control via a unified model neural network. In order to overcome nonsystematic design and long training time in nonlinear adaptive inverse control, we propose the approximate transformable technique to obtain a Chebyshev Polynomials Based Unified Model (CPBUM) neural network for the feedforward/recurrent neural networks. It turns out that the proposed method can use less training time to get an inverse model. Finally, we apply this proposed method to control magnetic bearing system. The experimental results show that the proposed nonlinear adaptive inverse control architecture provides a greater flexibility and better performance in controlling magnetic bearing systems.

  13. A nonlinear approach of elastic reflection waveform inversion

    KAUST Repository

    Guo, Qiang

    2016-09-06

    Elastic full waveform inversion (EFWI) embodies the original intention of waveform inversion at its inception as it is a better representation of the mostly solid Earth. However, compared with the acoustic P-wave assumption, EFWI for P- and S-wave velocities using multi-component data admitted mixed results. Full waveform inversion (FWI) is a highly nonlinear problem and this nonlinearity only increases under the elastic assumption. Reflection waveform inversion (RWI) can mitigate the nonlinearity by relying on transmissions from reflections focused on inverting low wavenumber components of the model. In our elastic endeavor, we split the P- and S-wave velocities into low wavenumber and perturbation components and propose a nonlinear approach to invert for both of them. The new optimization problem is built on an objective function that depends on both background and perturbation models. We utilize an equivalent stress source based on the model perturbation to generate reflection instead of demigrating from an image, which is applied in conventional RWI. Application on a slice of an ocean-bottom data shows that our method can efficiently update the low wavenumber parts of the model, but more so, obtain perturbations that can be added to the low wavenumbers for a high resolution output.

  14. A nonlinear approach of elastic reflection waveform inversion

    KAUST Repository

    Guo, Qiang; Alkhalifah, Tariq Ali

    2016-01-01

    Elastic full waveform inversion (EFWI) embodies the original intention of waveform inversion at its inception as it is a better representation of the mostly solid Earth. However, compared with the acoustic P-wave assumption, EFWI for P- and S-wave velocities using multi-component data admitted mixed results. Full waveform inversion (FWI) is a highly nonlinear problem and this nonlinearity only increases under the elastic assumption. Reflection waveform inversion (RWI) can mitigate the nonlinearity by relying on transmissions from reflections focused on inverting low wavenumber components of the model. In our elastic endeavor, we split the P- and S-wave velocities into low wavenumber and perturbation components and propose a nonlinear approach to invert for both of them. The new optimization problem is built on an objective function that depends on both background and perturbation models. We utilize an equivalent stress source based on the model perturbation to generate reflection instead of demigrating from an image, which is applied in conventional RWI. Application on a slice of an ocean-bottom data shows that our method can efficiently update the low wavenumber parts of the model, but more so, obtain perturbations that can be added to the low wavenumbers for a high resolution output.

  15. Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach

    Directory of Open Access Journals (Sweden)

    S. L. Han

    2012-01-01

    Full Text Available The nonlinear model is crucial to prepare, supervise, and analyze mechanical system. In this paper, a new nonparametric and output-only identification procedure for nonlinear damping is studied. By introducing the concept of the stochastic state space, we formulate a stochastic inverse problem for a nonlinear damping. The solution of the stochastic inverse problem is designed as probabilistic expression via the hierarchical Bayesian formulation by considering various uncertainties such as the information insufficiency in parameter of interests or errors in measurement. The probability space is estimated using Markov chain Monte Carlo (MCMC. The applicability of the proposed method is demonstrated through numerical experiment and particular application to a realistic problem related to ship roll motion.

  16. Massively Parallel Geostatistical Inversion of Coupled Processes in Heterogeneous Porous Media

    Science.gov (United States)

    Ngo, A.; Schwede, R. L.; Li, W.; Bastian, P.; Ippisch, O.; Cirpka, O. A.

    2012-04-01

    The quasi-linear geostatistical approach is an inversion scheme that can be used to estimate the spatial distribution of a heterogeneous hydraulic conductivity field. The estimated parameter field is considered to be a random variable that varies continuously in space, meets the measurements of dependent quantities (such as the hydraulic head, the concentration of a transported solute or its arrival time) and shows the required spatial correlation (described by certain variogram models). This is a method of conditioning a parameter field to observations. Upon discretization, this results in as many parameters as elements of the computational grid. For a full three dimensional representation of the heterogeneous subsurface it is hardly sufficient to work with resolutions (up to one million parameters) of the model domain that can be achieved on a serial computer. The forward problems to be solved within the inversion procedure consists of the elliptic steady-state groundwater flow equation and the formally elliptic but nearly hyperbolic steady-state advection-dominated solute transport equation in a heterogeneous porous medium. Both equations are discretized by Finite Element Methods (FEM) using fully scalable domain decomposition techniques. Whereas standard conforming FEM is sufficient for the flow equation, for the advection dominated transport equation, which rises well known numerical difficulties at sharp fronts or boundary layers, we use the streamline diffusion approach. The arising linear systems are solved using efficient iterative solvers with an AMG (algebraic multigrid) pre-conditioner. During each iteration step of the inversion scheme one needs to solve a multitude of forward and adjoint problems in order to calculate the sensitivities of each measurement and the related cross-covariance matrix of the unknown parameters and the observations. In order to reduce interprocess communications and to improve the scalability of the code on larger clusters

  17. Heeding the waveform inversion nonlinearity by unwrapping the model and data

    KAUST Repository

    Alkhalifah, Tariq Ali

    2012-01-01

    Unlike traveltime inversion, waveform inversion provides relatively higher-resolution inverted models. This feature, however, comes at the cost of introducing complex nonlinearity to the inversion operator complicating the convergence process. We use unwrapped-phase-based objective functions to reduce such nonlinearity in a domain in which the high-frequency component is given by the traveltime inversion. Such information is packaged in a frequency-dependent attribute (or traveltime) that can be easily manipulated at different frequencies. It unwraps the phase of the wavefield yielding far less nonlinearity in the objective function than those experienced with the conventional misfit objective function, and yet it still holds most of the critical waveform information in its frequency dependency. However, it suffers from nonlinearity introduced by the model (or reflectivity), as events interact with each other (something like cross talk). This stems from the sinusoidal nature of the band-limited reflectivity model. Unwrapping the phase for such a model can mitigate this nonlinearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced nonlinearity and, thus, make the inversion more convergent. Simple examples are used to highlight such features.

  18. Monte Carlo Analysis of Reservoir Models Using Seismic Data and Geostatistical Models

    Science.gov (United States)

    Zunino, A.; Mosegaard, K.; Lange, K.; Melnikova, Y.; Hansen, T. M.

    2013-12-01

    We present a study on the analysis of petroleum reservoir models consistent with seismic data and geostatistical constraints performed on a synthetic reservoir model. Our aim is to invert directly for structure and rock bulk properties of the target reservoir zone. To infer the rock facies, porosity and oil saturation seismology alone is not sufficient but a rock physics model must be taken into account, which links the unknown properties to the elastic parameters. We then combine a rock physics model with a simple convolutional approach for seismic waves to invert the "measured" seismograms. To solve this inverse problem, we employ a Markov chain Monte Carlo (MCMC) method, because it offers the possibility to handle non-linearity, complex and multi-step forward models and provides realistic estimates of uncertainties. However, for large data sets the MCMC method may be impractical because of a very high computational demand. To face this challenge one strategy is to feed the algorithm with realistic models, hence relying on proper prior information. To address this problem, we utilize an algorithm drawn from geostatistics to generate geologically plausible models which represent samples of the prior distribution. The geostatistical algorithm learns the multiple-point statistics from prototype models (in the form of training images), then generates thousands of different models which are accepted or rejected by a Metropolis sampler. To further reduce the computation time we parallelize the software and run it on multi-core machines. The solution of the inverse problem is then represented by a collection of reservoir models in terms of facies, porosity and oil saturation, which constitute samples of the posterior distribution. We are finally able to produce probability maps of the properties we are interested in by performing statistical analysis on the collection of solutions.

  19. Nonlinear Stimulated Raman Exact Passage by Resonance-Locked Inverse Engineering

    Science.gov (United States)

    Dorier, V.; Gevorgyan, M.; Ishkhanyan, A.; Leroy, C.; Jauslin, H. R.; Guérin, S.

    2017-12-01

    We derive an exact and robust stimulated Raman process for nonlinear quantum systems driven by pulsed external fields. The external fields are designed with closed-form expressions from the inverse engineering of a given efficient and stable dynamics. This technique allows one to induce a controlled population inversion which surpasses the usual nonlinear stimulated Raman adiabatic passage efficiency.

  20. Solving inverse problems through a smooth formulation of multiple-point geostatistics

    DEFF Research Database (Denmark)

    Melnikova, Yulia

    be inferred, for instance, from a conceptual geological model termed a training image.The main motivation for this study was the challenge posed by history matching, an inverse problem aimed at estimating rock properties from production data. We addressed two main difficulties of the history matching problem...... corresponding inverse problems. However, noise in data, non-linear relationships and sparse observations impede creation of realistic reservoir models. Including complex a priori information on reservoir parameters facilitates the process of obtaining acceptable solutions. Such a priori knowledge may...... strategies including both theoretical motivation and practical aspects of implementation. Finally, it is complemented by six research papers submitted, reviewed and/or published in the period 2010 - 2013....

  1. Explanation of the Inverse Doppler Effect Observed in Nonlinear Transmission Lines

    International Nuclear Information System (INIS)

    Kozyrev, Alexander B.; Weide, Daniel W. van der

    2005-01-01

    The theory of the inverse Doppler effect recently observed in magnetic nonlinear transmission lines is developed. We explain the crucial role of the backward spatial harmonic in the occurrence of an inverse Doppler effect and draw analogies of the magnetic nonlinear transmission line to the backward wave oscillator

  2. Heeding the waveform inversion nonlinearity by unwrapping the model and data

    KAUST Repository

    Alkhalifah, Tariq Ali; Choi, Yun Seok

    2012-01-01

    Unlike traveltime inversion, waveform inversion provides relatively higher-resolution inverted models. This feature, however, comes at the cost of introducing complex nonlinearity to the inversion operator complicating the convergence process. We

  3. A nonlinear inversion for the velocity background and perturbation models

    KAUST Repository

    Wu, Zedong; Alkhalifah, Tariq Ali

    2015-01-01

    Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the single scattered wavefield obtained using an image. However, current RWI methods usually neglect

  4. A geostatistical approach to the change-of-support problem and variable-support data fusion in spatial analysis

    Science.gov (United States)

    Wang, Jun; Wang, Yang; Zeng, Hui

    2016-01-01

    A key issue to address in synthesizing spatial data with variable-support in spatial analysis and modeling is the change-of-support problem. We present an approach for solving the change-of-support and variable-support data fusion problems. This approach is based on geostatistical inverse modeling that explicitly accounts for differences in spatial support. The inverse model is applied here to produce both the best predictions of a target support and prediction uncertainties, based on one or more measurements, while honoring measurements. Spatial data covering large geographic areas often exhibit spatial nonstationarity and can lead to computational challenge due to the large data size. We developed a local-window geostatistical inverse modeling approach to accommodate these issues of spatial nonstationarity and alleviate computational burden. We conducted experiments using synthetic and real-world raster data. Synthetic data were generated and aggregated to multiple supports and downscaled back to the original support to analyze the accuracy of spatial predictions and the correctness of prediction uncertainties. Similar experiments were conducted for real-world raster data. Real-world data with variable-support were statistically fused to produce single-support predictions and associated uncertainties. The modeling results demonstrate that geostatistical inverse modeling can produce accurate predictions and associated prediction uncertainties. It is shown that the local-window geostatistical inverse modeling approach suggested offers a practical way to solve the well-known change-of-support problem and variable-support data fusion problem in spatial analysis and modeling.

  5. Neural-Based Compensation of Nonlinearities in an Airplane Longitudinal Model with Dynamic-Inversion Control

    Directory of Open Access Journals (Sweden)

    YanBin Liu

    2017-01-01

    Full Text Available The inversion design approach is a very useful tool for the complex multiple-input-multiple-output nonlinear systems to implement the decoupling control goal, such as the airplane model and spacecraft model. In this work, the flight control law is proposed using the neural-based inversion design method associated with the nonlinear compensation for a general longitudinal model of the airplane. First, the nonlinear mathematic model is converted to the equivalent linear model based on the feedback linearization theory. Then, the flight control law integrated with this inversion model is developed to stabilize the nonlinear system and relieve the coupling effect. Afterwards, the inversion control combined with the neural network and nonlinear portion is presented to improve the transient performance and attenuate the uncertain effects on both external disturbances and model errors. Finally, the simulation results demonstrate the effectiveness of this controller.

  6. Efficient Monte Carlo sampling of inverse problems using a neural network-based forward—applied to GPR crosshole traveltime inversion

    Science.gov (United States)

    Hansen, T. M.; Cordua, K. S.

    2017-12-01

    Probabilistically formulated inverse problems can be solved using Monte Carlo-based sampling methods. In principle, both advanced prior information, based on for example, complex geostatistical models and non-linear forward models can be considered using such methods. However, Monte Carlo methods may be associated with huge computational costs that, in practice, limit their application. This is not least due to the computational requirements related to solving the forward problem, where the physical forward response of some earth model has to be evaluated. Here, it is suggested to replace a numerical complex evaluation of the forward problem, with a trained neural network that can be evaluated very fast. This will introduce a modeling error that is quantified probabilistically such that it can be accounted for during inversion. This allows a very fast and efficient Monte Carlo sampling of the solution to an inverse problem. We demonstrate the methodology for first arrival traveltime inversion of crosshole ground penetrating radar data. An accurate forward model, based on 2-D full-waveform modeling followed by automatic traveltime picking, is replaced by a fast neural network. This provides a sampling algorithm three orders of magnitude faster than using the accurate and computationally expensive forward model, and also considerably faster and more accurate (i.e. with better resolution), than commonly used approximate forward models. The methodology has the potential to dramatically change the complexity of non-linear and non-Gaussian inverse problems that have to be solved using Monte Carlo sampling techniques.

  7. Taming waveform inversion non-linearity through phase unwrapping of the model and objective functions

    KAUST Repository

    Alkhalifah, Tariq Ali

    2012-09-25

    Traveltime inversion focuses on the geometrical features of the waveform (traveltimes), which is generally smooth, and thus, tends to provide averaged (smoothed) information of the model. On other hand, general waveform inversion uses additional elements of the wavefield including amplitudes to extract higher resolution information, but this comes at the cost of introducing non-linearity to the inversion operator, complicating the convergence process. We use unwrapped phase-based objective functions in waveform inversion as a link between the two general types of inversions in a domain in which such contributions to the inversion process can be easily identified and controlled. The instantaneous traveltime is a measure of the average traveltime of the energy in a trace as a function of frequency. It unwraps the phase of wavefields yielding far less non-linearity in the objective function than that experienced with conventional wavefields, yet it still holds most of the critical wavefield information in its frequency dependency. However, it suffers from non-linearity introduced by the model (or reflectivity), as reflections from independent events in our model interact with each other. Unwrapping the phase of such a model can mitigate this non-linearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced non-linearity and, thus, make the inversion more convergent. Simple numerical examples demonstrate these assertions.

  8. Taming waveform inversion non-linearity through phase unwrapping of the model and objective functions

    KAUST Repository

    Alkhalifah, Tariq Ali; Choi, Yun Seok

    2012-01-01

    Traveltime inversion focuses on the geometrical features of the waveform (traveltimes), which is generally smooth, and thus, tends to provide averaged (smoothed) information of the model. On other hand, general waveform inversion uses additional elements of the wavefield including amplitudes to extract higher resolution information, but this comes at the cost of introducing non-linearity to the inversion operator, complicating the convergence process. We use unwrapped phase-based objective functions in waveform inversion as a link between the two general types of inversions in a domain in which such contributions to the inversion process can be easily identified and controlled. The instantaneous traveltime is a measure of the average traveltime of the energy in a trace as a function of frequency. It unwraps the phase of wavefields yielding far less non-linearity in the objective function than that experienced with conventional wavefields, yet it still holds most of the critical wavefield information in its frequency dependency. However, it suffers from non-linearity introduced by the model (or reflectivity), as reflections from independent events in our model interact with each other. Unwrapping the phase of such a model can mitigate this non-linearity as well. Specifically, a simple modification to the inverted domain (or model), can reduce the effect of the model-induced non-linearity and, thus, make the inversion more convergent. Simple numerical examples demonstrate these assertions.

  9. A practical primer on geostatistics

    Science.gov (United States)

    Olea, Ricardo A.

    2009-01-01

    The Challenge—Most geological phenomena are extraordinarily complex in their interrelationships and vast in their geographical extension. Ordinarily, engineers and geoscientists are faced with corporate or scientific requirements to properly prepare geological models with measurements involving a small fraction of the entire area or volume of interest. Exact description of a system such as an oil reservoir is neither feasible nor economically possible. The results are necessarily uncertain. Note that the uncertainty is not an intrinsic property of the systems; it is the result of incomplete knowledge by the observer.The Aim of Geostatistics—The main objective of geostatistics is the characterization of spatial systems that are incompletely known, systems that are common in geology. A key difference from classical statistics is that geostatistics uses the sampling location of every measurement. Unless the measurements show spatial correlation, the application of geostatistics is pointless. Ordinarily the need for additional knowledge goes beyond a few points, which explains the display of results graphically as fishnet plots, block diagrams, and maps.Geostatistical Methods—Geostatistics is a collection of numerical techniques for the characterization of spatial attributes using primarily two tools: probabilistic models, which are used for spatial data in a manner similar to the way in which time-series analysis characterizes temporal data, or pattern recognition techniques. The probabilistic models are used as a way to handle uncertainty in results away from sampling locations, making a radical departure from alternative approaches like inverse distance estimation methods.Differences with Time Series—On dealing with time-series analysis, users frequently concentrate their attention on extrapolations for making forecasts. Although users of geostatistics may be interested in extrapolation, the methods work at their best interpolating. This simple difference

  10. Frequency-domain full-waveform inversion with non-linear descent directions

    Science.gov (United States)

    Geng, Yu; Pan, Wenyong; Innanen, Kristopher A.

    2018-05-01

    Full-waveform inversion (FWI) is a highly non-linear inverse problem, normally solved iteratively, with each iteration involving an update constructed through linear operations on the residuals. Incorporating a flexible degree of non-linearity within each update may have important consequences for convergence rates, determination of low model wavenumbers and discrimination of parameters. We examine one approach for doing so, wherein higher order scattering terms are included within the sensitivity kernel during the construction of the descent direction, adjusting it away from that of the standard Gauss-Newton approach. These scattering terms are naturally admitted when we construct the sensitivity kernel by varying not the current but the to-be-updated model at each iteration. Linear and/or non-linear inverse scattering methodologies allow these additional sensitivity contributions to be computed from the current data residuals within any given update. We show that in the presence of pre-critical reflection data, the error in a second-order non-linear update to a background of s0 is, in our scheme, proportional to at most (Δs/s0)3 in the actual parameter jump Δs causing the reflection. In contrast, the error in a standard Gauss-Newton FWI update is proportional to (Δs/s0)2. For numerical implementation of more complex cases, we introduce a non-linear frequency-domain scheme, with an inner and an outer loop. A perturbation is determined from the data residuals within the inner loop, and a descent direction based on the resulting non-linear sensitivity kernel is computed in the outer loop. We examine the response of this non-linear FWI using acoustic single-parameter synthetics derived from the Marmousi model. The inverted results vary depending on data frequency ranges and initial models, but we conclude that the non-linear FWI has the capability to generate high-resolution model estimates in both shallow and deep regions, and to converge rapidly, relative to a

  11. Qualitative and quantitative comparison of geostatistical techniques of porosity prediction from the seismic and logging data: a case study from the Blackfoot Field, Alberta, Canada

    Science.gov (United States)

    Maurya, S. P.; Singh, K. H.; Singh, N. P.

    2018-05-01

    In present study, three recently developed geostatistical methods, single attribute analysis, multi-attribute analysis and probabilistic neural network algorithm have been used to predict porosity in inter well region for Blackfoot field, Alberta, Canada, an offshore oil field. These techniques make use of seismic attributes, generated by model based inversion and colored inversion techniques. The principle objective of the study is to find the suitable combination of seismic inversion and geostatistical techniques to predict porosity and identification of prospective zones in 3D seismic volume. The porosity estimated from these geostatistical approaches is corroborated with the well log porosity. The results suggest that all the three implemented geostatistical methods are efficient and reliable to predict the porosity but the multi-attribute and probabilistic neural network analysis provide more accurate and high resolution porosity sections. A low impedance (6000-8000 m/s g/cc) and high porosity (> 15%) zone is interpreted from inverted impedance and porosity sections respectively between 1060 and 1075 ms time interval and is characterized as reservoir. The qualitative and quantitative results demonstrate that of all the employed geostatistical methods, the probabilistic neural network along with model based inversion is the most efficient method for predicting porosity in inter well region.

  12. A 2D nonlinear inversion of well-seismic data

    International Nuclear Information System (INIS)

    Métivier, Ludovic; Lailly, Patrick; Delprat-Jannaud, Florence; Halpern, Laurence

    2011-01-01

    Well-seismic data such as vertical seismic profiles are supposed to provide detailed information about the elastic properties of the subsurface at the vicinity of the well. Heterogeneity of sedimentary terrains can lead to far from negligible multiple scattering, one of the manifestations of the nonlinearity involved in the mapping between elastic parameters and seismic data. We present a 2D extension of an existing 1D nonlinear inversion technique in the context of acoustic wave propagation. In the case of a subsurface with gentle lateral variations, we propose a regularization technique which aims at ensuring the stability of the inversion in a context where the recorded seismic waves provide a very poor illumination of the subsurface. We deal with a huge size inverse problem. Special care has been taken for its numerical solution, regarding both the choice of the algorithms and the implementation on a cluster-based supercomputer. Our tests on synthetic data show the effectiveness of our regularization. They also show that our efforts in accounting for the nonlinearities are rewarded by an exceptional seismic resolution at distances of about 100 m from the well. They also show that the result is not very sensitive to errors in the estimation of the velocity distribution, as far as these errors remain realistic in the context of a medium with gentle lateral variations

  13. Regional-scale geostatistical inverse modeling of North American CO2 fluxes: a synthetic data study

    Directory of Open Access Journals (Sweden)

    A. M. Michalak

    2010-07-01

    Full Text Available A series of synthetic data experiments is performed to investigate the ability of a regional atmospheric inversion to estimate grid-scale CO2 fluxes during the growing season over North America. The inversions are performed within a geostatistical framework without the use of any prior flux estimates or auxiliary variables, in order to focus on the atmospheric constraint provided by the nine towers collecting continuous, calibrated CO2 measurements in 2004. Using synthetic measurements and their associated concentration footprints, flux and model-data mismatch covariance parameters are first optimized, and then fluxes and their uncertainties are estimated at three different temporal resolutions. These temporal resolutions, which include a four-day average, a four-day-average diurnal cycle with 3-hourly increments, and 3-hourly fluxes, are chosen to help assess the impact of temporal aggregation errors on the estimated fluxes and covariance parameters. Estimating fluxes at a temporal resolution that can adjust the diurnal variability is found to be critical both for recovering covariance parameters directly from the atmospheric data, and for inferring accurate ecoregion-scale fluxes. Accounting for both spatial and temporal a priori covariance in the flux distribution is also found to be necessary for recovering accurate a posteriori uncertainty bounds on the estimated fluxes. Overall, the results suggest that even a fairly sparse network of 9 towers collecting continuous CO2 measurements across the continent, used with no auxiliary information or prior estimates of the flux distribution in time or space, can be used to infer relatively accurate monthly ecoregion scale CO2 surface fluxes over North America within estimated uncertainty bounds. Simulated random transport error is shown to decrease the quality of flux estimates in under-constrained areas at the ecoregion scale, although the uncertainty bounds remain realistic. While these synthetic

  14. Use of geostatistics for remediation planning to transcend urban political boundaries

    International Nuclear Information System (INIS)

    Milillo, Tammy M.; Sinha, Gaurav; Gardella, Joseph A.

    2012-01-01

    Soil remediation plans are often dictated by areas of jurisdiction or property lines instead of scientific information. This study exemplifies how geostatistically interpolated surfaces can substantially improve remediation planning. Ordinary kriging, ordinary co-kriging, and inverse distance weighting spatial interpolation methods were compared for analyzing surface and sub-surface soil sample data originally collected by the US EPA and researchers at the University at Buffalo in Hickory Woods, an industrial–residential neighborhood in Buffalo, NY, where both lead and arsenic contamination is present. Past clean-up efforts estimated contamination levels from point samples, but parcel and agency jurisdiction boundaries were used to define remediation sites, rather than geostatistical models estimating the spatial behavior of the contaminants in the soil. Residents were understandably dissatisfied with the arbitrariness of the remediation plan. In this study we show how geostatistical mapping and participatory assessment can make soil remediation scientifically defensible, socially acceptable, and economically feasible. - Highlights: ► Point samples and property boundaries do not appropriately determine the extent of soil contamination. ► Kriging and co-kriging provide best concentration estimates for mapping soil contamination and refining clean-up sites. ► Maps provide a visual representation of geostatistical results to communities to aid in geostatistical decision making. ► Incorporating community input into the assessment of neighborhoods is good public policy practice. - Using geostatistical interpolation and mapping results to involve the affected community can substantially improve remediation planning and promote its long-term effectiveness.

  15. Geostatistical inference using crosshole ground-penetrating radar

    DEFF Research Database (Denmark)

    Looms, Majken C; Hansen, Thomas Mejer; Cordua, Knud Skou

    2010-01-01

    of the subsurface are used to evaluate the uncertainty of the inversion estimate. We have explored the full potential of the geostatistical inference method using several synthetic models of varying correlation structures and have tested the influence of different assumptions concerning the choice of covariance...... reflection profile. Furthermore, the inferred values of the subsurface global variance and the mean velocity have been corroborated with moisturecontent measurements, obtained gravimetrically from samples collected at the field site....

  16. Elastic reflection based waveform inversion with a nonlinear approach

    KAUST Repository

    Guo, Qiang

    2017-08-16

    Full waveform inversion (FWI) is a highly nonlinear problem due to the complex reflectivity of the Earth, and this nonlinearity only increases under the more expensive elastic assumption. In elastic media, we need a good initial P-wave velocity and even a better initial S-wave velocity models with accurate representation of the low model wavenumbers for FWI to converge. However, inverting for the low wavenumber components of P- and S-wave velocities using reflection waveform inversion (RWI) with an objective to fit the reflection shape, rather than produce reflections, may mitigate the limitations of FWI. Because FWI, performing as a migration operator, is in preference of the high wavenumber updates along reflectors. We propose a nonlinear elastic RWI that inverts for both the low wavenumber and perturbation components of the P- and S-wave velocities. To generate the full elastic reflection wavefields, we derive an equivalent stress source made up by the inverted model perturbations and incident wavefields. We update both the perturbation and propagation parts of the velocity models in a nested fashion. Applications on synthetic isotropic models and field data show that our method can efficiently update the low and high wavenumber parts of the models.

  17. Elastic reflection based waveform inversion with a nonlinear approach

    KAUST Repository

    Guo, Qiang; Alkhalifah, Tariq Ali

    2017-01-01

    Full waveform inversion (FWI) is a highly nonlinear problem due to the complex reflectivity of the Earth, and this nonlinearity only increases under the more expensive elastic assumption. In elastic media, we need a good initial P-wave velocity and even a better initial S-wave velocity models with accurate representation of the low model wavenumbers for FWI to converge. However, inverting for the low wavenumber components of P- and S-wave velocities using reflection waveform inversion (RWI) with an objective to fit the reflection shape, rather than produce reflections, may mitigate the limitations of FWI. Because FWI, performing as a migration operator, is in preference of the high wavenumber updates along reflectors. We propose a nonlinear elastic RWI that inverts for both the low wavenumber and perturbation components of the P- and S-wave velocities. To generate the full elastic reflection wavefields, we derive an equivalent stress source made up by the inverted model perturbations and incident wavefields. We update both the perturbation and propagation parts of the velocity models in a nested fashion. Applications on synthetic isotropic models and field data show that our method can efficiently update the low and high wavenumber parts of the models.

  18. Comparative study of the geostatistical ore reserve estimation method over the conventional methods

    International Nuclear Information System (INIS)

    Kim, Y.C.; Knudsen, H.P.

    1975-01-01

    Part I contains a comprehensive treatment of the comparative study of the geostatistical ore reserve estimation method over the conventional methods. The conventional methods chosen for comparison were: (a) the polygon method, (b) the inverse of the distance squared method, and (c) a method similar to (b) but allowing different weights in different directions. Briefly, the overall result from this comparative study is in favor of the use of geostatistics in most cases because the method has lived up to its theoretical claims. A good exposition on the theory of geostatistics, the adopted study procedures, conclusions and recommended future research are given in Part I. Part II of this report contains the results of the second and the third study objectives, which are to assess the potential benefits that can be derived by the introduction of the geostatistical method to the current state-of-the-art in uranium reserve estimation method and to be instrumental in generating the acceptance of the new method by practitioners through illustrative examples, assuming its superiority and practicality. These are given in the form of illustrative examples on the use of geostatistics and the accompanying computer program user's guide

  19. Renormalized nonlinear sensitivity kernel and inverse thin-slab propagator in T-matrix formalism for wave-equation tomography

    International Nuclear Information System (INIS)

    Wu, Ru-Shan; Wang, Benfeng; Hu, Chunhua

    2015-01-01

    We derived the renormalized nonlinear sensitivity operator and the related inverse thin-slab propagator (ITSP) for nonlinear tomographic waveform inversion based on the theory of nonlinear partial derivative operator and its De Wolf approximation. The inverse propagator is based on a renormalization procedure to the forward and inverse transition matrix scattering series. The ITSP eliminates the divergence of the inverse Born series for strong perturbations by stepwise partial summation (renormalization). Numerical tests showed that the inverse Born T-series starts to diverge at moderate perturbation (20% for the given model of Gaussian ball with a radius of 5 wavelength), while the ITSP has no divergence problem for any strong perturbations (up to 100% perturbation for test model). In addition, the ITSP is a non-iterative, marching algorithm with only one sweep, and therefore very efficient in comparison with the iterative inversion based on the inverse-Born scattering series. This convergence and efficiency improvement has potential applications to the iterative procedure of waveform inversion. (paper)

  20. Estimation of biological parameters of marine organisms using linear and nonlinear acoustic scattering model-based inversion methods.

    Science.gov (United States)

    Chu, Dezhang; Lawson, Gareth L; Wiebe, Peter H

    2016-05-01

    The linear inversion commonly used in fisheries and zooplankton acoustics assumes a constant inversion kernel and ignores the uncertainties associated with the shape and behavior of the scattering targets, as well as other relevant animal parameters. Here, errors of the linear inversion due to uncertainty associated with the inversion kernel are quantified. A scattering model-based nonlinear inversion method is presented that takes into account the nonlinearity of the inverse problem and is able to estimate simultaneously animal abundance and the parameters associated with the scattering model inherent to the kernel. It uses sophisticated scattering models to estimate first, the abundance, and second, the relevant shape and behavioral parameters of the target organisms. Numerical simulations demonstrate that the abundance, size, and behavior (tilt angle) parameters of marine animals (fish or zooplankton) can be accurately inferred from the inversion by using multi-frequency acoustic data. The influence of the singularity and uncertainty in the inversion kernel on the inversion results can be mitigated by examining the singular values for linear inverse problems and employing a non-linear inversion involving a scattering model-based kernel.

  1. Introduction to Geostatistics

    Science.gov (United States)

    Kitanidis, P. K.

    1997-05-01

    Introduction to Geostatistics presents practical techniques for engineers and earth scientists who routinely encounter interpolation and estimation problems when analyzing data from field observations. Requiring no background in statistics, and with a unique approach that synthesizes classic and geostatistical methods, this book offers linear estimation methods for practitioners and advanced students. Well illustrated with exercises and worked examples, Introduction to Geostatistics is designed for graduate-level courses in earth sciences and environmental engineering.

  2. Success Stories in Control: Nonlinear Dynamic Inversion Control

    Science.gov (United States)

    Bosworth, John T.

    2010-01-01

    NASA plays an important role in advancing the state of the art in flight control systems. In the case of Nonlinear Dynamic Inversion (NDI) NASA supported initial implementation of the theory in an aircraft and demonstration in a space vehicle. Dr. Dale Enns of Honeywell Aerospace Advanced Technology performed this work in cooperation with NASA and under NASA contract. Honeywell and Lockheed Martin were subsequently contracted by AFRL to create "Design Guidelines for Multivariable Control Theory". This foundational work directly contributed to the advancement of the technology and the credibility of the control law as a design option. As a result Honeywell collaborated with Lockheed Martin to produce a Nonlinear Dynamic Inversion controller for the X-35 and subsequently Lockheed Martin did the same for the production Lockheed Martin F-35 vehicle. The theory behind NDI is to use a systematic generalized approach to controlling a vehicle. Using general aircraft nonlinear equations of motion and onboard aerodynamic, mass properties, and engine models specific to the vehicle, a relationship between control effectors and desired aircraft motion can be formulated. Using this formulation a control combination is used that provides a predictable response to commanded motion. Control loops around this formulation shape the response as desired and provide robustness to modeling errors. Once the control law is designed it can be used on a similar class of vehicle with only an update to the vehicle specific onboard models.

  3. A Projected Non-linear Conjugate Gradient Method for Interactive Inverse Kinematics

    DEFF Research Database (Denmark)

    Engell-Nørregård, Morten; Erleben, Kenny

    2009-01-01

    Inverse kinematics is the problem of posing an articulated figure to obtain a wanted goal, without regarding inertia and forces. Joint limits are modeled as bounds on individual degrees of freedom, leading to a box-constrained optimization problem. We present A projected Non-linear Conjugate...... Gradient optimization method suitable for box-constrained optimization problems for inverse kinematics. We show application on inverse kinematics positioning of a human figure. Performance is measured and compared to a traditional Jacobian Transpose method. Visual quality of the developed method...

  4. How to evaluate the risks of exceeding limits: geostatistical models and their application to air pollution

    International Nuclear Information System (INIS)

    Fouquet, Ch. de; Deraisme, J.; Bobbia, M.

    2007-01-01

    Geo-statistics is increasingly applied to the study of environmental risks in a variety of sectors, especially in the fields of soil decontamination and the evaluation of the risks due to air pollution. Geo-statistics offers a rigorous stochastic modeling approach that makes it possible to answer questions expressed in terms of uncertainty and risk. This article focusses on nonlinear geo-statistical methods, based on the Gaussian random function model, whose essential properties are summarised. We use two examples to characterize situations where direct and thus rapid methods provide appropriate solutions and cases that inevitably require more laborious simulation techniques. Exposure of the population of the Rouen metropolitan area to the risk of NO 2 pollution is assessed by simulations, but the surface area where the pollution exceeds the threshold limit can be easily estimated with nonlinear conditional expectation techniques. A second example is used to discuss the bias introduced by direct simulation, here of a percentile of daily SO 2 concentration for one year in the city of Le Havre; an operational solution is proposed. (authors)

  5. Reducing uncertainty in geostatistical description with well testing pressure data

    Energy Technology Data Exchange (ETDEWEB)

    Reynolds, A.C.; He, Nanqun [Univ. of Tulsa, OK (United States); Oliver, D.S. [Chevron Petroleum Technology Company, La Habra, CA (United States)

    1997-08-01

    Geostatistics has proven to be an effective tool for generating realizations of reservoir properties conditioned to static data, e.g., core and log data and geologic knowledge. Due to the lack of closely spaced data in the lateral directions, there will be significant variability in reservoir descriptions generated by geostatistical simulation, i.e., significant uncertainty in the reservoir descriptions. In past work, we have presented procedures based on inverse problem theory for generating reservoir descriptions (rock property fields) conditioned to pressure data and geostatistical information represented as prior means for log-permeability and porosity and variograms. Although we have shown that the incorporation of pressure data reduces the uncertainty below the level contained in the geostatistical model based only on static information (the prior model), our previous results assumed did not explicitly account for uncertainties in the prior means and the parameters defining the variogram model. In this work, we investigate how pressure data can help detect errors in the prior means. If errors in the prior means are large and are not taken into account, realizations conditioned to pressure data represent incorrect samples of the a posteriori probability density function for the rock property fields, whereas, if the uncertainty in the prior mean is incorporated properly into the model, one obtains realistic realizations of the rock property fields.

  6. Intrinsic nonlinearity and method of disturbed observations in inverse problems of celestial mechanics

    Science.gov (United States)

    Avdyushev, Victor A.

    2017-12-01

    Orbit determination from a small sample of observations over a very short observed orbital arc is a strongly nonlinear inverse problem. In such problems an evaluation of orbital uncertainty due to random observation errors is greatly complicated, since linear estimations conventionally used are no longer acceptable for describing the uncertainty even as a rough approximation. Nevertheless, if an inverse problem is weakly intrinsically nonlinear, then one can resort to the so-called method of disturbed observations (aka observational Monte Carlo). Previously, we showed that the weaker the intrinsic nonlinearity, the more efficient the method, i.e. the more accurate it enables one to simulate stochastically the orbital uncertainty, while it is strictly exact only when the problem is intrinsically linear. However, as we ascertained experimentally, its efficiency was found to be higher than that of other stochastic methods widely applied in practice. In the present paper we investigate the intrinsic nonlinearity in complicated inverse problems of Celestial Mechanics when orbits are determined from little informative samples of observations, which typically occurs for recently discovered asteroids. To inquire into the question, we introduce an index of intrinsic nonlinearity. In asteroid problems it evinces that the intrinsic nonlinearity can be strong enough to affect appreciably probabilistic estimates, especially at the very short observed orbital arcs that the asteroids travel on for about a hundredth of their orbital periods and less. As it is known from regression analysis, the source of intrinsic nonlinearity is the nonflatness of the estimation subspace specified by a dynamical model in the observation space. Our numerical results indicate that when determining asteroid orbits it is actually very slight. However, in the parametric space the effect of intrinsic nonlinearity is exaggerated mainly by the ill-conditioning of the inverse problem. Even so, as for the

  7. Inverse Boundary Value Problem for Non-linear Hyperbolic Partial Differential Equations

    OpenAIRE

    Nakamura, Gen; Vashisth, Manmohan

    2017-01-01

    In this article we are concerned with an inverse boundary value problem for a non-linear wave equation of divergence form with space dimension $n\\geq 3$. This non-linear wave equation has a trivial solution, i.e. zero solution. By linearizing this equation at the trivial solution, we have the usual linear isotropic wave equation with the speed $\\sqrt{\\gamma(x)}$ at each point $x$ in a given spacial domain. For any small solution $u=u(t,x)$ of this non-linear equation, we have the linear isotr...

  8. Inverse operator theory method and its applications in nonlinear physics

    International Nuclear Information System (INIS)

    Fang Jinqing

    1993-01-01

    Inverse operator theory method, which has been developed by G. Adomian in recent years, and its applications in nonlinear physics are described systematically. The method can be an unified effective procedure for solution of nonlinear and/or stochastic continuous dynamical systems without usual restrictive assumption. It is realized by Mathematical Mechanization by us. It will have a profound on the modelling of problems of physics, mathematics, engineering, economics, biology, and so on. Some typical examples of the application are given and reviewed

  9. Designing a Robust Nonlinear Dynamic Inversion Controller for Spacecraft Formation Flying

    Directory of Open Access Journals (Sweden)

    Inseok Yang

    2014-01-01

    Full Text Available The robust nonlinear dynamic inversion (RNDI control technique is proposed to keep the relative position of spacecrafts while formation flying. The proposed RNDI control method is based on nonlinear dynamic inversion (NDI. NDI is nonlinear control method that replaces the original dynamics into the user-selected desired dynamics. Because NDI removes nonlinearities in the model by inverting the original dynamics directly, it also eliminates the need of designing suitable controllers for each equilibrium point; that is, NDI works as self-scheduled controller. Removing the original model also provides advantages of ease to satisfy the specific requirements by simply handling desired dynamics. Therefore, NDI is simple and has many similarities to classical control. In real applications, however, it is difficult to achieve perfect cancellation of the original dynamics due to uncertainties that lead to performance degradation and even make the system unstable. This paper proposes robustness assurance method for NDI. The proposed RNDI is designed by combining NDI and sliding mode control (SMC. SMC is inherently robust using high-speed switching inputs. This paper verifies similarities of NDI and SMC, firstly. And then RNDI control method is proposed. The performance of the proposed method is evaluated by simulations applied to spacecraft formation flying problem.

  10. Full Waveform Inversion Using Nonlinearly Smoothed Wavefields

    KAUST Repository

    Li, Y.; Choi, Yun Seok; Alkhalifah, Tariq Ali; Li, Z.

    2017-01-01

    The lack of low frequency information in the acquired data makes full waveform inversion (FWI) conditionally converge to the accurate solution. An initial velocity model that results in data with events within a half cycle of their location in the observed data was required to converge. The multiplication of wavefields with slightly different frequencies generates artificial low frequency components. This can be effectively utilized by multiplying the wavefield with itself, which is nonlinear operation, followed by a smoothing operator to extract the artificially produced low frequency information. We construct the objective function using the nonlinearly smoothed wavefields with a global-correlation norm to properly handle the energy imbalance in the nonlinearly smoothed wavefield. Similar to the multi-scale strategy, we progressively reduce the smoothing width applied to the multiplied wavefield to welcome higher resolution. We calculate the gradient of the objective function using the adjoint-state technique, which is similar to the conventional FWI except for the adjoint source. Examples on the Marmousi 2 model demonstrate the feasibility of the proposed FWI method to mitigate the cycle-skipping problem in the case of a lack of low frequency information.

  11. Full Waveform Inversion Using Nonlinearly Smoothed Wavefields

    KAUST Repository

    Li, Y.

    2017-05-26

    The lack of low frequency information in the acquired data makes full waveform inversion (FWI) conditionally converge to the accurate solution. An initial velocity model that results in data with events within a half cycle of their location in the observed data was required to converge. The multiplication of wavefields with slightly different frequencies generates artificial low frequency components. This can be effectively utilized by multiplying the wavefield with itself, which is nonlinear operation, followed by a smoothing operator to extract the artificially produced low frequency information. We construct the objective function using the nonlinearly smoothed wavefields with a global-correlation norm to properly handle the energy imbalance in the nonlinearly smoothed wavefield. Similar to the multi-scale strategy, we progressively reduce the smoothing width applied to the multiplied wavefield to welcome higher resolution. We calculate the gradient of the objective function using the adjoint-state technique, which is similar to the conventional FWI except for the adjoint source. Examples on the Marmousi 2 model demonstrate the feasibility of the proposed FWI method to mitigate the cycle-skipping problem in the case of a lack of low frequency information.

  12. A nonlinear inversion for the velocity background and perturbation models

    KAUST Repository

    Wu, Zedong

    2015-08-19

    Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the single scattered wavefield obtained using an image. However, current RWI methods usually neglect diving waves, which is an important source of information for extracting the long wavelength components of the velocity model. Thus, we propose a new optimization problem through breaking the velocity model into the background and the perturbation in the wave equation directly. In this case, the perturbed model is no longer the single scattering model, but includes all scattering. We optimize both components simultaneously, and thus, the objective function is nonlinear with respect to both the background and perturbation. The new introduced w can absorb the non-smooth update of background naturally. Application to the Marmousi model with frequencies that start at 5 Hz shows that this method can converge to the accurate velocity starting from a linearly increasing initial velocity. Application to the SEG2014 demonstrates the versatility of the approach.

  13. One-dimensional nonlinear inverse heat conduction technique

    International Nuclear Information System (INIS)

    Hills, R.G.; Hensel, E.C. Jr.

    1986-01-01

    The one-dimensional nonlinear problem of heat conduction is considered. A noniterative space-marching finite-difference algorithm is developed to estimate the surface temperature and heat flux from temperature measurements at subsurface locations. The trade-off between resolution and variance of the estimates of the surface conditions is discussed quantitatively. The inverse algorithm is stabilized through the use of digital filters applied recursively. The effect of the filters on the resolution and variance of the surface estimates is quantified. Results are presented which indicate that the technique is capable of handling noisy measurement data

  14. Large-scale inverse model analyses employing fast randomized data reduction

    Science.gov (United States)

    Lin, Youzuo; Le, Ellen B.; O'Malley, Daniel; Vesselinov, Velimir V.; Bui-Thanh, Tan

    2017-08-01

    When the number of observations is large, it is computationally challenging to apply classical inverse modeling techniques. We have developed a new computationally efficient technique for solving inverse problems with a large number of observations (e.g., on the order of 107 or greater). Our method, which we call the randomized geostatistical approach (RGA), is built upon the principal component geostatistical approach (PCGA). We employ a data reduction technique combined with the PCGA to improve the computational efficiency and reduce the memory usage. Specifically, we employ a randomized numerical linear algebra technique based on a so-called "sketching" matrix to effectively reduce the dimension of the observations without losing the information content needed for the inverse analysis. In this way, the computational and memory costs for RGA scale with the information content rather than the size of the calibration data. Our algorithm is coded in Julia and implemented in the MADS open-source high-performance computational framework (http://mads.lanl.gov). We apply our new inverse modeling method to invert for a synthetic transmissivity field. Compared to a standard geostatistical approach (GA), our method is more efficient when the number of observations is large. Most importantly, our method is capable of solving larger inverse problems than the standard GA and PCGA approaches. Therefore, our new model inversion method is a powerful tool for solving large-scale inverse problems. The method can be applied in any field and is not limited to hydrogeological applications such as the characterization of aquifer heterogeneity.

  15. 4th International Geostatistics Congress

    CERN Document Server

    1993-01-01

    The contributions in this book were presented at the Fourth International Geostatistics Congress held in Tróia, Portugal, in September 1992. They provide a comprehensive account of the current state of the art of geostatistics, including recent theoretical developments and new applications. In particular, readers will find descriptions and applications of the more recent methods of stochastic simulation together with data integration techniques applied to the modelling of hydrocabon reservoirs. In other fields there are stationary and non-stationary geostatistical applications to geology, climatology, pollution control, soil science, hydrology and human sciences. The papers also provide an insight into new trends in geostatistics particularly the increasing interaction with many other scientific disciplines. This book is a significant reference work for practitioners of geostatistics both in academia and industry.

  16. 7th International Geostatistics Congress

    CERN Document Server

    Deutsch, Clayton

    2005-01-01

    The conference proceedings consist of approximately 120 technical papers presented at the Seventh International Geostatistics Congress held in Banff, Alberta, Canada in 2004. All the papers were reviewed by an international panel of leading geostatisticians. The five major sections are: theory, mining, petroleum, environmental and other applications. The first section showcases new and innovative ideas in the theoretical development of geostatistics as a whole; these ideas will have large impact on (1) the directions of future geostatistical research, and (2) the conventional approaches to heterogeneity modelling in a wide range of natural resource industries. The next four sections are focused on applications and innovations relating to the use of geostatistics in specific industries. Historically, mining, petroleum and environmental industries have embraced the use of geostatistics for uncertainty characterization, so these three industries are identified as major application areas. The last section is open...

  17. Complex nonlinear Fourier transform and its inverse

    International Nuclear Information System (INIS)

    Saksida, Pavle

    2015-01-01

    We study the nonlinear Fourier transform associated to the integrable systems of AKNS-ZS type. Two versions of this transform appear in connection with the AKNS-ZS systems. These two versions can be considered as two real forms of a single complex transform F c . We construct an explicit algorithm for the calculation of the inverse transform (F c ) -1 (h) for an arbitrary argument h. The result is given in the form of a convergent series of functions in the domain space and the terms of this series can be computed explicitly by means of finitely many integrations. (paper)

  18. Exact Solutions of Five Complex Nonlinear Schrödinger Equations by Semi-Inverse Variational Principle

    International Nuclear Information System (INIS)

    Najafi Mohammad; Arbabi Somayeh

    2014-01-01

    In this paper, we establish exact solutions for five complex nonlinear Schrödinger equations. The semi-inverse variational principle (SVP) is used to construct exact soliton solutions of five complex nonlinear Schrödinger equations. Many new families of exact soliton solutions of five complex nonlinear Schrödinger equations are successfully obtained. (general)

  19. Overview and technical and practical aspects for use of geostatistics in hazardous-, toxic-, and radioactive-waste-site investigations

    International Nuclear Information System (INIS)

    Bossong, C.R.; Karlinger, M.R.; Troutman, B.M.; Vecchia, A.V.

    1999-01-01

    Technical and practical aspects of applying geostatistics are developed for individuals involved in investigation at hazardous-, toxic-, and radioactive-waste sites. Important geostatistical concepts, such as variograms and ordinary, universal, and indicator kriging, are described in general terms for introductory purposes and in more detail for practical applications. Variogram modeling using measured ground-water elevation data is described in detail to illustrate principles of stationarity, anisotropy, transformations, and cross validation. Several examples of kriging applications are described using ground-water-level elevations, bedrock elevations, and ground-water-quality data. A review of contemporary literature and selected public domain software associated with geostatistics also is provided, as is a discussion of alternative methods for spatial modeling, including inverse distance weighting, triangulation, splines, trend-surface analysis, and simulation

  20. Geostatistical models for air pollution

    International Nuclear Information System (INIS)

    Pereira, M.J.; Soares, A.; Almeida, J.; Branquinho, C.

    2000-01-01

    The objective of this paper is to present geostatistical models applied to the spatial characterisation of air pollution phenomena. A concise presentation of the geostatistical methodologies is illustrated with practical examples. The case study was conducted in an underground copper-mine located on the southern of Portugal, where a biomonitoring program using lichens has been implemented. Given the characteristics of lichens as indicators of air pollution it was possible to gather a great amount of data in space, which enabled the development and application of geostatistical methodologies. The advantages of using geostatistical models compared with deterministic models, as environmental control tools, are highlighted. (author)

  1. A Reduced-Order Successive Linear Estimator for Geostatistical Inversion and its Application in Hydraulic Tomography

    Science.gov (United States)

    Zha, Yuanyuan; Yeh, Tian-Chyi J.; Illman, Walter A.; Zeng, Wenzhi; Zhang, Yonggen; Sun, Fangqiang; Shi, Liangsheng

    2018-03-01

    Hydraulic tomography (HT) is a recently developed technology for characterizing high-resolution, site-specific heterogeneity using hydraulic data (nd) from a series of cross-hole pumping tests. To properly account for the subsurface heterogeneity and to flexibly incorporate additional information, geostatistical inverse models, which permit a large number of spatially correlated unknowns (ny), are frequently used to interpret the collected data. However, the memory storage requirements for the covariance of the unknowns (ny × ny) in these models are prodigious for large-scale 3-D problems. Moreover, the sensitivity evaluation is often computationally intensive using traditional difference method (ny forward runs). Although employment of the adjoint method can reduce the cost to nd forward runs, the adjoint model requires intrusive coding effort. In order to resolve these issues, this paper presents a Reduced-Order Successive Linear Estimator (ROSLE) for analyzing HT data. This new estimator approximates the covariance of the unknowns using Karhunen-Loeve Expansion (KLE) truncated to nkl order, and it calculates the directional sensitivities (in the directions of nkl eigenvectors) to form the covariance and cross-covariance used in the Successive Linear Estimator (SLE). In addition, the covariance of unknowns is updated every iteration by updating the eigenvalues and eigenfunctions. The computational advantages of the proposed algorithm are demonstrated through numerical experiments and a 3-D transient HT analysis of data from a highly heterogeneous field site.

  2. A geostatistical analysis of geostatistics

    NARCIS (Netherlands)

    Hengl, T.; Minasny, B.; Gould, M.

    2009-01-01

    The bibliometric indices of the scientific field of geostatistics were analyzed using statistical and spatial data analysis. The publications and their citation statistics were obtained from the Web of Science (4000 most relevant), Scopus (2000 most relevant) and Google Scholar (5389). The focus was

  3. 10th International Geostatistics Congress

    CERN Document Server

    Rodrigo-Ilarri, Javier; Rodrigo-Clavero, María; Cassiraga, Eduardo; Vargas-Guzmán, José

    2017-01-01

    This book contains selected contributions presented at the 10th International Geostatistics Congress held in Valencia from 5 to 9 September, 2016. This is a quadrennial congress that serves as the meeting point for any engineer, professional, practitioner or scientist working in geostatistics. The book contains carefully reviewed papers on geostatistical theory and applications in fields such as mining engineering, petroleum engineering, environmental science, hydrology, ecology, and other fields.

  4. Application of geostatistics in Beach Placer

    International Nuclear Information System (INIS)

    Sundar, G.

    2016-01-01

    The goal of Geostatistics is in the prediction of possible spatial distribution of a property. Application of Geostatistics has gained significance in the field of exploration, evaluation and mining. In the case of beach and inland placer sands exploration, geostatistics can be used in optimising the drill hole spacing, estimate resources of the total heavy minerals (THM), estimation on different grid pattern and grade - tonnage curves. Steps involved in a geostatistical study are exploratory data analysis, creation of experimental variogram, variogram model fitting, kriging and cross validation. Basic tools in geostatistics are variogram and kriging. Characteristics of a variogram are sill, range and nugget. There is a necessity for variogram model fitting prior to kriging. Commonly used variogram models are spherical, exponential and gaussian

  5. A space and time scale-dependent nonlinear geostatistical approach for downscaling daily precipitation and temperature

    KAUST Repository

    Jha, Sanjeev Kumar

    2015-07-21

    A geostatistical framework is proposed to downscale daily precipitation and temperature. The methodology is based on multiple-point geostatistics (MPS), where a multivariate training image is used to represent the spatial relationship between daily precipitation and daily temperature over several years. Here, the training image consists of daily rainfall and temperature outputs from the Weather Research and Forecasting (WRF) model at 50 km and 10 km resolution for a twenty year period ranging from 1985 to 2004. The data are used to predict downscaled climate variables for the year 2005. The result, for each downscaled pixel, is daily time series of precipitation and temperature that are spatially dependent. Comparison of predicted precipitation and temperature against a reference dataset indicates that both the seasonal average climate response together with the temporal variability are well reproduced. The explicit inclusion of time dependence is explored by considering the climate properties of the previous day as an additional variable. Comparison of simulations with and without inclusion of time dependence shows that the temporal dependence only slightly improves the daily prediction because the temporal variability is already well represented in the conditioning data. Overall, the study shows that the multiple-point geostatistics approach is an efficient tool to be used for statistical downscaling to obtain local scale estimates of precipitation and temperature from General Circulation Models. This article is protected by copyright. All rights reserved.

  6. Multiobjective design of aquifer monitoring networks for optimal spatial prediction and geostatistical parameter estimation

    Science.gov (United States)

    Alzraiee, Ayman H.; Bau, Domenico A.; Garcia, Luis A.

    2013-06-01

    Effective sampling of hydrogeological systems is essential in guiding groundwater management practices. Optimal sampling of groundwater systems has previously been formulated based on the assumption that heterogeneous subsurface properties can be modeled using a geostatistical approach. Therefore, the monitoring schemes have been developed to concurrently minimize the uncertainty in the spatial distribution of systems' states and parameters, such as the hydraulic conductivity K and the hydraulic head H, and the uncertainty in the geostatistical model of system parameters using a single objective function that aggregates all objectives. However, it has been shown that the aggregation of possibly conflicting objective functions is sensitive to the adopted aggregation scheme and may lead to distorted results. In addition, the uncertainties in geostatistical parameters affect the uncertainty in the spatial prediction of K and H according to a complex nonlinear relationship, which has often been ineffectively evaluated using a first-order approximation. In this study, we propose a multiobjective optimization framework to assist the design of monitoring networks of K and H with the goal of optimizing their spatial predictions and estimating the geostatistical parameters of the K field. The framework stems from the combination of a data assimilation (DA) algorithm and a multiobjective evolutionary algorithm (MOEA). The DA algorithm is based on the ensemble Kalman filter, a Monte-Carlo-based Bayesian update scheme for nonlinear systems, which is employed to approximate the posterior uncertainty in K, H, and the geostatistical parameters of K obtained by collecting new measurements. Multiple MOEA experiments are used to investigate the trade-off among design objectives and identify the corresponding monitoring schemes. The methodology is applied to design a sampling network for a shallow unconfined groundwater system located in Rocky Ford, Colorado. Results indicate that

  7. Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions.

    Science.gov (United States)

    Omori, Toshiaki; Kuwatani, Tatsu; Okamoto, Atsushi; Hukushima, Koji

    2016-09-01

    It is essential to extract nonlinear dynamics from time-series data as an inverse problem in natural sciences. We propose a Bayesian statistical framework for extracting nonlinear dynamics of surface heterogeneous reactions from sparse and noisy observable data. Surface heterogeneous reactions are chemical reactions with conjugation of multiple phases, and they have the intrinsic nonlinearity of their dynamics caused by the effect of surface-area between different phases. We adapt a belief propagation method and an expectation-maximization (EM) algorithm to partial observation problem, in order to simultaneously estimate the time course of hidden variables and the kinetic parameters underlying dynamics. The proposed belief propagation method is performed by using sequential Monte Carlo algorithm in order to estimate nonlinear dynamical system. Using our proposed method, we show that the rate constants of dissolution and precipitation reactions, which are typical examples of surface heterogeneous reactions, as well as the temporal changes of solid reactants and products, were successfully estimated only from the observable temporal changes in the concentration of the dissolved intermediate product.

  8. Three-Dimensional Induced Polarization Parallel Inversion Using Nonlinear Conjugate Gradients Method

    Directory of Open Access Journals (Sweden)

    Huan Ma

    2015-01-01

    Full Text Available Four kinds of array of induced polarization (IP methods (surface, borehole-surface, surface-borehole, and borehole-borehole are widely used in resource exploration. However, due to the presence of large amounts of the sources, it will take much time to complete the inversion. In the paper, a new parallel algorithm is described which uses message passing interface (MPI and graphics processing unit (GPU to accelerate 3D inversion of these four methods. The forward finite differential equation is solved by ILU0 preconditioner and the conjugate gradient (CG solver. The inverse problem is solved by nonlinear conjugate gradients (NLCG iteration which is used to calculate one forward and two “pseudo-forward” modelings and update the direction, space, and model in turn. Because each source is independent in forward and “pseudo-forward” modelings, multiprocess modes are opened by calling MPI library. The iterative matrix solver within CULA is called in each process. Some tables and synthetic data examples illustrate that this parallel inversion algorithm is effective. Furthermore, we demonstrate that the joint inversion of surface and borehole data produces resistivity and chargeability results are superior to those obtained from inversions of individual surface data.

  9. Joint Bayesian Stochastic Inversion of Well Logs and Seismic Data for Volumetric Uncertainty Analysis

    Directory of Open Access Journals (Sweden)

    Moslem Moradi

    2015-06-01

    Full Text Available Here in, an application of a new seismic inversion algorithm in one of Iran’s oilfields is described. Stochastic (geostatistical seismic inversion, as a complementary method to deterministic inversion, is perceived as contribution combination of geostatistics and seismic inversion algorithm. This method integrates information from different data sources with different scales, as prior information in Bayesian statistics. Data integration leads to a probability density function (named as a posteriori probability that can yield a model of subsurface. The Markov Chain Monte Carlo (MCMC method is used to sample the posterior probability distribution, and the subsurface model characteristics can be extracted by analyzing a set of the samples. In this study, the theory of stochastic seismic inversion in a Bayesian framework was described and applied to infer P-impedance and porosity models. The comparison between the stochastic seismic inversion and the deterministic model based seismic inversion indicates that the stochastic seismic inversion can provide more detailed information of subsurface character. Since multiple realizations are extracted by this method, an estimation of pore volume and uncertainty in the estimation were analyzed.

  10. Reconfigurable Flight Control Using Nonlinear Dynamic Inversion with a Special Accelerometer Implementation

    Science.gov (United States)

    Bacon, Barton J.; Ostroff, Aaron J.

    2000-01-01

    This paper presents an approach to on-line control design for aircraft that have suffered either actuator failure, missing effector surfaces, surface damage, or any combination. The approach is based on a modified version of nonlinear dynamic inversion. The approach does not require a model of the baseline vehicle (effectors at zero deflection), but does require feedback of accelerations and effector positions. Implementation issues are addressed and the method is demonstrated on an advanced tailless aircraft. An experimental simulation analysis tool is used to directly evaluate the nonlinear system's stability robustness.

  11. Parameter estimation of a nonlinear Burger's model using nanoindentation and finite element-based inverse analysis

    Science.gov (United States)

    Hamim, Salah Uddin Ahmed

    Nanoindentation involves probing a hard diamond tip into a material, where the load and the displacement experienced by the tip is recorded continuously. This load-displacement data is a direct function of material's innate stress-strain behavior. Thus, theoretically it is possible to extract mechanical properties of a material through nanoindentation. However, due to various nonlinearities associated with nanoindentation the process of interpreting load-displacement data into material properties is difficult. Although, simple elastic behavior can be characterized easily, a method to characterize complicated material behavior such as nonlinear viscoelasticity is still lacking. In this study, a nanoindentation-based material characterization technique is developed to characterize soft materials exhibiting nonlinear viscoelasticity. Nanoindentation experiment was modeled in finite element analysis software (ABAQUS), where a nonlinear viscoelastic behavior was incorporated using user-defined subroutine (UMAT). The model parameters were calibrated using a process called inverse analysis. In this study, a surrogate model-based approach was used for the inverse analysis. The different factors affecting the surrogate model performance are analyzed in order to optimize the performance with respect to the computational cost.

  12. Geostatistical evaluation of travel time uncertainties

    International Nuclear Information System (INIS)

    Devary, J.L.

    1983-08-01

    Data on potentiometric head and hydraulic conductivity, gathered from the Wolfcamp Formation of the Permian System, have exhibited tremendous spatial variability as a result of heterogeneities in the media and the presence of petroleum and natural gas deposits. Geostatistical data analysis and error propagation techniques (kriging and conditional simulation) were applied to determine the effect of potentiometric head uncertainties on radionuclide travel paths and travel times through the Wolfcamp Formation. Blok-average kriging was utilized to remove measurement error from potentiometric head data. The travel time calculations have been enhanced by the use of an inverse technique to determine the relative hydraulic conductivity along travel paths. In this way, the spatial variability of the hydraulic conductivity corresponding to streamline convergence and divergence may be included in the analysis. 22 references, 11 figures, 1 table

  13. Full-waveform inversion using a nonlinearly smoothed wavefield

    KAUST Repository

    Li, Yuanyuan

    2017-12-08

    Conventional full-waveform inversion (FWI) based on the least-squares misfit function faces problems in converging to the global minimum when using gradient methods because of the cycle-skipping phenomena. An initial model producing data that are at most a half-cycle away from the observed data is needed for convergence to the global minimum. Low frequencies are helpful in updating low-wavenumber components of the velocity model to avoid cycle skipping. However, low enough frequencies are usually unavailable in field cases. The multiplication of wavefields of slightly different frequencies adds artificial low-frequency components in the data, which can be used for FWI to generate a convergent result and avoid cycle skipping. We generalize this process by multiplying the wavefield with itself and then applying a smoothing operator to the multiplied wavefield or its square to derive the nonlinearly smoothed wavefield, which is rich in low frequencies. The global correlation-norm-based objective function can mitigate the dependence on the amplitude information of the nonlinearly smoothed wavefield. Therefore, we have evaluated the use of this objective function when using the nonlinearly smoothed wavefield. The proposed objective function has much larger convexity than the conventional objective functions. We calculate the gradient of the objective function using the adjoint-state technique, which is similar to that of the conventional FWI except for the adjoint source. We progressively reduce the smoothing width applied to the nonlinear wavefield to naturally adopt the multiscale strategy. Using examples on the Marmousi 2 model, we determine that the proposed FWI helps to generate convergent results without the need for low-frequency information.

  14. Inverse operator method for solutions of nonlinear dynamical equations and some typical applications

    International Nuclear Information System (INIS)

    Fang Jinqing; Yao Weiguang

    1993-01-01

    The inverse operator method (IOM) is described briefly. We have realized the IOM for the solutions of nonlinear dynamical equations by the mathematics-mechanization (MM) with computers. They can then offer a new and powerful method applicable to many areas of physics. We have applied them successfully to study the chaotic behaviors of some nonlinear dynamical equations. As typical examples, the well-known Lorentz equation, generalized Duffing equation and two coupled generalized Duffing equations are investigated by using the IOM and the MM. The results are in good agreement with those given by Runge-Kutta method. So the IOM realized by the MM is of potential application valuable in nonlinear physics and many other fields

  15. Efficient scattering-angle enrichment for a nonlinear inversion of the background and perturbations components of a velocity model

    KAUST Repository

    Wu, Zedong; Alkhalifah, Tariq Ali

    2017-01-01

    Reflection-waveform inversion (RWI) can help us reduce the nonlinearity of the standard full-waveform inversion (FWI) by inverting for the background velocity model using the wave-path of a single scattered wavefield to an image. However, current

  16. Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations

    Energy Technology Data Exchange (ETDEWEB)

    Chen, Peng, E-mail: peng@ices.utexas.edu [The Institute for Computational Engineering and Sciences, The University of Texas at Austin, 201 East 24th Street, Stop C0200, Austin, TX 78712-1229 (United States); Schwab, Christoph, E-mail: christoph.schwab@sam.math.ethz.ch [Seminar für Angewandte Mathematik, Eidgenössische Technische Hochschule, Römistrasse 101, CH-8092 Zürich (Switzerland)

    2016-07-01

    We extend the reduced basis (RB) accelerated Bayesian inversion methods for affine-parametric, linear operator equations which are considered in [16,17] to non-affine, nonlinear parametric operator equations. We generalize the analysis of sparsity of parametric forward solution maps in [20] and of Bayesian inversion in [48,49] to the fully discrete setting, including Petrov–Galerkin high-fidelity (“HiFi”) discretization of the forward maps. We develop adaptive, stochastic collocation based reduction methods for the efficient computation of reduced bases on the parametric solution manifold. The nonaffinity and nonlinearity with respect to (w.r.t.) the distributed, uncertain parameters and the unknown solution is collocated; specifically, by the so-called Empirical Interpolation Method (EIM). For the corresponding Bayesian inversion problems, computational efficiency is enhanced in two ways: first, expectations w.r.t. the posterior are computed by adaptive quadratures with dimension-independent convergence rates proposed in [49]; the present work generalizes [49] to account for the impact of the PG discretization in the forward maps on the convergence rates of the Quantities of Interest (QoI for short). Second, we propose to perform the Bayesian estimation only w.r.t. a parsimonious, RB approximation of the posterior density. Based on the approximation results in [49], the infinite-dimensional parametric, deterministic forward map and operator admit N-term RB and EIM approximations which converge at rates which depend only on the sparsity of the parametric forward map. In several numerical experiments, the proposed algorithms exhibit dimension-independent convergence rates which equal, at least, the currently known rate estimates for N-term approximation. We propose to accelerate Bayesian estimation by first offline construction of reduced basis surrogates of the Bayesian posterior density. The parsimonious surrogates can then be employed for online data

  17. Geostatistical investigations of rock masses

    International Nuclear Information System (INIS)

    Matar, J.A.; Sarquis, M.A.; Girardi, J.P.; Tabbia, G.H.

    1987-01-01

    The geostatistical tehniques applied for the selection of a minimun fracturation volume in Sierra del Medio allow to quantify and qualify the variability of mechanic characteristics and density of fracture and also the level of reliability in estimations. The role of geostatistics is discussed in this work so as to select minimun fracturation blocks as a very important site selection step. The only variable used is the 'jointing density' so as to detect the principal fracture systems affecting the rocky massif. It was used on the semivariograms corresponding to the previously mentioned regionalized variables. The different results of fracturation are compared with the deep and shallow geological survey to obtain two and three dimensional models. The range of the geostatistical techniques to detect local geological phenomena such as faults is discussed. The variability model obtained from the borehole data computations is investigated taking as basis the vertical Columnar Model of Discontinuity (fractures) hypothesis derived from geological studies about spatial behaviour of the joint systems and from geostatistical interpretation. (Author) [es

  18. Application of Bayesian geostatistics for evaluation of mass discharge uncertainty at contaminated sites

    Science.gov (United States)

    Troldborg, Mads; Nowak, Wolfgang; Lange, Ida V.; Santos, Marta C.; Binning, Philip J.; Bjerg, Poul L.

    2012-09-01

    Mass discharge estimates are increasingly being used when assessing risks of groundwater contamination and designing remedial systems at contaminated sites. Such estimates are, however, rather uncertain as they integrate uncertain spatial distributions of both concentration and groundwater flow. Here a geostatistical simulation method for quantifying the uncertainty of the mass discharge across a multilevel control plane is presented. The method accounts for (1) heterogeneity of both the flow field and the concentration distribution through Bayesian geostatistics, (2) measurement uncertainty, and (3) uncertain source zone and transport parameters. The method generates conditional realizations of the spatial flow and concentration distribution. An analytical macrodispersive transport solution is employed to simulate the mean concentration distribution, and a geostatistical model of the Box-Cox transformed concentration data is used to simulate observed deviations from this mean solution. By combining the flow and concentration realizations, a mass discharge probability distribution is obtained. The method has the advantage of avoiding the heavy computational burden of three-dimensional numerical flow and transport simulation coupled with geostatistical inversion. It may therefore be of practical relevance to practitioners compared to existing methods that are either too simple or computationally demanding. The method is demonstrated on a field site contaminated with chlorinated ethenes. For this site, we show that including a physically meaningful concentration trend and the cosimulation of hydraulic conductivity and hydraulic gradient across the transect helps constrain the mass discharge uncertainty. The number of sampling points required for accurate mass discharge estimation and the relative influence of different data types on mass discharge uncertainty is discussed.

  19. Inverse scattering solution of non-linear evolution equations in one space dimension: an introduction

    International Nuclear Information System (INIS)

    Alvarez-Estrada, R.F.

    1979-01-01

    A comprehensive review of the inverse scattering solution of certain non-linear evolution equations of physical interest in one space dimension is presented. We explain in some detail the interrelated techniques which allow to linearize exactly the following equations: (1) the Korteweg and de Vries equation; (2) the non-linear Schrodinger equation; (3) the modified Korteweg and de Vries equation; (4) the Sine-Gordon equation. We concentrate in discussing the pairs of linear operators which accomplish such an exact linearization and the solution of the associated initial value problem. The application of the method to other non-linear evolution equations is reviewed very briefly

  20. Application of the concept of dynamic trim control and nonlinear system inverses to automatic control of a vertical attitude takeoff and landing aircraft

    Science.gov (United States)

    Smith, G. A.; Meyer, G.

    1981-01-01

    A full envelope automatic flight control system based on nonlinear inverse systems concepts has been applied to a vertical attitude takeoff and landing (VATOL) fighter aircraft. A new method for using an airborne digital aircraft model to perform the inversion of a nonlinear aircraft model is presented together with the results of a simulation study of the nonlinear inverse system concept for the vertical-attitude hover mode. The system response to maneuver commands in the vertical attitude was found to be excellent; and recovery from large initial offsets and large disturbances was found to be very satisfactory.

  1. Inverse operator method for solutions of nonlinear dynamical system and application to Lorentz equation

    International Nuclear Information System (INIS)

    Fang Jinqing; Yao Weiguang

    1993-01-01

    The inverse operator method (IOM) for solutions of nonlinear dynamical systems (NDS) is briefly described and realized by the Mathematics-Mechanization (MM) in computers. For the first time IOM and MM are successfully applied to study the chaotic behaviors of Lorentz equation

  2. 3D stochastic inversion and joint inversion of potential fields for multi scale parameters

    Science.gov (United States)

    Shamsipour, Pejman

    In this thesis we present the development of new techniques for the interpretation of potential field (gravity and magnetic data), which are the most widespread economic geophysical methods used for oil and mineral exploration. These new techniques help to address the long-standing issue with the interpretation of potential fields, namely the intrinsic non-uniqueness inversion of these types of data. The thesis takes the form of three papers (four including Appendix), which have been published, or soon to be published, in respected international journals. The purpose of the thesis is to introduce new methods based on 3D stochastical approaches for: 1) Inversion of potential field data (magnetic), 2) Multiscale Inversion using surface and borehole data and 3) Joint inversion of geophysical potential field data. We first present a stochastic inversion method based on a geostatistical approach to recover 3D susceptibility models from magnetic data. The aim of applying geostatistics is to provide quantitative descriptions of natural variables distributed in space or in time and space. We evaluate the uncertainty on the parameter model by using geostatistical unconditional simulations. The realizations are post-conditioned by cokriging to observation data. In order to avoid the natural tendency of the estimated structure to lay near the surface, depth weighting is included in the cokriging system. Then, we introduce algorithm for multiscale inversion, the presented algorithm has the capability of inverting data on multiple supports. The method involves four main steps: i. upscaling of borehole parameters (It could be density or susceptibility) to block parameters, ii. selection of block to use as constraints based on a threshold on kriging variance, iii. inversion of observation data with selected block densities as constraints, and iv. downscaling of inverted parameters to small prisms. Two modes of application are presented: estimation and simulation. Finally, a novel

  3. Data-driven methods towards learning the highly nonlinear inverse kinematics of tendon-driven surgical manipulators.

    Science.gov (United States)

    Xu, Wenjun; Chen, Jie; Lau, Henry Y K; Ren, Hongliang

    2017-09-01

    Accurate motion control of flexible surgical manipulators is crucial in tissue manipulation tasks. The tendon-driven serpentine manipulator (TSM) is one of the most widely adopted flexible mechanisms in minimally invasive surgery because of its enhanced maneuverability in torturous environments. TSM, however, exhibits high nonlinearities and conventional analytical kinematics model is insufficient to achieve high accuracy. To account for the system nonlinearities, we applied a data driven approach to encode the system inverse kinematics. Three regression methods: extreme learning machine (ELM), Gaussian mixture regression (GMR) and K-nearest neighbors regression (KNNR) were implemented to learn a nonlinear mapping from the robot 3D position states to the control inputs. The performance of the three algorithms was evaluated both in simulation and physical trajectory tracking experiments. KNNR performed the best in the tracking experiments, with the lowest RMSE of 2.1275 mm. The proposed inverse kinematics learning methods provide an alternative and efficient way to accurately model the tendon driven flexible manipulator. Copyright © 2016 John Wiley & Sons, Ltd.

  4. Uncertainties in the 2004 Sumatra–Andaman source through nonlinear stochastic inversion of tsunami waves

    Science.gov (United States)

    Venugopal, M.; Roy, D.; Rajendran, K.; Guillas, S.; Dias, F.

    2017-01-01

    Numerical inversions for earthquake source parameters from tsunami wave data usually incorporate subjective elements to stabilize the search. In addition, noisy and possibly insufficient data result in instability and non-uniqueness in most deterministic inversions, which are barely acknowledged. Here, we employ the satellite altimetry data for the 2004 Sumatra–Andaman tsunami event to invert the source parameters. We also include kinematic parameters that improve the description of tsunami generation and propagation, especially near the source. Using a finite fault model that represents the extent of rupture and the geometry of the trench, we perform a new type of nonlinear joint inversion of the slips, rupture velocities and rise times with minimal a priori constraints. Despite persistently good waveform fits, large uncertainties in the joint parameter distribution constitute a remarkable feature of the inversion. These uncertainties suggest that objective inversion strategies should incorporate more sophisticated physical models of seabed deformation in order to significantly improve the performance of early warning systems. PMID:28989311

  5. Mixed linear-nonlinear fault slip inversion: Bayesian inference of model, weighting, and smoothing parameters

    Science.gov (United States)

    Fukuda, J.; Johnson, K. M.

    2009-12-01

    Studies utilizing inversions of geodetic data for the spatial distribution of coseismic slip on faults typically present the result as a single fault plane and slip distribution. Commonly the geometry of the fault plane is assumed to be known a priori and the data are inverted for slip. However, sometimes there is not strong a priori information on the geometry of the fault that produced the earthquake and the data is not always strong enough to completely resolve the fault geometry. We develop a method to solve for the full posterior probability distribution of fault slip and fault geometry parameters in a Bayesian framework using Monte Carlo methods. The slip inversion problem is particularly challenging because it often involves multiple data sets with unknown relative weights (e.g. InSAR, GPS), model parameters that are related linearly (slip) and nonlinearly (fault geometry) through the theoretical model to surface observations, prior information on model parameters, and a regularization prior to stabilize the inversion. We present the theoretical framework and solution method for a Bayesian inversion that can handle all of these aspects of the problem. The method handles the mixed linear/nonlinear nature of the problem through combination of both analytical least-squares solutions and Monte Carlo methods. We first illustrate and validate the inversion scheme using synthetic data sets. We then apply the method to inversion of geodetic data from the 2003 M6.6 San Simeon, California earthquake. We show that the uncertainty in strike and dip of the fault plane is over 20 degrees. We characterize the uncertainty in the slip estimate with a volume around the mean fault solution in which the slip most likely occurred. Slip likely occurred somewhere in a volume that extends 5-10 km in either direction normal to the fault plane. We implement slip inversions with both traditional, kinematic smoothing constraints on slip and a simple physical condition of uniform stress

  6. Nonlinear inversion of borehole-radar tomography data to reconstruct velocity and attenuation distribution in earth materials

    Science.gov (United States)

    Zhou, C.; Liu, L.; Lane, J.W.

    2001-01-01

    A nonlinear tomographic inversion method that uses first-arrival travel-time and amplitude-spectra information from cross-hole radar measurements was developed to simultaneously reconstruct electromagnetic velocity and attenuation distribution in earth materials. Inversion methods were developed to analyze single cross-hole tomography surveys and differential tomography surveys. Assuming the earth behaves as a linear system, the inversion methods do not require estimation of source radiation pattern, receiver coupling, or geometrical spreading. The data analysis and tomographic inversion algorithm were applied to synthetic test data and to cross-hole radar field data provided by the US Geological Survey (USGS). The cross-hole radar field data were acquired at the USGS fractured-rock field research site at Mirror Lake near Thornton, New Hampshire, before and after injection of a saline tracer, to monitor the transport of electrically conductive fluids in the image plane. Results from the synthetic data test demonstrate the algorithm computational efficiency and indicate that the method robustly can reconstruct electromagnetic (EM) wave velocity and attenuation distribution in earth materials. The field test results outline zones of velocity and attenuation anomalies consistent with the finding of previous investigators; however, the tomograms appear to be quite smooth. Further work is needed to effectively find the optimal smoothness criterion in applying the Tikhonov regularization in the nonlinear inversion algorithms for cross-hole radar tomography. ?? 2001 Elsevier Science B.V. All rights reserved.

  7. Inverse chaos synchronization in linearly and nonlinearly coupled systems with multiple time-delays

    International Nuclear Information System (INIS)

    Shahverdiev, E.M.; Hashimov, R.H.; Nuriev, R.A.; Hashimova, L.H.; Huseynova, E.M.; Shore, K.A.

    2005-04-01

    We report on inverse chaos synchronization between two unidirectionally linearly and nonlinearly coupled chaotic systems with multiple time-delays and find the existence and stability conditions for different synchronization regimes. We also study the effect of parameter mismatches on synchonization regimes. The method is tested on the famous Ikeda model. Numerical simulations fully support the analytical approach. (author)

  8. Computational system for geostatistical analysis

    Directory of Open Access Journals (Sweden)

    Vendrusculo Laurimar Gonçalves

    2004-01-01

    Full Text Available Geostatistics identifies the spatial structure of variables representing several phenomena and its use is becoming more intense in agricultural activities. This paper describes a computer program, based on Windows Interfaces (Borland Delphi, which performs spatial analyses of datasets through geostatistic tools: Classical statistical calculations, average, cross- and directional semivariograms, simple kriging estimates and jackknifing calculations. A published dataset of soil Carbon and Nitrogen was used to validate the system. The system was useful for the geostatistical analysis process, for the manipulation of the computational routines in a MS-DOS environment. The Windows development approach allowed the user to model the semivariogram graphically with a major degree of interaction, functionality rarely available in similar programs. Given its characteristic of quick prototypation and simplicity when incorporating correlated routines, the Delphi environment presents the main advantage of permitting the evolution of this system.

  9. Adaptive discretizations for the choice of a Tikhonov regularization parameter in nonlinear inverse problems

    International Nuclear Information System (INIS)

    Kaltenbacher, Barbara; Kirchner, Alana; Vexler, Boris

    2011-01-01

    Parameter identification problems for partial differential equations usually lead to nonlinear inverse problems. A typical property of such problems is their instability, which requires regularization techniques, like, e.g., Tikhonov regularization. The main focus of this paper will be on efficient methods for determining a suitable regularization parameter by using adaptive finite element discretizations based on goal-oriented error estimators. A well-established method for the determination of a regularization parameter is the discrepancy principle where the residual norm, considered as a function i of the regularization parameter, should equal an appropriate multiple of the noise level. We suggest to solve the resulting scalar nonlinear equation by an inexact Newton method, where in each iteration step, a regularized problem is solved at a different discretization level. The proposed algorithm is an extension of the method suggested in Griesbaum A et al (2008 Inverse Problems 24 025025) for linear inverse problems, where goal-oriented error estimators for i and its derivative are used for adaptive refinement strategies in order to keep the discretization level as coarse as possible to save computational effort but fine enough to guarantee global convergence of the inexact Newton method. This concept leads to a highly efficient method for determining the Tikhonov regularization parameter for nonlinear ill-posed problems. Moreover, we prove that with the so-obtained regularization parameter and an also adaptively discretized Tikhonov minimizer, usual convergence and regularization results from the continuous setting can be recovered. As a matter of fact, it is shown that it suffices to use stationary points of the Tikhonov functional. The efficiency of the proposed method is demonstrated by means of numerical experiments. (paper)

  10. A Nonlinear Dynamic Inversion Predictor-Based Model Reference Adaptive Controller for a Generic Transport Model

    Science.gov (United States)

    Campbell, Stefan F.; Kaneshige, John T.

    2010-01-01

    Presented here is a Predictor-Based Model Reference Adaptive Control (PMRAC) architecture for a generic transport aircraft. At its core, this architecture features a three-axis, non-linear, dynamic-inversion controller. Command inputs for this baseline controller are provided by pilot roll-rate, pitch-rate, and sideslip commands. This paper will first thoroughly present the baseline controller followed by a description of the PMRAC adaptive augmentation to this control system. Results are presented via a full-scale, nonlinear simulation of NASA s Generic Transport Model (GTM).

  11. Learning Inverse Rig Mappings by Nonlinear Regression.

    Science.gov (United States)

    Holden, Daniel; Saito, Jun; Komura, Taku

    2017-03-01

    We present a framework to design inverse rig-functions-functions that map low level representations of a character's pose such as joint positions or surface geometry to the representation used by animators called the animation rig. Animators design scenes using an animation rig, a framework widely adopted in animation production which allows animators to design character poses and geometry via intuitive parameters and interfaces. Yet most state-of-the-art computer animation techniques control characters through raw, low level representations such as joint angles, joint positions, or vertex coordinates. This difference often stops the adoption of state-of-the-art techniques in animation production. Our framework solves this issue by learning a mapping between the low level representations of the pose and the animation rig. We use nonlinear regression techniques, learning from example animation sequences designed by the animators. When new motions are provided in the skeleton space, the learned mapping is used to estimate the rig controls that reproduce such a motion. We introduce two nonlinear functions for producing such a mapping: Gaussian process regression and feedforward neural networks. The appropriate solution depends on the nature of the rig and the amount of data available for training. We show our framework applied to various examples including articulated biped characters, quadruped characters, facial animation rigs, and deformable characters. With our system, animators have the freedom to apply any motion synthesis algorithm to arbitrary rigging and animation pipelines for immediate editing. This greatly improves the productivity of 3D animation, while retaining the flexibility and creativity of artistic input.

  12. On the internal stability of non-linear dynamic inversion: application to flight control

    Czech Academy of Sciences Publication Activity Database

    Alam, M.; Čelikovský, Sergej

    2017-01-01

    Roč. 11, č. 12 (2017), s. 1849-1861 ISSN 1751-8644 R&D Projects: GA ČR(CZ) GA17-04682S Institutional support: RVO:67985556 Keywords : flight control * non-linear dynamic inversion * stability Subject RIV: BC - Control Systems Theory OBOR OECD: Automation and control systems Impact factor: 2.536, year: 2016 http://library.utia.cas.cz/separaty/2017/TR/celikovsky-0476150.pdf

  13. Inverse periodic problem for the discrete approximation of the Schroedinger nonlinear equation

    International Nuclear Information System (INIS)

    Bogolyubov, N.N.; Prikarpatskij, A.K.; AN Ukrainskoj SSR, Lvov. Inst. Prikladnykh Problem Mekhaniki i Matematiki)

    1982-01-01

    The problem of numerical solution of the Schroedinger nonlinear equation (1) iPSIsub(t) = PSIsub(xx)+-2(PSI)sup(2)PSI. The numerical solution of nonlinear differential equation supposes its discrete approximation is required for the realization of the computer calculation process. Tor the equation (1) there exists the following discrete approximation by variable x(2) iPSIsub(n, t) = (PSIsub(n+1)-2PSIsub(n)+PSIsub(n-1))/(Δx)sup(2)+-(PSIsub(n))sup(2)(PSIsub(n+1)+PSIsub(n-1)), n=0, +-1, +-2... where PSIsub(n)(+) is the corresponding value of PSI(x, t) function in the node and divisions with the equilibrium step Δx. The main problem is obtaining analytically exact solutions of the equations (2). The analysis of the equation system (2) is performed on the base of the discrete analogue of the periodic variant of the inverse scattering problem method developed with the aid of nonlinear equations of the Korteweg-de Vries type. Obtained in explicit form are analytical solutions of the equations system (2). The solutions are expressed through the Riemann THETA-function [ru

  14. On the quantum inverse problem for a new type of nonlinear Schroedinger equation for Alfven waves in plasma

    International Nuclear Information System (INIS)

    Sen, S.; Roy Chowdhury, A.

    1989-06-01

    The nonlinear Alfven waves are governed by the Vector Derivative nonlinear Schroedinger (VDNLS) equation, which for parallel or quasi parallel propagation reduces to the Derivative Nonlinear Schroedinger (DNLS) equation for the circularly polarized waves. We have formulated the Quantum Inverse problem for a new type of Nonlinear Schroedinger Equation which has many properties similar to the usual NLS problem but the structure of classical and quantum R matrix are distinctly different. The commutation rules of the scattering data are obtained and the Algebraic Bethe Ansatz is formulated to derive the eigenvalue equation for the energy of the excited states. 10 refs

  15. A nonlinear least-squares inverse analysis of strike-slip faulting with application to the San Andreas fault

    Science.gov (United States)

    Williams, Charles A.; Richardson, Randall M.

    1988-01-01

    A nonlinear weighted least-squares analysis was performed for a synthetic elastic layer over a viscoelastic half-space model of strike-slip faulting. Also, an inversion of strain rate data was attempted for the locked portions of the San Andreas fault in California. Based on an eigenvector analysis of synthetic data, it is found that the only parameter which can be resolved is the average shear modulus of the elastic layer and viscoelastic half-space. The other parameters were obtained by performing a suite of inversions for the fault. The inversions on data from the northern San Andreas resulted in predicted parameter ranges similar to those produced by inversions on data from the whole fault.

  16. Inverse operator theory method mathematics-mechanization for the solutions of nonlinear equations and some typical applications in nonlinear physics

    International Nuclear Information System (INIS)

    Fang Jinqing; Yao Weiguang

    1992-12-01

    Inverse operator theory method (IOTM) has developed rapidly in the last few years. It is an effective and useful procedure for quantitative solution of nonlinear or stochastic continuous dynamical systems. Solutions are obtained in series form for deterministic equations, and in the case of stochastic equation it gives statistic measures of the solution process. A very important advantage of the IOTM is to eliminate a number of restrictive and assumption on the nature of stochastic processes. Therefore, it provides more realistic solutions. The IOTM and its mathematics-mechanization (MM) are briefly introduced. They are used successfully to study the chaotic behaviors of the nonlinear dynamical systems for the first time in the world. As typical examples, the Lorentz equation, generalized Duffing equation, two coupled generalized Duffing equations are investigated by the use of the IOTM and the MM. The results are in good agreement with ones by the Runge-Kutta method (RKM). It has higher accuracy and faster convergence. So the IOTM realized by the MM is of potential application valuable in nonlinear science

  17. Nonlinear Rayleigh wave inversion based on the shuffled frog-leaping algorithm

    Science.gov (United States)

    Sun, Cheng-Yu; Wang, Yan-Yan; Wu, Dun-Shi; Qin, Xiao-Jun

    2017-12-01

    At present, near-surface shear wave velocities are mainly calculated through Rayleigh wave dispersion-curve inversions in engineering surface investigations, but the required calculations pose a highly nonlinear global optimization problem. In order to alleviate the risk of falling into a local optimal solution, this paper introduces a new global optimization method, the shuffle frog-leaping algorithm (SFLA), into the Rayleigh wave dispersion-curve inversion process. SFLA is a swarm-intelligence-based algorithm that simulates a group of frogs searching for food. It uses a few parameters, achieves rapid convergence, and is capability of effective global searching. In order to test the reliability and calculation performance of SFLA, noise-free and noisy synthetic datasets were inverted. We conducted a comparative analysis with other established algorithms using the noise-free dataset, and then tested the ability of SFLA to cope with data noise. Finally, we inverted a real-world example to examine the applicability of SFLA. Results from both synthetic and field data demonstrated the effectiveness of SFLA in the interpretation of Rayleigh wave dispersion curves. We found that SFLA is superior to the established methods in terms of both reliability and computational efficiency, so it offers great potential to improve our ability to solve geophysical inversion problems.

  18. Nonlinear Spatial Inversion Without Monte Carlo Sampling

    Science.gov (United States)

    Curtis, A.; Nawaz, A.

    2017-12-01

    High-dimensional, nonlinear inverse or inference problems usually have non-unique solutions. The distribution of solutions are described by probability distributions, and these are usually found using Monte Carlo (MC) sampling methods. These take pseudo-random samples of models in parameter space, calculate the probability of each sample given available data and other information, and thus map out high or low probability values of model parameters. However, such methods would converge to the solution only as the number of samples tends to infinity; in practice, MC is found to be slow to converge, convergence is not guaranteed to be achieved in finite time, and detection of convergence requires the use of subjective criteria. We propose a method for Bayesian inversion of categorical variables such as geological facies or rock types in spatial problems, which requires no sampling at all. The method uses a 2-D Hidden Markov Model over a grid of cells, where observations represent localized data constraining the model in each cell. The data in our example application are seismic properties such as P- and S-wave impedances or rock density; our model parameters are the hidden states and represent the geological rock types in each cell. The observations at each location are assumed to depend on the facies at that location only - an assumption referred to as `localized likelihoods'. However, the facies at a location cannot be determined solely by the observation at that location as it also depends on prior information concerning its correlation with the spatial distribution of facies elsewhere. Such prior information is included in the inversion in the form of a training image which represents a conceptual depiction of the distribution of local geologies that might be expected, but other forms of prior information can be used in the method as desired. The method provides direct (pseudo-analytic) estimates of posterior marginal probability distributions over each variable

  19. The application of geostatistics in erosion hazard mapping

    NARCIS (Netherlands)

    Beurden, S.A.H.A. van; Riezebos, H.Th.

    1988-01-01

    Geostatistical interpolation or kriging of soil and vegetation variables has become an important alternative to other mapping techniques. Although a reconnaissance sampling is necessary and basic requirements of geostatistics have to be met, kriging has the advantage of giving estimates with a

  20. A limited memory BFGS method for a nonlinear inverse problem in digital breast tomosynthesis

    Science.gov (United States)

    Landi, G.; Loli Piccolomini, E.; Nagy, J. G.

    2017-09-01

    Digital breast tomosynthesis (DBT) is an imaging technique that allows the reconstruction of a pseudo three-dimensional image of the breast from a finite number of low-dose two-dimensional projections obtained by different x-ray tube angles. An issue that is often ignored in DBT is the fact that an x-ray beam is polyenergetic, i.e. it is composed of photons with different levels of energy. The polyenergetic model requires solving a large-scale, nonlinear inverse problem, which is more expensive than the typically used simplified, linear monoenergetic model. However, the polyenergetic model is much less susceptible to beam hardening artifacts, which show up as dark streaks and cupping (i.e. background nonuniformities) in the reconstructed image. In addition, it has been shown that the polyenergetic model can be exploited to obtain additional quantitative information about the material of the object being imaged. In this paper we consider the multimaterial polyenergetic DBT model, and solve the nonlinear inverse problem with a limited memory BFGS quasi-Newton method. Regularization is enforced at each iteration using a diagonally modified approximation of the Hessian matrix, and by truncating the iterations.

  1. Optimizing Groundwater Monitoring Networks Using Integrated Statistical and Geostatistical Approaches

    Directory of Open Access Journals (Sweden)

    Jay Krishna Thakur

    2015-08-01

    Full Text Available The aim of this work is to investigate new approaches using methods based on statistics and geo-statistics for spatio-temporal optimization of groundwater monitoring networks. The formulated and integrated methods were tested with the groundwater quality data set of Bitterfeld/Wolfen, Germany. Spatially, the monitoring network was optimized using geo-statistical methods. Temporal optimization of the monitoring network was carried out using Sen’s method (1968. For geostatistical network optimization, a geostatistical spatio-temporal algorithm was used to identify redundant wells in 2- and 2.5-D Quaternary and Tertiary aquifers. Influences of interpolation block width, dimension, contaminant association, groundwater flow direction and aquifer homogeneity on statistical and geostatistical methods for monitoring network optimization were analysed. The integrated approach shows 37% and 28% redundancies in the monitoring network in Quaternary aquifer and Tertiary aquifer respectively. The geostatistical method also recommends 41 and 22 new monitoring wells in the Quaternary and Tertiary aquifers respectively. In temporal optimization, an overall optimized sampling interval was recommended in terms of lower quartile (238 days, median quartile (317 days and upper quartile (401 days in the research area of Bitterfeld/Wolfen. Demonstrated methods for improving groundwater monitoring network can be used in real monitoring network optimization with due consideration given to influencing factors.

  2. Support minimized inversion of acoustic and elastic wave scattering

    International Nuclear Information System (INIS)

    Safaeinili, A.

    1994-01-01

    This report discusses the following topics on support minimized inversion of acoustic and elastic wave scattering: Minimum support inversion; forward modelling of elastodynamic wave scattering; minimum support linearized acoustic inversion; support minimized nonlinear acoustic inversion without absolute phase; and support minimized nonlinear elastic inversion

  3. Particle simulations of nonlinear whistler and Alfven wave instabilities - Amplitude modulation, decay, soliton and inverse cascading

    International Nuclear Information System (INIS)

    Omura, Yoshiharu; Matsumoto, Hiroshi.

    1989-01-01

    Past theoretical and numerical studies of the nonlinear evolution of electromagnetic cyclotron waves are reviewed. Such waves are commonly observed in space plasmas such as Alfven waves in the solar wind or VLF whistler mode waves in the magnetosphere. The use of an electromagnetic full-particle code to study an electron cyclotron wave and of an electromagnetic hybrid code to study an ion cyclotron wave is demonstrated. Recent achievements in the simulations of nonlinear revolution of electromagnetic cyclotron waves are discussed. The inverse cascading processes of finite-amplitude whistler and Alfven waves is interpreted in terms of physical elementary processes. 65 refs

  4. Incremental Nonlinear Dynamic Inversion and Multihole Pressure Probes for Disturbance Rejection Control of Fixed-wing Micro Air Vehicles

    NARCIS (Netherlands)

    Smeur, E.J.J.; Remes, B.D.W.; de Wagter, C.; Chu, Q.; J.-M. Moschetta G. Hattenberger, H. de Plinval

    2017-01-01

    Maintaining stable flight during high turbulence intensities is challenging for fixed-wing micro air vehicles (MAV). Two methods are proposed
    to improve the disturbance rejection performance of the MAV: incremental nonlinear dynamic inversion (INDI) control and phaseadvanced pitch probes. INDI

  5. Rayleigh scattering and nonlinear inversion of elastic waves

    Energy Technology Data Exchange (ETDEWEB)

    Gritto, Roland [Univ. of California, Berkeley, CA (United States)

    1995-12-01

    Rayleigh scattering of elastic waves by an inclusion is investigated and the limitations determined. In the near field of the inhomogeneity, the scattered waves are up to a factor of 300 stronger than in the far field, excluding the application of the far field Rayleigh approximation for this range. The investigation of the relative error as a function of parameter perturbation shows a range of applicability broader than previously assumed, with errors of 37% and 17% for perturbations of -100% and +100%, respectively. The validity range for the Rayleigh limit is controlled by large inequalities, and therefore, the exact limit is determined as a function of various parameter configurations, resulting in surprisingly high values of up to kpR = 0.9. The nonlinear scattering problem can be solved by inverting for equivalent source terms (moments) of the scatterer, before the elastic parameters are determined. The nonlinear dependence between the moments and the elastic parameters reveals a strong asymmetry around the origin, which will produce different results for weak scattering approximations depending on the sign of the anomaly. Numerical modeling of cross hole situations shows that near field terms are important to yield correct estimates of the inhomogeneities in the vicinity of the receivers, while a few well positioned sources and receivers considerably increase the angular coverage, and thus the model resolution of the inversion parameters. The pattern of scattered energy by an inhomogeneity is complicated and varies depending on the object, the wavelength of the incident wave, and the elastic parameters involved. Therefore, it is necessary to investigate the direction of scattered amplitudes to determine the best survey geometry.

  6. Nonlinear Dynamic Inversion Baseline Control Law: Architecture and Performance Predictions

    Science.gov (United States)

    Miller, Christopher J.

    2011-01-01

    A model reference dynamic inversion control law has been developed to provide a baseline control law for research into adaptive elements and other advanced flight control law components. This controller has been implemented and tested in a hardware-in-the-loop simulation; the simulation results show excellent handling qualities throughout the limited flight envelope. A simple angular momentum formulation was chosen because it can be included in the stability proofs for many basic adaptive theories, such as model reference adaptive control. Many design choices and implementation details reflect the requirements placed on the system by the nonlinear flight environment and the desire to keep the system as basic as possible to simplify the addition of the adaptive elements. Those design choices are explained, along with their predicted impact on the handling qualities.

  7. Local Geostatistical Models and Big Data in Hydrological and Ecological Applications

    Science.gov (United States)

    Hristopulos, Dionissios

    2015-04-01

    The advent of the big data era creates new opportunities for environmental and ecological modelling but also presents significant challenges. The availability of remote sensing images and low-cost wireless sensor networks implies that spatiotemporal environmental data to cover larger spatial domains at higher spatial and temporal resolution for longer time windows. Handling such voluminous data presents several technical and scientific challenges. In particular, the geostatistical methods used to process spatiotemporal data need to overcome the dimensionality curse associated with the need to store and invert large covariance matrices. There are various mathematical approaches for addressing the dimensionality problem, including change of basis, dimensionality reduction, hierarchical schemes, and local approximations. We present a Stochastic Local Interaction (SLI) model that can be used to model local correlations in spatial data. SLI is a random field model suitable for data on discrete supports (i.e., regular lattices or irregular sampling grids). The degree of localization is determined by means of kernel functions and appropriate bandwidths. The strength of the correlations is determined by means of coefficients. In the "plain vanilla" version the parameter set involves scale and rigidity coefficients as well as a characteristic length. The latter determines in connection with the rigidity coefficient the correlation length of the random field. The SLI model is based on statistical field theory and extends previous research on Spartan spatial random fields [2,3] from continuum spaces to explicitly discrete supports. The SLI kernel functions employ adaptive bandwidths learned from the sampling spatial distribution [1]. The SLI precision matrix is expressed explicitly in terms of the model parameter and the kernel function. Hence, covariance matrix inversion is not necessary for parameter inference that is based on leave-one-out cross validation. This property

  8. Inverse Problems in Geosciences: Modelling the Rock Properties of an Oil Reservoir

    DEFF Research Database (Denmark)

    Lange, Katrine

    . We have developed and implemented the Frequency Matching method that uses the closed form expression of the a priori probability density function to formulate an inverse problem and compute the maximum a posteriori solution to it. Other methods for computing models that simultaneously fit data...... of the subsurface of the reservoirs. Hence the focus of this work has been on acquiring models of spatial parameters describing rock properties of the subsurface using geostatistical a priori knowledge and available geophysical data. Such models are solutions to often severely under-determined, inverse problems...

  9. Fast nonlinear gravity inversion in spherical coordinates with application to the South American Moho

    Science.gov (United States)

    Uieda, Leonardo; Barbosa, Valéria C. F.

    2017-01-01

    Estimating the relief of the Moho from gravity data is a computationally intensive nonlinear inverse problem. What is more, the modelling must take the Earths curvature into account when the study area is of regional scale or greater. We present a regularized nonlinear gravity inversion method that has a low computational footprint and employs a spherical Earth approximation. To achieve this, we combine the highly efficient Bott's method with smoothness regularization and a discretization of the anomalous Moho into tesseroids (spherical prisms). The computational efficiency of our method is attained by harnessing the fact that all matrices involved are sparse. The inversion results are controlled by three hyperparameters: the regularization parameter, the anomalous Moho density-contrast, and the reference Moho depth. We estimate the regularization parameter using the method of hold-out cross-validation. Additionally, we estimate the density-contrast and the reference depth using knowledge of the Moho depth at certain points. We apply the proposed method to estimate the Moho depth for the South American continent using satellite gravity data and seismological data. The final Moho model is in accordance with previous gravity-derived models and seismological data. The misfit to the gravity and seismological data is worse in the Andes and best in oceanic areas, central Brazil and Patagonia, and along the Atlantic coast. Similarly to previous results, the model suggests a thinner crust of 30-35 km under the Andean foreland basins. Discrepancies with the seismological data are greatest in the Guyana Shield, the central Solimões and Amazonas Basins, the Paraná Basin, and the Borborema province. These differences suggest the existence of crustal or mantle density anomalies that were unaccounted for during gravity data processing.

  10. Gstat: a program for geostatistical modelling, prediction and simulation

    Science.gov (United States)

    Pebesma, Edzer J.; Wesseling, Cees G.

    1998-01-01

    Gstat is a computer program for variogram modelling, and geostatistical prediction and simulation. It provides a generic implementation of the multivariable linear model with trends modelled as a linear function of coordinate polynomials or of user-defined base functions, and independent or dependent, geostatistically modelled, residuals. Simulation in gstat comprises conditional or unconditional (multi-) Gaussian sequential simulation of point values or block averages, or (multi-) indicator sequential simulation. Besides many of the popular options found in other geostatistical software packages, gstat offers the unique combination of (i) an interactive user interface for modelling variograms and generalized covariances (residual variograms), that uses the device-independent plotting program gnuplot for graphical display, (ii) support for several ascii and binary data and map file formats for input and output, (iii) a concise, intuitive and flexible command language, (iv) user customization of program defaults, (v) no built-in limits, and (vi) free, portable ANSI-C source code. This paper describes the class of problems gstat can solve, and addresses aspects of efficiency and implementation, managing geostatistical projects, and relevant technical details.

  11. On parameterization of the inverse problem for estimating aquifer properties using tracer data

    International Nuclear Information System (INIS)

    Kowalsky, M. B.; Finsterle, Stefan A.; Williams, Kenneth H.; Murray, Christopher J.; Commer, Michael; Newcomer, Darrell R.; Englert, Andreas L.; Steefel, Carl I.; Hubbard, Susan

    2012-01-01

    We consider a field-scale tracer experiment conducted in 2007 in a shallow uranium-contaminated aquifer at Rifle, Colorado. In developing a reliable approach for inferring hydrological properties at the site through inverse modeling of the tracer data, decisions made on how to parameterize heterogeneity (i.e., how to represent a heterogeneous distribution using a limited number of parameters that are amenable to estimation) are of paramount importance. We present an approach for hydrological inversion of the tracer data and explore, using a 2D synthetic example at first, how parameterization affects the solution, and how additional characterization data could be incorporated to reduce uncertainty. Specifically, we examine sensitivity of the results to the configuration of pilot points used in a geostatistical parameterization, and to the sampling frequency and measurement error of the concentration data. A reliable solution of the inverse problem is found when the pilot point configuration is carefully implemented. In addition, we examine the use of a zonation parameterization, in which the geometry of the geological facies is known (e.g., from geophysical data or core data), to reduce the non-uniqueness of the solution and the number of unknown parameters to be estimated. When zonation information is only available for a limited region, special treatment in the remainder of the model is necessary, such as using a geostatistical parameterization. Finally, inversion of the actual field data is performed using 2D and 3D models, and results are compared with slug test data.

  12. A Bayesian geostatistical approach for evaluating the uncertainty of contaminant mass discharges from point sources

    Science.gov (United States)

    Troldborg, M.; Nowak, W.; Binning, P. J.; Bjerg, P. L.

    2012-12-01

    Estimates of mass discharge (mass/time) are increasingly being used when assessing risks of groundwater contamination and designing remedial systems at contaminated sites. Mass discharge estimates are, however, prone to rather large uncertainties as they integrate uncertain spatial distributions of both concentration and groundwater flow velocities. For risk assessments or any other decisions that are being based on mass discharge estimates, it is essential to address these uncertainties. We present a novel Bayesian geostatistical approach for quantifying the uncertainty of the mass discharge across a multilevel control plane. The method decouples the flow and transport simulation and has the advantage of avoiding the heavy computational burden of three-dimensional numerical flow and transport simulation coupled with geostatistical inversion. It may therefore be of practical relevance to practitioners compared to existing methods that are either too simple or computationally demanding. The method is based on conditional geostatistical simulation and accounts for i) heterogeneity of both the flow field and the concentration distribution through Bayesian geostatistics (including the uncertainty in covariance functions), ii) measurement uncertainty, and iii) uncertain source zone geometry and transport parameters. The method generates multiple equally likely realizations of the spatial flow and concentration distribution, which all honour the measured data at the control plane. The flow realizations are generated by analytical co-simulation of the hydraulic conductivity and the hydraulic gradient across the control plane. These realizations are made consistent with measurements of both hydraulic conductivity and head at the site. An analytical macro-dispersive transport solution is employed to simulate the mean concentration distribution across the control plane, and a geostatistical model of the Box-Cox transformed concentration data is used to simulate observed

  13. Industrial experience feedback of a geostatistical estimation of contaminated soil volumes - 59181

    International Nuclear Information System (INIS)

    Faucheux, Claire; Jeannee, Nicolas

    2012-01-01

    Geo-statistics meets a growing interest for the remediation forecast of potentially contaminated sites, by providing adapted methods to perform both chemical and radiological pollution mapping, to estimate contaminated volumes, potentially integrating auxiliary information, and to set up adaptive sampling strategies. As part of demonstration studies carried out for GeoSiPol (Geo-statistics for Polluted Sites), geo-statistics has been applied for the detailed diagnosis of a former oil depot in France. The ability within the geo-statistical framework to generate pessimistic / probable / optimistic scenarios for the contaminated volumes allows a quantification of the risks associated to the remediation process: e.g. the financial risk to excavate clean soils, the sanitary risk to leave contaminated soils in place. After a first mapping, an iterative approach leads to collect additional samples in areas previously identified as highly uncertain. Estimated volumes are then updated and compared to the volumes actually excavated. This benchmarking therefore provides a practical feedback on the performance of the geo-statistical methodology. (authors)

  14. Geostatistics - bloodhound of uranium exploration

    International Nuclear Information System (INIS)

    David, Michel

    1979-01-01

    Geostatistics makes possible the efficient use of the information contained in core samples obtained by diamond drilling. The probability that a core represents the true content of a deposit, and the likely content of an orebody between two core samples can both be estimated using geostatistical methods. A confidence interval can be given for the mean grade of a deposit. The use of a computer is essential in the calculation of the continuity function, the variogram, when as many as 800,000 core samples may be involved. The results may be used to determine where additional samples need to be taken, and to develop a picture of the probable grades throughout the deposit. The basic mathematical model is about 15 years old, but applications to different types of deposit require various adaptations. The Ecole Polytechnique is currently developing methods for uranium deposits. (LL)

  15. Integration of dynamical data in a geostatistical model of reservoir; Integration des donnees dynamiques dans un modele geostatistique de reservoir

    Energy Technology Data Exchange (ETDEWEB)

    Costa Reis, L.

    2001-01-01

    We have developed in this thesis a methodology of integrated characterization of heterogeneous reservoirs, from geologic modeling to history matching. This methodology is applied to the reservoir PBR, situated in Campos Basin, offshore Brazil, which has been producing since June 1979. This work is an extension of two other thesis concerning geologic and geostatistical modeling of the reservoir PBR from well data and seismic information. We extended the geostatistical litho-type model to the whole reservoir by using a particular approach of the non-stationary truncated Gaussian simulation method. This approach facilitated the application of the gradual deformation method to history matching. The main stages of the methodology for dynamic data integration in a geostatistical reservoir model are presented. We constructed a reservoir model and the initial difficulties in the history matching led us to modify some choices in the geological, geostatistical and flow models. These difficulties show the importance of dynamic data integration in reservoir modeling. The petrophysical property assignment within the litho-types was done by using well test data. We used an inversion procedure to evaluate the petrophysical parameters of the litho-types. The up-scaling is a necessary stage to reduce the flow simulation time. We compared several up-scaling methods and we show that the passage from the fine geostatistical model to the coarse flow model should be done very carefully. The choice of the fitting parameter depends on the objective of the study. In the case of the reservoir PBR, where water is injected in order to improve the oil recovery, the water rate of the producing wells is directly related to the reservoir heterogeneity. Thus, the water rate was chosen as the fitting parameter. We obtained significant improvements in the history matching of the reservoir PBR. First, by using a method we have proposed, called patchwork. This method allows us to built a coherent

  16. Inverse scattering transform for the vector nonlinear Schroedinger equation with nonvanishing boundary conditions

    International Nuclear Information System (INIS)

    Prinari, Barbara; Ablowitz, Mark J.; Biondini, Gino

    2006-01-01

    The inverse scattering transform for the vector defocusing nonlinear Schroedinger (NLS) equation with nonvanishing boundary values at infinity is constructed. The direct scattering problem is formulated on a two-sheeted covering of the complex plane. Two out of the six Jost eigenfunctions, however, do not admit an analytic extension on either sheet of the Riemann surface. Therefore, a suitable modification of both the direct and the inverse problem formulations is necessary. On the direct side, this is accomplished by constructing two additional analytic eigenfunctions which are expressed in terms of the adjoint eigenfunctions. The discrete spectrum, bound states and symmetries of the direct problem are then discussed. In the most general situation, a discrete eigenvalue corresponds to a quartet of zeros (poles) of certain scattering data. The inverse scattering problem is formulated in terms of a generalized Riemann-Hilbert (RH) problem in the upper/lower half planes of a suitable uniformization variable. Special soliton solutions are constructed from the poles in the RH problem, and include dark-dark soliton solutions, which have dark solitonic behavior in both components, as well as dark-bright soliton solutions, which have one dark and one bright component. The linear limit is obtained from the RH problem and is shown to correspond to the Fourier transform solution obtained from the linearized vector NLS system

  17. Geostatistics and GIS: tools for characterizing environmental contamination.

    Science.gov (United States)

    Henshaw, Shannon L; Curriero, Frank C; Shields, Timothy M; Glass, Gregory E; Strickland, Paul T; Breysse, Patrick N

    2004-08-01

    Geostatistics is a set of statistical techniques used in the analysis of georeferenced data that can be applied to environmental contamination and remediation studies. In this study, the 1,1-dichloro-2,2-bis(p-chlorophenyl)ethylene (DDE) contamination at a Superfund site in western Maryland is evaluated. Concern about the site and its future clean up has triggered interest within the community because residential development surrounds the area. Spatial statistical methods, of which geostatistics is a subset, are becoming increasingly popular, in part due to the availability of geographic information system (GIS) software in a variety of application packages. In this article, the joint use of ArcGIS software and the R statistical computing environment are demonstrated as an approach for comprehensive geostatistical analyses. The spatial regression method, kriging, is used to provide predictions of DDE levels at unsampled locations both within the site and the surrounding areas where residential development is ongoing.

  18. Multi-Body Ski Jumper Model with Nonlinear Dynamic Inversion Muscle Control for Trajectory Optimization

    Directory of Open Access Journals (Sweden)

    Patrick Piprek

    2018-02-01

    Full Text Available This paper presents an approach to model a ski jumper as a multi-body system for an optimal control application. The modeling is based on the constrained Newton-Euler-Equations. Within this paper the complete multi-body modeling methodology as well as the musculoskeletal modeling is considered. For the musculoskeletal modeling and its incorporation in the optimization model, we choose a nonlinear dynamic inversion control approach. This approach uses the muscle models as nonlinear reference models and links them to the ski jumper movement by a control law. This strategy yields a linearized input-output behavior, which makes the optimal control problem easier to solve. The resulting model of the ski jumper can then be used for trajectory optimization whose results are compared to literature jumps. Ultimately, this enables the jumper to get a very detailed feedback of the flight. To achieve the maximal jump length, exact positioning of his body with respect to the air can be displayed.

  19. Numerical methods for the design of large-scale nonlinear discrete ill-posed inverse problems

    International Nuclear Information System (INIS)

    Haber, E; Horesh, L; Tenorio, L

    2010-01-01

    Design of experiments for discrete ill-posed problems is a relatively new area of research. While there has been some limited work concerning the linear case, little has been done to study design criteria and numerical methods for ill-posed nonlinear problems. We present an algorithmic framework for nonlinear experimental design with an efficient numerical implementation. The data are modeled as indirect, noisy observations of the model collected via a set of plausible experiments. An inversion estimate based on these data is obtained by a weighted Tikhonov regularization whose weights control the contribution of the different experiments to the data misfit term. These weights are selected by minimization of an empirical estimate of the Bayes risk that is penalized to promote sparsity. This formulation entails a bilevel optimization problem that is solved using a simple descent method. We demonstrate the viability of our design with a problem in electromagnetic imaging based on direct current resistivity and magnetotelluric data

  20. Geostatistics for radiological characterization: overview and application cases

    International Nuclear Information System (INIS)

    Desnoyers, Yvon

    2016-01-01

    The objective of radiological characterization is to find a suitable balance between gathering data (constrained by cost, deadlines, accessibility or radiation) and managing the issues (waste volumes, levels of activity or exposure). It is necessary to have enough information to have confidence in the results without multiplying useless data. Geo-statistics processing of data considers all available pieces of information: historical data, non-destructive measurements and laboratory analyses of samples. The spatial structure modelling is then used to produce maps and to estimate the extent of radioactive contamination (surface and depth). Quantifications of local and global uncertainties are powerful decision-making tools for better management of remediation projects at contaminated sites, and for decontamination and dismantling projects at nuclear facilities. They can be used to identify hot spots, estimate contamination of surfaces and volumes, classify radioactive waste according to thresholds, estimate source terms, and so on. The spatial structure of radioactive contamination makes the optimization of sampling (number and position of data points) particularly important. Geo-statistics methodology can help determine the initial mesh size and reduce estimation uncertainties. Several show cases are presented to illustrate why and how geo-statistics can be applied to a range of radiological characterization where investigated units can represent very small areas (a few m 2 or a few m 3 ) or very large sites (at a country scale). The focus is then put on experience gained over years in the use of geo-statistics and sampling optimization. (author)

  1. Inexact Newton–Landweber iteration for solving nonlinear inverse problems in Banach spaces

    International Nuclear Information System (INIS)

    Jin, Qinian

    2012-01-01

    By making use of duality mappings, we formulate an inexact Newton–Landweber iteration method for solving nonlinear inverse problems in Banach spaces. The method consists of two components: an outer Newton iteration and an inner scheme providing the increments by applying the Landweber iteration in Banach spaces to the local linearized equations. It has the advantage of reducing computational work by computing more cheap steps in each inner scheme. We first prove a convergence result for the exact data case. When the data are given approximately, we terminate the method by a discrepancy principle and obtain a weak convergence result. Finally, we test the method by reporting some numerical simulations concerning the sparsity recovery and the noisy data containing outliers. (paper)

  2. Nonlinear inversion of potential-field data using a hybrid-encoding genetic algorithm

    Science.gov (United States)

    Chen, C.; Xia, J.; Liu, J.; Feng, G.

    2006-01-01

    Using a genetic algorithm to solve an inverse problem of complex nonlinear geophysical equations is advantageous because it does not require computer gradients of models or "good" initial models. The multi-point search of a genetic algorithm makes it easier to find the globally optimal solution while avoiding falling into a local extremum. As is the case in other optimization approaches, the search efficiency for a genetic algorithm is vital in finding desired solutions successfully in a multi-dimensional model space. A binary-encoding genetic algorithm is hardly ever used to resolve an optimization problem such as a simple geophysical inversion with only three unknowns. The encoding mechanism, genetic operators, and population size of the genetic algorithm greatly affect search processes in the evolution. It is clear that improved operators and proper population size promote the convergence. Nevertheless, not all genetic operations perform perfectly while searching under either a uniform binary or a decimal encoding system. With the binary encoding mechanism, the crossover scheme may produce more new individuals than with the decimal encoding. On the other hand, the mutation scheme in a decimal encoding system will create new genes larger in scope than those in the binary encoding. This paper discusses approaches of exploiting the search potential of genetic operations in the two encoding systems and presents an approach with a hybrid-encoding mechanism, multi-point crossover, and dynamic population size for geophysical inversion. We present a method that is based on the routine in which the mutation operation is conducted in the decimal code and multi-point crossover operation in the binary code. The mix-encoding algorithm is called the hybrid-encoding genetic algorithm (HEGA). HEGA provides better genes with a higher probability by a mutation operator and improves genetic algorithms in resolving complicated geophysical inverse problems. Another significant

  3. 3D Hydraulic tomography from joint inversion of the hydraulic heads and self-potential data. (Invited)

    Science.gov (United States)

    Jardani, A.; Soueid Ahmed, A.; Revil, A.; Dupont, J.

    2013-12-01

    Pumping tests are usually employed to predict the hydraulic conductivity filed from the inversion of the head measurements. Nevertheless, the inverse problem is strongly underdetermined and a reliable imaging requires a considerable number of wells. We propose to add more information to the inversion of the heads by adding (non-intrusive) streaming potentials (SP) data. The SP corresponds to perturbations in the local electrical field caused directly by the fow of the ground water. These SP are obtained with a set of the non-polarising electrodes installed at the ground surface. We developed a geostatistical method for the estimation of the hydraulic conductivity field from measurements of hydraulic heads and SP during pumping and injection experiments. We use the adjoint state method and a recent petrophysical formulation of the streaming potential problem in which the streaming coupling coefficient is derived from the hydraulic conductivity allowed reducing of the unknown parameters. The geostatistical inverse framework is applied to three synthetic case studies with different number of the wells and electrodes used to measure the hydraulic heads and the streaming potentials. To evaluate the benefits of the incorporating of the streaming potential to the hydraulic data, we compared the cases in which the data are coupled or not to map the hydraulic conductivity. The results of the inversion revealed that a dense distribution of electrodes can be used to infer the heterogeneities in the hydraulic conductivity field. Incorporating the streaming potential information to the hydraulic head data improves the estimate of hydraulic conductivity field especially when the number of piezometers is limited.

  4. Dimensionality of heavy metal distribution in waste disposal sites using nonlinear dynamics

    International Nuclear Information System (INIS)

    Modis, Kostas; Komnitsas, Kostas

    2008-01-01

    Mapping of heavy metal contamination in mining and waste disposal sites usually relies on geostatistical approaches and linear stochastic dynamics. The present paper aims to identify, using the Grassberger-Procaccia correlation dimension (CD) algorithm, the existence of a nonlinear deterministic and chaotic dynamic behaviour in the spatial pattern of arsenic, manganese and zinc concentration in a Russian coal waste disposal site. The analysis carried out yielded embedding dimension values ranging between 7 and 8 suggesting thus from a chaotic dynamic perspective that arsenic, manganese and zinc concentration in space is a medium dimensional problem for the regionalized scale considered in this study. This alternative nonlinear dynamics approach may complement conventional geostatistical studies and may be also used for the estimation of risk and the subsequent screening and selection of a feasible remediation scheme in wider mining and waste disposal sites. Finally, the synergistic effect of this study may be further elaborated if additional factors including among others presence of hot spots, density and depth of sampling, mineralogy of wastes and sensitivity of analytical techniques are taken into account

  5. Modeling of long-range memory processes with inverse cubic distributions by the nonlinear stochastic differential equations

    Science.gov (United States)

    Kaulakys, B.; Alaburda, M.; Ruseckas, J.

    2016-05-01

    A well-known fact in the financial markets is the so-called ‘inverse cubic law’ of the cumulative distributions of the long-range memory fluctuations of market indicators such as a number of events of trades, trading volume and the logarithmic price change. We propose the nonlinear stochastic differential equation (SDE) giving both the power-law behavior of the power spectral density and the long-range dependent inverse cubic law of the cumulative distribution. This is achieved using the suggestion that when the market evolves from calm to violent behavior there is a decrease of the delay time of multiplicative feedback of the system in comparison to the driving noise correlation time. This results in a transition from the Itô to the Stratonovich sense of the SDE and yields a long-range memory process.

  6. 3D vadose zone modeling using geostatistical inferences

    International Nuclear Information System (INIS)

    Knutson, C.F.; Lee, C.B.

    1991-01-01

    In developing a 3D model of the 600 ft thick interbedded basalt and sediment complex that constitutes the vadose zone at the Radioactive Waste Management Complex (RWMC) at the Idaho National Engineering Laboratory (INEL) geostatistical data were captured for 12--15 parameters (e.g. permeability, porosity, saturation, etc. and flow height, flow width, flow internal zonation, etc.). This two scale data set was generated from studies of subsurface core and geophysical log suites at RWMC and from surface outcrop exposures located at the Box Canyon of the Big Lost River and from Hell's Half Acre lava field all located in the general RWMC area. Based on these currently available data, it is possible to build a 3D stochastic model that utilizes: cumulative distribution functions obtained from the geostatistical data; backstripping and rebuilding of stratigraphic units; an ''expert'' system that incorporates rules based on expert geologic analysis and experimentally derived geostatistics for providing: (a) a structural and isopach map of each layer, (b) a realization of the flow geometry of each basalt flow unit, and (c) a realization of the internal flow parameters (eg permeability, porosity, and saturation) for each flow. 10 refs., 4 figs., 1 tab

  7. Sheared Layers in the Continental Crust: Nonlinear and Linearized inversion for Ps receiver functions

    Science.gov (United States)

    Park, J. J.

    2017-12-01

    Sheared Layers in the Continental Crust: Nonlinear and Linearized inversion for Ps receiver functions Jeffrey Park, Yale University The interpretation of seismic receiver functions (RFs) in terms of isotropic and anisotropic layered structure can be complex. The relationship between structure and body-wave scattering is nonlinear. The anisotropy can involve more parameters than the observations can readily constrain. Finally, reflectivity-predicted layer reverberations are often not prominent in data, so that nonlinear waveform inversion can search in vain to match ghost signals. Multiple-taper correlation (MTC) receiver functions have uncertainties in the frequency domain that follow Gaussian statistics [Park and Levin, 2016a], so grid-searches for the best-fitting collections of interfaces can be performed rapidly to minimize weighted misfit variance. Tests for layer-reverberations can be performed in the frequency domain without reflectivity calculations, allowing flexible modelling of weak, but nonzero, reverberations. Park and Levin [2016b] linearized the hybridization of P and S body waves in an anisotropic layer to predict first-order Ps conversion amplitudes at crust and mantle interfaces. In an anisotropic layer, the P wave acquires small SV and SH components. To ensure continuity of displacement and traction at the top and bottom boundaries of the layer, shear waves are generated. Assuming hexagonal symmetry with an arbitrary symmetry axis, theory confirms the empirical stacking trick of phase-shifting transverse RFs by 90 degrees in back-azimuth [Shiomi and Park, 2008; Schulte-Pelkum and Mahan, 2014] to enhance 2-lobed and 4-lobed harmonic variation. Ps scattering is generated by sharp interfaces, so that RFs resemble the first derivative of the model. MTC RFs in the frequency domain can be manipulated to obtain a first-order reconstruction of the layered anisotropy, under the above modeling constraints and neglecting reverberations. Examples from long

  8. On Inverse Coefficient Heat-Conduction Problems on Reconstruction of Nonlinear Components of the Thermal-Conductivity Tensor of Anisotropic Bodies

    Science.gov (United States)

    Formalev, V. F.; Kolesnik, S. A.

    2017-11-01

    The authors are the first to present a closed procedure for numerical solution of inverse coefficient problems of heat conduction in anisotropic materials used as heat-shielding ones in rocket and space equipment. The reconstructed components of the thermal-conductivity tensor depend on temperature (are nonlinear). The procedure includes the formation of experimental data, the implicit gradient-descent method, the economical absolutely stable method of numerical solution of parabolic problems containing mixed derivatives, the parametric identification, construction, and numerical solution of the problem for elements of sensitivity matrices, the development of a quadratic residual functional and regularizing functionals, and also the development of algorithms and software systems. The implicit gradient-descent method permits expanding the quadratic functional in a Taylor series with retention of the linear terms for the increments of the sought functions. This substantially improves the exactness and stability of solution of the inverse problems. Software systems are developed with account taken of the errors in experimental data and disregarding them. On the basis of a priori assumptions of the qualitative behavior of the functional dependences of the components of the thermal-conductivity tensor on temperature, regularizing functionals are constructed by means of which one can reconstruct the components of the thermal-conductivity tensor with an error no higher than the error of the experimental data. Results of the numerical solution of the inverse coefficient problems on reconstruction of nonlinear components of the thermal-conductivity tensor have been obtained and are discussed.

  9. 2nd European Conference on Geostatistics for Environmental Applications

    CERN Document Server

    Soares, Amílcar; Froidevaux, Roland

    1999-01-01

    The Second European Conference on Geostatistics for Environmental Ap­ plications took place in Valencia, November 18-20, 1998. Two years have past from the first meeting in Lisbon and the geostatistical community has kept active in the environmental field. In these days of congress inflation, we feel that continuity can only be achieved by ensuring quality in the papers. For this reason, all papers in the book have been reviewed by, at least, two referees, and care has been taken to ensure that the reviewer comments have been incorporated in the final version of the manuscript. We are thankful to the members of the scientific committee for their timely review of the scripts. All in all, there are three keynote papers from experts in soil science, climatology and ecology and 43 contributed papers providing a good indication of the status of geostatistics as applied in the environ­ mental field all over the world. We feel now confident that the geoENV conference series, seeded around a coffee table almost six...

  10. A Bayesian Markov geostatistical model for estimation of hydrogeological properties

    International Nuclear Information System (INIS)

    Rosen, L.; Gustafson, G.

    1996-01-01

    A geostatistical methodology based on Markov-chain analysis and Bayesian statistics was developed for probability estimations of hydrogeological and geological properties in the siting process of a nuclear waste repository. The probability estimates have practical use in decision-making on issues such as siting, investigation programs, and construction design. The methodology is nonparametric which makes it possible to handle information that does not exhibit standard statistical distributions, as is often the case for classified information. Data do not need to meet the requirements on additivity and normality as with the geostatistical methods based on regionalized variable theory, e.g., kriging. The methodology also has a formal way for incorporating professional judgments through the use of Bayesian statistics, which allows for updating of prior estimates to posterior probabilities each time new information becomes available. A Bayesian Markov Geostatistical Model (BayMar) software was developed for implementation of the methodology in two and three dimensions. This paper gives (1) a theoretical description of the Bayesian Markov Geostatistical Model; (2) a short description of the BayMar software; and (3) an example of application of the model for estimating the suitability for repository establishment with respect to the three parameters of lithology, hydraulic conductivity, and rock quality designation index (RQD) at 400--500 meters below ground surface in an area around the Aespoe Hard Rock Laboratory in southeastern Sweden

  11. Optimized nonlinear inversion of surface-wave dispersion data

    International Nuclear Information System (INIS)

    Raykova, Reneta B.

    2014-01-01

    A new code for inversion of surface wave dispersion data is developed to obtain Earth’s crustal and upper mantle velocity structure. The author developed Optimized Non–Linear Inversion ( ONLI ) software, based on Monte-Carlo search. The values of S–wave velocity VS and thickness h for a number of horizontal homogeneous layers are parameterized. Velocity of P–wave VP and density ρ of relevant layers are calculated by empirical or theoretical relations. ONLI explores parameters space in two modes, selective and full search, and the main innovation of software is evaluation of tested models. Theoretical dispersion curves are calculated if tested model satisfied specific conditions only, reducing considerably the computation time. A number of tests explored impact of parameterization and proved the ability of ONLI approach to deal successfully with non–uniqueness of inversion problem. Key words: Earth’s structure, surface–wave dispersion, non–linear inversion, software

  12. Geostatistical ore reserve estimation for a roll-front type uranium deposit (practitioner's guide)

    International Nuclear Information System (INIS)

    Kim, Y.C.; Knudsen, H.P.

    1977-01-01

    This report comprises two parts. Part I contains illustrative examples of each phase of a geostatistical study using a roll-front type uranium deposit. Part II contains five computer programs and comprehensive users' manuals for these programs which are necessary to make a practical geostatistical study

  13. A comparison between geostatistical analyses and sedimentological studies at the Hartbeestfontien gold mine

    International Nuclear Information System (INIS)

    Magri, E.J.

    1978-01-01

    For life-of-mine planning, as well as for short- and medium-term planning of grades and mine layouts, it is extremely important to have a clear understanding of the patterns followed by the distribution of gold and uranium within the mining area. This study is an attempt to reconcile the geostatistical approach to the determination of ore-shoot directions, via an analysis of the spatial distribution of gold and uranium values, with the sedimentological approach, which is based on the direct measurement of geological features. For the routine geostatistical estimation of ore reserves, the Hartebeestfontein gold mine was divided into ll sections. In each of these sections, the ore-shoot directions were calculated for gold and uranium from the anisotropies disclosed by geostatistical variogram analyses. This study presents a comparison of these results with those obtained from direct geological measurements of paleo-current directions. The results suggest that geological and geostatistical studies could be of significant mutual benefit [af

  14. A comparison of geostatistically based inverse techniques for use in performance assessment analysis at the Waste Isolation Pilot Plant Site: Results from Test Case No. 1

    International Nuclear Information System (INIS)

    Zimmerman, D.A.; Gallegos, D.P.

    1993-10-01

    The groundwater flow pathway in the Culebra Dolomite aquifer at the Waste Isolation Pilot Plant (WIPP) has been identified as a potentially important pathway for radionuclide migration to the accessible environment. Consequently, uncertainties in the models used to describe flow and transport in the Culebra need to be addressed. A ''Geostatistics Test Problem'' is being developed to evaluate a number of inverse techniques that may be used for flow calculations in the WIPP performance assessment (PA). The Test Problem is actually a series of test cases, each being developed as a highly complex synthetic data set; the intent is for the ensemble of these data sets to span the range of possible conceptual models of groundwater flow at the WIPP site. The Test Problem analysis approach is to use a comparison of the probabilistic groundwater travel time (GWTT) estimates produced by each technique as the basis for the evaluation. Participants are given observations of head and transmissivity (possibly including measurement error) or other information such as drawdowns from pumping wells, and are asked to develop stochastic models of groundwater flow for the synthetic system. Cumulative distribution functions (CDFs) of groundwater flow (computed via particle tracking) are constructed using the head and transmissivity data generated through the application of each technique; one semi-analytical method generates the CDFs of groundwater flow directly. This paper describes the results from Test Case No. 1

  15. Measuring the linear and nonlinear elastic properties of brain tissue with shear waves and inverse analysis.

    Science.gov (United States)

    Jiang, Yi; Li, Guoyang; Qian, Lin-Xue; Liang, Si; Destrade, Michel; Cao, Yanping

    2015-10-01

    We use supersonic shear wave imaging (SSI) technique to measure not only the linear but also the nonlinear elastic properties of brain matter. Here, we tested six porcine brains ex vivo and measured the velocities of the plane shear waves induced by acoustic radiation force at different states of pre-deformation when the ultrasonic probe is pushed into the soft tissue. We relied on an inverse method based on the theory governing the propagation of small-amplitude acoustic waves in deformed solids to interpret the experimental data. We found that, depending on the subjects, the resulting initial shear modulus [Formula: see text] varies from 1.8 to 3.2 kPa, the stiffening parameter [Formula: see text] of the hyperelastic Demiray-Fung model from 0.13 to 0.73, and the third- [Formula: see text] and fourth-order [Formula: see text] constants of weakly nonlinear elasticity from [Formula: see text]1.3 to [Formula: see text]20.6 kPa and from 3.1 to 8.7 kPa, respectively. Paired [Formula: see text] test performed on the experimental results of the left and right lobes of the brain shows no significant difference. These values are in line with those reported in the literature on brain tissue, indicating that the SSI method, combined to the inverse analysis, is an efficient and powerful tool for the mechanical characterization of brain tissue, which is of great importance for computer simulation of traumatic brain injury and virtual neurosurgery.

  16. Geostatistical methodology for waste optimization of contaminated premises - 59344

    International Nuclear Information System (INIS)

    Desnoyers, Yvon; Dubot, Didier

    2012-01-01

    The presented methodological study illustrates a Geo-statistical approach suitable for radiological evaluation in nuclear premises. The waste characterization is mainly focused on floor concrete surfaces. By modeling the spatial continuity of activities, Geo-statistics provide sound methods to estimate and map radiological activities, together with their uncertainty. The multivariate approach allows the integration of numerous surface radiation measurements in order to improve the estimation of activity levels from concrete samples. This way, a sequential and iterative investigation strategy proves to be relevant to fulfill the different evaluation objectives. Waste characterization is performed on risk maps rather than on direct interpolation maps (due to bias of the selection on kriging results). The use of several estimation supports (punctual, 1 m 2 , room) allows a relevant radiological waste categorization thanks to cost-benefit analysis according to the risk of exceeding a given activity threshold. Global results, mainly total activity, are similarly quantified to precociously lead the waste management for the dismantling and decommissioning project. This paper recalled the geo-statistics principles and demonstrated how this methodology provides innovative tools for the radiological evaluation of contaminated premises. The relevance of this approach relies on the presence of a spatial continuity for radiological contamination. In this case, geo-statistics provides reliable activity estimates, uncertainty quantification and risk analysis, which are essential decision-making tools for decommissioning and dismantling projects of nuclear installations. Waste characterization is then performed taking all relevant information into account: historical knowledge, surface measurements and samples. Thanks to the multivariate processing, the different investigation stages can be rationalized as regards quantity and positioning. Waste characterization is finally

  17. Connection between Dirac and matrix Schroedinger inverse-scattering transforms

    International Nuclear Information System (INIS)

    Jaulent, M.; Leon, J.J.P.

    1978-01-01

    The connection between two applications of the inverse scattering method for solving nonlinear equations is established. The inverse method associated with the massive Dirac system (D) : (iσ 3 d/dx - i q 3 σ 1 - q 1 σ 2 + mσ 2 )Y = epsilonY is rediscovered from the inverse method associated with the 2 x 2 matrix Schroedinger equation (S) : Ysub(xx) + (k 2 -Q)Y = 0. Here Q obeys a nonlinear constraint equivalent to a linear constraint on the reflection coefficient for (S). (author)

  18. Surface waves tomography and non-linear inversion in the southeast Carpathians

    International Nuclear Information System (INIS)

    Raykova, R.B.; Panza, G.F.

    2005-11-01

    A set of shear-wave velocity models of the lithosphere-asthenosphere system in the southeast Carpathians is determined by the non-linear inversion of surface wave group velocity data, obtained from a tomographic analysis. The local dispersion curves are assembled for the period range 7 s - 150 s, combining regional group velocity measurements and published global Rayleigh wave dispersion data. The lithosphere-asthenosphere velocity structure is reliably reconstructed to depths of about 250 km. The thickness of the lithosphere in the region varies from about 120 km to 250 km and the depth of the asthenosphere between 150 km and 250 km. Mantle seismicity concentrates where the high velocity lid is detected just below the Moho. The obtained results are in agreement with recent seismic refraction, receiver function, and travel time P-wave tomography investigations in the region. The similarity among the results obtained from different kinds of structural investigations (including the present work) highlights some new features of the lithosphere-asthenosphere system in southeast Carpathians, as the relatively thin crust under Transylvania basin and Vrancea zone. (author)

  19. Bayesian Analysis of Geostatistical Models With an Auxiliary Lattice

    KAUST Repository

    Park, Jincheol

    2012-04-01

    The Gaussian geostatistical model has been widely used for modeling spatial data. However, this model suffers from a severe difficulty in computation: it requires users to invert a large covariance matrix. This is infeasible when the number of observations is large. In this article, we propose an auxiliary lattice-based approach for tackling this difficulty. By introducing an auxiliary lattice to the space of observations and defining a Gaussian Markov random field on the auxiliary lattice, our model completely avoids the requirement of matrix inversion. It is remarkable that the computational complexity of our method is only O(n), where n is the number of observations. Hence, our method can be applied to very large datasets with reasonable computational (CPU) times. The numerical results indicate that our model can approximate Gaussian random fields very well in terms of predictions, even for those with long correlation lengths. For real data examples, our model can generally outperform conventional Gaussian random field models in both prediction errors and CPU times. Supplemental materials for the article are available online. © 2012 American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of North America.

  20. Efficient scattering-angle enrichment for a nonlinear inversion of the background and perturbations components of a velocity model

    KAUST Repository

    Wu, Zedong

    2017-07-04

    Reflection-waveform inversion (RWI) can help us reduce the nonlinearity of the standard full-waveform inversion (FWI) by inverting for the background velocity model using the wave-path of a single scattered wavefield to an image. However, current RWI implementations usually neglect the multi-scattered energy, which will cause some artifacts in the image and the update of the background. To improve existing RWI implementations in taking multi-scattered energy into consideration, we split the velocity model into background and perturbation components, integrate them directly in the wave equation, and formulate a new optimization problem for both components. In this case, the perturbed model is no longer a single-scattering model, but includes all scattering. Through introducing a new cheap implementation of scattering angle enrichment, the separation of the background and perturbation components can be implemented efficiently. We optimize both components simultaneously to produce updates to the velocity model that is nonlinear with respect to both the background and the perturbation. The newly introduced perturbation model can absorb the non-smooth update of the background in a more consistent way. We apply the proposed approach on the Marmousi model with data that contain frequencies starting from 5 Hz to show that this method can converge to an accurate velocity starting from a linearly increasing initial velocity. Also, our proposed method works well when applied to a field data set.

  1. On quasiclassical approximation in the inverse scattering method

    International Nuclear Information System (INIS)

    Geogdzhaev, V.V.

    1985-01-01

    Using as an example quasiclassical limits of the Korteweg-de Vries equation and nonlinear Schroedinger equation, the quasiclassical limiting variant of the inverse scattering problem method is presented. In quasiclassical approximation the inverse scattering problem for the Schroedinger equation is reduced to the classical inverse scattering problem

  2. Nonlinear inversion of resistivity sounding data for 1-D earth models using the Neighbourhood Algorithm

    Science.gov (United States)

    Ojo, A. O.; Xie, Jun; Olorunfemi, M. O.

    2018-01-01

    To reduce ambiguity related to nonlinearities in the resistivity model-data relationships, an efficient direct-search scheme employing the Neighbourhood Algorithm (NA) was implemented to solve the 1-D resistivity problem. In addition to finding a range of best-fit models which are more likely to be global minimums, this method investigates the entire multi-dimensional model space and provides additional information about the posterior model covariance matrix, marginal probability density function and an ensemble of acceptable models. This provides new insights into how well the model parameters are constrained and make assessing trade-offs between them possible, thus avoiding some common interpretation pitfalls. The efficacy of the newly developed program is tested by inverting both synthetic (noisy and noise-free) data and field data from other authors employing different inversion methods so as to provide a good base for comparative performance. In all cases, the inverted model parameters were in good agreement with the true and recovered model parameters from other methods and remarkably correlate with the available borehole litho-log and known geology for the field dataset. The NA method has proven to be useful whilst a good starting model is not available and the reduced number of unknowns in the 1-D resistivity inverse problem makes it an attractive alternative to the linearized methods. Hence, it is concluded that the newly developed program offers an excellent complementary tool for the global inversion of the layered resistivity structure.

  3. Support Minimized Inversion of Acoustic and Elastic Wave Scattering

    Science.gov (United States)

    Safaeinili, Ali

    Inversion of limited data is common in many areas of NDE such as X-ray Computed Tomography (CT), Ultrasonic and eddy current flaw characterization and imaging. In many applications, it is common to have a bias toward a solution with minimum (L^2)^2 norm without any physical justification. When it is a priori known that objects are compact as, say, with cracks and voids, by choosing "Minimum Support" functional instead of the minimum (L^2)^2 norm, an image can be obtained that is equally in agreement with the available data, while it is more consistent with what is most probably seen in the real world. We have utilized a minimum support functional to find a solution with the smallest volume. This inversion algorithm is most successful in reconstructing objects that are compact like voids and cracks. To verify this idea, we first performed a variational nonlinear inversion of acoustic backscatter data using minimum support objective function. A full nonlinear forward model was used to accurately study the effectiveness of the minimized support inversion without error due to the linear (Born) approximation. After successful inversions using a full nonlinear forward model, a linearized acoustic inversion was developed to increase speed and efficiency in imaging process. The results indicate that by using minimum support functional, we can accurately size and characterize voids and/or cracks which otherwise might be uncharacterizable. An extremely important feature of support minimized inversion is its ability to compensate for unknown absolute phase (zero-of-time). Zero-of-time ambiguity is a serious problem in the inversion of the pulse-echo data. The minimum support inversion was successfully used for the inversion of acoustic backscatter data due to compact scatterers without the knowledge of the zero-of-time. The main drawback to this type of inversion is its computer intensiveness. In order to make this type of constrained inversion available for common use, work

  4. A Comparison of Closed-Loop Performance of Multirotor Configurations Using Non-Linear Dynamic Inversion Control

    Directory of Open Access Journals (Sweden)

    Murray L. Ireland

    2015-06-01

    Full Text Available Multirotor is the umbrella term for the family of unmanned aircraft, which include the quadrotor, hexarotor and other vertical take-off and landing (VTOL aircraft that employ multiple main rotors for lift and control. Development and testing of novel multirotor designs has been aided by the proliferation of 3D printing and inexpensive flight controllers and components. Different multirotor configurations exhibit specific strengths, while presenting unique challenges with regards to design and control. This article highlights the primary differences between three multirotor platforms: a quadrotor; a fully-actuated hexarotor; and an octorotor. Each platform is modelled and then controlled using non-linear dynamic inversion. The differences in dynamics, control and performance are then discussed.

  5. Geostatistical methods applied to field model residuals

    DEFF Research Database (Denmark)

    Maule, Fox; Mosegaard, K.; Olsen, Nils

    consists of measurement errors and unmodelled signal), and is typically assumed to be uncorrelated and Gaussian distributed. We have applied geostatistical methods to analyse the residuals of the Oersted(09d/04) field model [http://www.dsri.dk/Oersted/Field_models/IGRF_2005_candidates/], which is based...

  6. Satellite Magnetic Residuals Investigated With Geostatistical Methods

    DEFF Research Database (Denmark)

    Fox Maule, Chaterine; Mosegaard, Klaus; Olsen, Nils

    2005-01-01

    (which consists of measurement errors and unmodeled signal), and is typically assumed to be uncorrelated and Gaussian distributed. We have applied geostatistical methods to analyze the residuals of the Oersted (09d/04) field model (www.dsri.dk/Oersted/Field models/IGRF 2005 candidates/), which is based...

  7. Riemann–Hilbert problem approach for two-dimensional flow inverse scattering

    Energy Technology Data Exchange (ETDEWEB)

    Agaltsov, A. D., E-mail: agalets@gmail.com [Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, 119991 Moscow (Russian Federation); Novikov, R. G., E-mail: novikov@cmap.polytechnique.fr [CNRS (UMR 7641), Centre de Mathématiques Appliquées, Ecole Polytechnique, 91128 Palaiseau (France); IEPT RAS, 117997 Moscow (Russian Federation); Moscow Institute of Physics and Technology, Dolgoprudny (Russian Federation)

    2014-10-15

    We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given.

  8. Riemann–Hilbert problem approach for two-dimensional flow inverse scattering

    International Nuclear Information System (INIS)

    Agaltsov, A. D.; Novikov, R. G.

    2014-01-01

    We consider inverse scattering for the time-harmonic wave equation with first-order perturbation in two dimensions. This problem arises in particular in the acoustic tomography of moving fluid. We consider linearized and nonlinearized reconstruction algorithms for this problem of inverse scattering. Our nonlinearized reconstruction algorithm is based on the non-local Riemann–Hilbert problem approach. Comparisons with preceding results are given

  9. Effective property determination for input to a geostatistical model of regional groundwater flow: Wellenberg T→K

    International Nuclear Information System (INIS)

    Lanyon, G.W.; Marschall, P.; Vomvoris, S.; Jaquet, O.; Mazurek, M.

    1998-01-01

    This paper describes the methodology used to estimate effective hydraulic properties for input into a regional geostatistical model of groundwater flow at the Wellenberg site in Switzerland. The methodology uses a geologically-based discrete fracture network model to calculate effective hydraulic properties for 100m blocks along each borehole. A description of the most transmissive features (Water Conducting Features or WCFs) in each borehole is used to determine local transmissivity distributions which are combined with descriptions of WCF extent, orientation and channelling to create fracture network models. WCF geometry is dependent on the class of WCF. WCF classes are defined for each type of geological structure associated with identified borehole inflows. Local to each borehole, models are conditioned on the observed transmissivity and occurrence of WCFs. Multiple realisations are calculated for each 100m block over approximately 400m of borehole. The results from the numerical upscaling are compared with conservative estimates of hydraulic conductivity. Results from unconditioned models are also compared to identify the consequences of conditioning and interval of boreholes that appear to be atypical. An inverse method is also described by which realisations of the geostatistical model can be used to condition discrete fracture network models away from the boreholes. The method can be used as a verification of the modelling approach by prediction of data at borehole locations. Applications of the models to estimation of post-closure repository performance, including cavern inflow and seal zone modelling, are illustrated

  10. On a new series of integrable nonlinear evolution equations

    International Nuclear Information System (INIS)

    Ichikawa, Y.H.; Wadati, Miki; Konno, Kimiaki; Shimizu, Tohru.

    1980-10-01

    Recent results of our research are surveyed in this report. The derivative nonlinear Schroedinger equation for the circular polarized Alfven wave admits the spiky soliton solutions for the plane wave boundary condition. The nonlinear equation for complex amplitude associated with the carrier wave is shown to be a generalized nonlinear Schroedinger equation, having the ordinary cubic nonlinear term and the derivative of cubic nonlinear term. A generalized scheme of the inverse scattering transformation has confirmed that superposition of the A-K-N-S scheme and the K-N scheme for the component equations valids for the generalized nonlinear Schroedinger equation. Then, two types of new integrable nonlinear evolution equation have been derived from our scheme of the inverse scattering transformation. One is the type of nonlinear Schroedinger equation, while the other is the type of Korteweg-de Vries equation. Brief discussions are presented for physical phenomena, which could be accounted by the second type of the new integrable nonlinear evolution equation. Lastly, the stationary solitary wave solutions have been constructed for the integrable nonlinear evolution equation of the second type. These solutions have peculiar structure that they are singular and discrete. It is a new challenge to construct singular potentials by the inverse scattering transformation. (author)

  11. Two-dimensional probabilistic inversion of plane-wave electromagnetic data: Methodology, model constraints and joint inversion with electrical resistivity data

    NARCIS (Netherlands)

    Rosas-Carbajal, M.; Linde, N.; Kalscheuer, T.; Vrugt, J.A.

    2014-01-01

    Probabilistic inversion methods based on Markov chain Monte Carlo (MCMC) simulation are well suited to quantify parameter and model uncertainty of nonlinear inverse problems. Yet, application of such methods to CPU-intensive forward models can be a daunting task, particularly if the parameter space

  12. Assessment and modeling of the groundwater hydrogeochemical quality parameters via geostatistical approaches

    Science.gov (United States)

    Karami, Shawgar; Madani, Hassan; Katibeh, Homayoon; Fatehi Marj, Ahmad

    2018-03-01

    Geostatistical methods are one of the advanced techniques used for interpolation of groundwater quality data. The results obtained from geostatistics will be useful for decision makers to adopt suitable remedial measures to protect the quality of groundwater sources. Data used in this study were collected from 78 wells in Varamin plain aquifer located in southeast of Tehran, Iran, in 2013. Ordinary kriging method was used in this study to evaluate groundwater quality parameters. According to what has been mentioned in this paper, seven main quality parameters (i.e. total dissolved solids (TDS), sodium adsorption ratio (SAR), electrical conductivity (EC), sodium (Na+), total hardness (TH), chloride (Cl-) and sulfate (SO4 2-)), have been analyzed and interpreted by statistical and geostatistical methods. After data normalization by Nscore method in WinGslib software, variography as a geostatistical tool to define spatial regression was compiled and experimental variograms were plotted by GS+ software. Then, the best theoretical model was fitted to each variogram based on the minimum RSS. Cross validation method was used to determine the accuracy of the estimated data. Eventually, estimation maps of groundwater quality were prepared in WinGslib software and estimation variance map and estimation error map were presented to evaluate the quality of estimation in each estimated point. Results showed that kriging method is more accurate than the traditional interpolation methods.

  13. Seismic waveform inversion best practices: regional, global and exploration test cases

    Science.gov (United States)

    Modrak, Ryan; Tromp, Jeroen

    2016-09-01

    Reaching the global minimum of a waveform misfit function requires careful choices about the nonlinear optimization, preconditioning and regularization methods underlying an inversion. Because waveform inversion problems are susceptible to erratic convergence associated with strong nonlinearity, one or two test cases are not enough to reliably inform such decisions. We identify best practices, instead, using four seismic near-surface problems, one regional problem and two global problems. To make meaningful quantitative comparisons between methods, we carry out hundreds of inversions, varying one aspect of the implementation at a time. Comparing nonlinear optimization algorithms, we find that limited-memory BFGS provides computational savings over nonlinear conjugate gradient methods in a wide range of test cases. Comparing preconditioners, we show that a new diagonal scaling derived from the adjoint of the forward operator provides better performance than two conventional preconditioning schemes. Comparing regularization strategies, we find that projection, convolution, Tikhonov regularization and total variation regularization are effective in different contexts. Besides questions of one strategy or another, reliability and efficiency in waveform inversion depend on close numerical attention and care. Implementation details involving the line search and restart conditions have a strong effect on computational cost, regardless of the chosen nonlinear optimization algorithm.

  14. Particle Swarm Optimization and Uncertainty Assessment in Inverse Problems

    Directory of Open Access Journals (Sweden)

    José L. G. Pallero

    2018-01-01

    Full Text Available Most inverse problems in the industry (and particularly in geophysical exploration are highly underdetermined because the number of model parameters too high to achieve accurate data predictions and because the sampling of the data space is scarce and incomplete; it is always affected by different kinds of noise. Additionally, the physics of the forward problem is a simplification of the reality. All these facts result in that the inverse problem solution is not unique; that is, there are different inverse solutions (called equivalent, compatible with the prior information that fits the observed data within similar error bounds. In the case of nonlinear inverse problems, these equivalent models are located in disconnected flat curvilinear valleys of the cost-function topography. The uncertainty analysis consists of obtaining a representation of this complex topography via different sampling methodologies. In this paper, we focus on the use of a particle swarm optimization (PSO algorithm to sample the region of equivalence in nonlinear inverse problems. Although this methodology has a general purpose, we show its application for the uncertainty assessment of the solution of a geophysical problem concerning gravity inversion in sedimentary basins, showing that it is possible to efficiently perform this task in a sampling-while-optimizing mode. Particularly, we explain how to use and analyze the geophysical models sampled by exploratory PSO family members to infer different descriptors of nonlinear uncertainty.

  15. Nonlinear transport of dynamic system phase space

    International Nuclear Information System (INIS)

    Xie Xi; Xia Jiawen

    1993-01-01

    The inverse transform of any order solution of the differential equation of general nonlinear dynamic systems is derived, realizing theoretically the nonlinear transport for the phase space of nonlinear dynamic systems. The result is applicable to general nonlinear dynamic systems, with the transport of accelerator beam phase space as a typical example

  16. A geostatistical method applied to the geochemical study of the Chichinautzin Volcanic Field in Mexico

    Science.gov (United States)

    Robidoux, P.; Roberge, J.; Urbina Oviedo, C. A.

    2011-12-01

    The origin of magmatism and the role of the subducted Coco's Plate in the Chichinautzin volcanic field (CVF), Mexico is still a subject of debate. It has been established that mafic magmas of alkali type (subduction) and calc-alkali type (OIB) are produced in the CVF and both groups cannot be related by simple fractional crystallization. Therefore, many geochemical studies have been done, and many models have been proposed. The main goal of the work present here is to provide a new tool for the visualization and interpretation of geochemical data using geostatistics and geospatial analysis techniques. It contains a complete geodatabase built from referred samples over the 2500 km2 area of CVF and its neighbour stratovolcanoes (Popocatepetl, Iztaccihuatl and Nevado de Toluca). From this database, map of different geochemical markers were done to visualise geochemical signature in a geographical manner, to test the statistic distribution with a cartographic technique and highlight any spatial correlations. The distribution and regionalization of the geochemical signatures can be viewed in a two-dimensional space using a specific spatial analysis tools from a Geographic Information System (GIS). The model of spatial distribution is tested with Linear Decrease (LD) and Inverse Distance Weight (IDW) interpolation technique because they best represent the geostatistical characteristics of the geodatabase. We found that ratio of Ba/Nb, Nb/Ta, Th/Nb show first order tendency, which means visible spatial variation over a large scale area. Monogenetic volcanoes in the center of the CVF have distinct values compare to those of the Popocatepetl-Iztaccihuatl polygenetic complex which are spatially well defined. Inside the Valley of Mexico, a large quantity of monogenetic cone in the eastern portion of CVF has ratios similar to the Iztaccihuatl and Popocatepetl complex. Other ratios like alkalis vs SiO2, V/Ti, La/Yb, Zr/Y show different spatial tendencies. In that case, second

  17. Constrained optimisation of spatial sampling : a geostatistical approach

    NARCIS (Netherlands)

    Groenigen, van J.W.

    1999-01-01

    Aims

    This thesis aims at the development of optimal sampling strategies for geostatistical studies. Special emphasis is on the optimal use of ancillary data, such as co-related imagery, preliminary observations and historic knowledge. Although the object of all studies

  18. Waveform inversion for acoustic VTI media in frequency domain

    KAUST Repository

    Wu, Zedong; Alkhalifah, Tariq Ali

    2016-01-01

    Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the background model using a single scattered wavefield from an inverted perturbation. However, current

  19. Geostatistical interpolation for modelling SPT data in northern Izmir

    Indian Academy of Sciences (India)

    data scatter' stems from the natural randomness of the system under con- ... Geostatistical methods were originally used for ore reserve calculations by the ... ing grain size distribution, plasticity, strength parameters and water content, for ...

  20. A model reduction approach to numerical inversion for a parabolic partial differential equation

    International Nuclear Information System (INIS)

    Borcea, Liliana; Druskin, Vladimir; Zaslavsky, Mikhail; Mamonov, Alexander V

    2014-01-01

    We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss–Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments. (paper)

  1. A model reduction approach to numerical inversion for a parabolic partial differential equation

    Science.gov (United States)

    Borcea, Liliana; Druskin, Vladimir; Mamonov, Alexander V.; Zaslavsky, Mikhail

    2014-12-01

    We propose a novel numerical inversion algorithm for the coefficients of parabolic partial differential equations, based on model reduction. The study is motivated by the application of controlled source electromagnetic exploration, where the unknown is the subsurface electrical resistivity and the data are time resolved surface measurements of the magnetic field. The algorithm presented in this paper considers inversion in one and two dimensions. The reduced model is obtained with rational interpolation in the frequency (Laplace) domain and a rational Krylov subspace projection method. It amounts to a nonlinear mapping from the function space of the unknown resistivity to the small dimensional space of the parameters of the reduced model. We use this mapping as a nonlinear preconditioner for the Gauss-Newton iterative solution of the inverse problem. The advantage of the inversion algorithm is twofold. First, the nonlinear preconditioner resolves most of the nonlinearity of the problem. Thus the iterations are less likely to get stuck in local minima and the convergence is fast. Second, the inversion is computationally efficient because it avoids repeated accurate simulations of the time-domain response. We study the stability of the inversion algorithm for various rational Krylov subspaces, and assess its performance with numerical experiments.

  2. Transient Inverse Calibration of the Site-Wide Groundwater Flow Model (ACM-2): FY03 Progress Report

    International Nuclear Information System (INIS)

    Vermeul, Vince R.; Bergeron, Marcel P.; Cole, C R.; Murray, Christopher J.; Nichols, William E.; Scheibe, Timothy D.; Thorne, Paul D.; Waichler, Scott R.; Xie, YuLong

    2003-01-01

    DOE and PNNL are working to strengthen the technical defensibility of the groundwater flow and transport model at the Hanford Site and to incorporate uncertainty into the model. One aspect of the initiative is developing and using a three-dimensional transient inverse model to estimate the hydraulic conductivities, specific yields, and other parameters using data from Hanford since 1943. The focus of the alternative conceptual model (ACM-2) inverse modeling initiative documented in this report was to address limitations identified in the ACM-1 model, complete the facies-based approach for representing the hydraulic conductivity distribution in the Hanford and middle Ringold Formations, develop the approach and implementation methodology for generating multiple ACMs based on geostatistical data analysis, and develop an approach for inverse modeling of these stochastic ACMs. The primary modifications to ACM-2 transient inverse model include facies-based zonation of Units 1 (Hanford ) and 5 (middle Ringold); an improved approach for handling run-on recharge from upland areas based on watershed modeling results; an improved approach for representing artificial discharges from site operations; and minor changes to the geologic conceptual model. ACM-2 is the first attempt to fully incorporate the facies-based approach to represent the hydrogeologic structure. Further refinement and additional improvements to overall model fit will be realized during future inverse simulations of groundwater flow and transport. In addition, preliminary work was completed on an approach and implementation for generating an inverse modeling of stochastic ACMs. These techniques were applied to assess the uncertainty in the facies-based zonation of the Hanford formation and the geological structure of Ringold mud units. The geostatistical analysis used a preliminary interpretation of the facies-based zonation that was not consistent with that used in ACM-2. Although the overall objective of

  3. The forced nonlinear Schroedinger equation

    International Nuclear Information System (INIS)

    Kaup, D.J.; Hansen, P.J.

    1985-01-01

    The nonlinear Schroedinger equation describes the behaviour of a radio frequency wave in the ionosphere near the reflexion point where nonlinear processes are important. A simple model of this phenomenon leads to the forced nonlinear Schroedinger equation in terms of a nonlinear boundary value problem. A WKB analysis of the time evolution equations for the nonlinear Schroedinger equation in the inverse scattering transform formalism gives a crude order of magnitude estimation of the qualitative behaviour of the solutions. This estimation is compared with the numerical solutions. (D.Gy.)

  4. Multivariate Analysis and Modeling of Sediment Pollution Using Neural Network Models and Geostatistics

    Science.gov (United States)

    Golay, Jean; Kanevski, Mikhaïl

    2013-04-01

    The present research deals with the exploration and modeling of a complex dataset of 200 measurement points of sediment pollution by heavy metals in Lake Geneva. The fundamental idea was to use multivariate Artificial Neural Networks (ANN) along with geostatistical models and tools in order to improve the accuracy and the interpretability of data modeling. The results obtained with ANN were compared to those of traditional geostatistical algorithms like ordinary (co)kriging and (co)kriging with an external drift. Exploratory data analysis highlighted a great variety of relationships (i.e. linear, non-linear, independence) between the 11 variables of the dataset (i.e. Cadmium, Mercury, Zinc, Copper, Titanium, Chromium, Vanadium and Nickel as well as the spatial coordinates of the measurement points and their depth). Then, exploratory spatial data analysis (i.e. anisotropic variography, local spatial correlations and moving window statistics) was carried out. It was shown that the different phenomena to be modeled were characterized by high spatial anisotropies, complex spatial correlation structures and heteroscedasticity. A feature selection procedure based on General Regression Neural Networks (GRNN) was also applied to create subsets of variables enabling to improve the predictions during the modeling phase. The basic modeling was conducted using a Multilayer Perceptron (MLP) which is a workhorse of ANN. MLP models are robust and highly flexible tools which can incorporate in a nonlinear manner different kind of high-dimensional information. In the present research, the input layer was made of either two (spatial coordinates) or three neurons (when depth as auxiliary information could possibly capture an underlying trend) and the output layer was composed of one (univariate MLP) to eight neurons corresponding to the heavy metals of the dataset (multivariate MLP). MLP models with three input neurons can be referred to as Artificial Neural Networks with EXternal

  5. Solution of the nonlinear inverse scattering problem by T-matrix completion. I. Theory.

    Science.gov (United States)

    Levinson, Howard W; Markel, Vadim A

    2016-10-01

    We propose a conceptually different method for solving nonlinear inverse scattering problems (ISPs) such as are commonly encountered in tomographic ultrasound imaging, seismology, and other applications. The method is inspired by the theory of nonlocality of physical interactions and utilizes the relevant formalism. We formulate the ISP as a problem whose goal is to determine an unknown interaction potential V from external scattering data. Although we seek a local (diagonally dominated) V as the solution to the posed problem, we allow V to be nonlocal at the intermediate stages of iterations. This allows us to utilize the one-to-one correspondence between V and the T matrix of the problem. Here it is important to realize that not every T corresponds to a diagonal V and we, therefore, relax the usual condition of strict diagonality (locality) of V. An iterative algorithm is proposed in which we seek T that is (i) compatible with the measured scattering data and (ii) corresponds to an interaction potential V that is as diagonally dominated as possible. We refer to this algorithm as to the data-compatible T-matrix completion. This paper is Part I in a two-part series and contains theory only. Numerical examples of image reconstruction in a strongly nonlinear regime are given in Part II [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043318 (2016)10.1103/PhysRevE.94.043318]. The method described in this paper is particularly well suited for very large data sets that become increasingly available with the use of modern measurement techniques and instrumentation.

  6. Resolving model parameter values from carbon and nitrogen stock measurements in a wide range of tropical mature forests using nonlinear inversion and regression trees

    Science.gov (United States)

    Shuguang Liua; Pamela Anderson; Guoyi Zhoud; Boone Kauffman; Flint Hughes; David Schimel; Vicente Watson; Joseph. Tosi

    2008-01-01

    Objectively assessing the performance of a model and deriving model parameter values from observations are critical and challenging in landscape to regional modeling. In this paper, we applied a nonlinear inversion technique to calibrate the ecosystem model CENTURY against carbon (C) and nitrogen (N) stock measurements collected from 39 mature tropical forest sites in...

  7. Benchmarking a geostatistical procedure for the homogenisation of annual precipitation series

    Science.gov (United States)

    Caineta, Júlio; Ribeiro, Sara; Henriques, Roberto; Soares, Amílcar; Costa, Ana Cristina

    2014-05-01

    The European project COST Action ES0601, Advances in homogenisation methods of climate series: an integrated approach (HOME), has brought to attention the importance of establishing reliable homogenisation methods for climate data. In order to achieve that, a benchmark data set, containing monthly and daily temperature and precipitation data, was created to be used as a comparison basis for the effectiveness of those methods. Several contributions were submitted and evaluated by a number of performance metrics, validating the results against realistic inhomogeneous data. HOME also led to the development of new homogenisation software packages, which included feedback and lessons learned during the project. Preliminary studies have suggested a geostatistical stochastic approach, which uses Direct Sequential Simulation (DSS), as a promising methodology for the homogenisation of precipitation data series. Based on the spatial and temporal correlation between the neighbouring stations, DSS calculates local probability density functions at a candidate station to detect inhomogeneities. The purpose of the current study is to test and compare this geostatistical approach with the methods previously presented in the HOME project, using surrogate precipitation series from the HOME benchmark data set. The benchmark data set contains monthly precipitation surrogate series, from which annual precipitation data series were derived. These annual precipitation series were subject to exploratory analysis and to a thorough variography study. The geostatistical approach was then applied to the data set, based on different scenarios for the spatial continuity. Implementing this procedure also promoted the development of a computer program that aims to assist on the homogenisation of climate data, while minimising user interaction. Finally, in order to compare the effectiveness of this methodology with the homogenisation methods submitted during the HOME project, the obtained results

  8. Analysis and simulation of wireless signal propagation applying geostatistical interpolation techniques

    Science.gov (United States)

    Kolyaie, S.; Yaghooti, M.; Majidi, G.

    2011-12-01

    This paper is a part of an ongoing research to examine the capability of geostatistical analysis for mobile networks coverage prediction, simulation and tuning. Mobile network coverage predictions are used to find network coverage gaps and areas with poor serviceability. They are essential data for engineering and management in order to make better decision regarding rollout, planning and optimisation of mobile networks.The objective of this research is to evaluate different interpolation techniques in coverage prediction. In method presented here, raw data collected from drive testing a sample of roads in study area is analysed and various continuous surfaces are created using different interpolation methods. Two general interpolation methods are used in this paper with different variables; first, Inverse Distance Weighting (IDW) with various powers and number of neighbours and second, ordinary kriging with Gaussian, spherical, circular and exponential semivariogram models with different number of neighbours. For the result comparison, we have used check points coming from the same drive test data. Prediction values for check points are extracted from each surface and the differences with actual value are computed. The output of this research helps finding an optimised and accurate model for coverage prediction.

  9. Wave-equation reflection traveltime inversion

    KAUST Repository

    Zhang, Sanzong; Schuster, Gerard T.; Luo, Yi

    2011-01-01

    The main difficulty with iterative waveform inversion using a gradient optimization method is that it tends to get stuck in local minima associated within the waveform misfit function. This is because the waveform misfit function is highly nonlinear

  10. Characterization of a viscoelastic heterogeneous object with an effective model by nonlinear full waveform inversion

    Science.gov (United States)

    Mesgouez, A.

    2018-05-01

    The determination of equivalent viscoelastic properties of heterogeneous objects remains challenging in various scientific fields such as (geo)mechanics, geophysics or biomechanics. The present investigation addresses the issue of the identification of effective constitutive properties of a binary object by using a nonlinear and full waveform inversion scheme. The inversion process, without any regularization technique or a priori information, aims at minimizing directly the discrepancy between the full waveform responses of a bi-material viscoelastic cylindrical object and its corresponding effective homogeneous object. It involves the retrieval of five constitutive equivalent parameters. Numerical simulations are performed in a laboratory-scale two-dimensional configuration: a transient acoustic plane wave impacts the object and the diffracted fluid pressure, solid stress or velocity component fields are determined using a semi-analytical approach. Results show that the retrieval of the density and of the real parts of both the compressional and the shear wave velocities have been carried out successfully regarding the number and location of sensors, the type of sensors, the size of the searching space, the frequency range of the incident plane pressure wave, and the change in the geometric or mechanical constitution of the bi-material object. The retrieval of the imaginary parts of the wave velocities can reveal in some cases the limitations of the proposed approach.

  11. Quantifying natural delta variability using a multiple-point geostatistics prior uncertainty model

    Science.gov (United States)

    Scheidt, Céline; Fernandes, Anjali M.; Paola, Chris; Caers, Jef

    2016-10-01

    We address the question of quantifying uncertainty associated with autogenic pattern variability in a channelized transport system by means of a modern geostatistical method. This question has considerable relevance for practical subsurface applications as well, particularly those related to uncertainty quantification relying on Bayesian approaches. Specifically, we show how the autogenic variability in a laboratory experiment can be represented and reproduced by a multiple-point geostatistical prior uncertainty model. The latter geostatistical method requires selection of a limited set of training images from which a possibly infinite set of geostatistical model realizations, mimicking the training image patterns, can be generated. To that end, we investigate two methods to determine how many training images and what training images should be provided to reproduce natural autogenic variability. The first method relies on distance-based clustering of overhead snapshots of the experiment; the second method relies on a rate of change quantification by means of a computer vision algorithm termed the demon algorithm. We show quantitatively that with either training image selection method, we can statistically reproduce the natural variability of the delta formed in the experiment. In addition, we study the nature of the patterns represented in the set of training images as a representation of the "eigenpatterns" of the natural system. The eigenpattern in the training image sets display patterns consistent with previous physical interpretations of the fundamental modes of this type of delta system: a highly channelized, incisional mode; a poorly channelized, depositional mode; and an intermediate mode between the two.

  12. Data analysis for radiological characterisation: Geostatistical and statistical complementarity

    International Nuclear Information System (INIS)

    Desnoyers, Yvon; Dubot, Didier

    2012-01-01

    Radiological characterisation may cover a large range of evaluation objectives during a decommissioning and dismantling (D and D) project: removal of doubt, delineation of contaminated materials, monitoring of the decontamination work and final survey. At each stage, collecting relevant data to be able to draw the conclusions needed is quite a big challenge. In particular two radiological characterisation stages require an advanced sampling process and data analysis, namely the initial categorization and optimisation of the materials to be removed and the final survey to demonstrate compliance with clearance levels. On the one hand the latter is widely used and well developed in national guides and norms, using random sampling designs and statistical data analysis. On the other hand a more complex evaluation methodology has to be implemented for the initial radiological characterisation, both for sampling design and for data analysis. The geostatistical framework is an efficient way to satisfy the radiological characterisation requirements providing a sound decision-making approach for the decommissioning and dismantling of nuclear premises. The relevance of the geostatistical methodology relies on the presence of a spatial continuity for radiological contamination. Thus geo-statistics provides reliable methods for activity estimation, uncertainty quantification and risk analysis, leading to a sound classification of radiological waste (surfaces and volumes). This way, the radiological characterization of contaminated premises can be divided into three steps. First, the most exhaustive facility analysis provides historical and qualitative information. Then, a systematic (exhaustive or not) surface survey of the contamination is implemented on a regular grid. Finally, in order to assess activity levels and contamination depths, destructive samples are collected at several locations within the premises (based on the surface survey results) and analysed. Combined with

  13. Inverse scattering transform and soliton solutions for square matrix nonlinear Schrödinger equations with non-zero boundary conditions

    Science.gov (United States)

    Prinari, Barbara; Demontis, Francesco; Li, Sitai; Horikis, Theodoros P.

    2018-04-01

    The inverse scattering transform (IST) with non-zero boundary conditions at infinity is developed for an m × m matrix nonlinear Schrödinger-type equation which, in the case m = 2, has been proposed as a model to describe hyperfine spin F = 1 spinor Bose-Einstein condensates with either repulsive interatomic interactions and anti-ferromagnetic spin-exchange interactions (self-defocusing case), or attractive interatomic interactions and ferromagnetic spin-exchange interactions (self-focusing case). The IST for this system was first presented by Ieda et al. (2007) , using a different approach. In our formulation, both the direct and the inverse problems are posed in terms of a suitable uniformization variable which allows to develop the IST on the standard complex plane, instead of a two-sheeted Riemann surface or the cut plane with discontinuities along the cuts. Analyticity of the scattering eigenfunctions and scattering data, symmetries, properties of the discrete spectrum, and asymptotics are derived. The inverse problem is posed as a Riemann-Hilbert problem for the eigenfunctions, and the reconstruction formula of the potential in terms of eigenfunctions and scattering data is provided. In addition, the general behavior of the soliton solutions is analyzed in detail in the 2 × 2 self-focusing case, including some special solutions not previously discussed in the literature.

  14. The Use of Geostatistics in the Study of Floral Phenology of Vulpia geniculata (L. Link

    Directory of Open Access Journals (Sweden)

    Eduardo J. León Ruiz

    2012-01-01

    Full Text Available Traditionally phenology studies have been focused on changes through time, but there exist many instances in ecological research where it is necessary to interpolate among spatially stratified samples. The combined use of Geographical Information Systems (GIS and Geostatistics can be an essential tool for spatial analysis in phenological studies. Geostatistics are a family of statistics that describe correlations through space/time and they can be used for both quantifying spatial correlation and interpolating unsampled points. In the present work, estimations based upon Geostatistics and GIS mapping have enabled the construction of spatial models that reflect phenological evolution of Vulpia geniculata (L. Link throughout the study area during sampling season. Ten sampling points, scattered troughout the city and low mountains in the “Sierra de Córdoba” were chosen to carry out the weekly phenological monitoring during flowering season. The phenological data were interpolated by applying the traditional geostatitical method of Kriging, which was used to ellaborate weekly estimations of V. geniculata phenology in unsampled areas. Finally, the application of Geostatistics and GIS to create phenological maps could be an essential complement in pollen aerobiological studies, given the increased interest in obtaining automatic aerobiological forecasting maps.

  15. NLSE: Parameter-Based Inversion Algorithm

    Science.gov (United States)

    Sabbagh, Harold A.; Murphy, R. Kim; Sabbagh, Elias H.; Aldrin, John C.; Knopp, Jeremy S.

    Chapter 11 introduced us to the notion of an inverse problem and gave us some examples of the value of this idea to the solution of realistic industrial problems. The basic inversion algorithm described in Chap. 11 was based upon the Gauss-Newton theory of nonlinear least-squares estimation and is called NLSE in this book. In this chapter we will develop the mathematical background of this theory more fully, because this algorithm will be the foundation of inverse methods and their applications during the remainder of this book. We hope, thereby, to introduce the reader to the application of sophisticated mathematical concepts to engineering practice without introducing excessive mathematical sophistication.

  16. Risk Assessment of Sediment Pollution Using Geostatistical Simulations

    Science.gov (United States)

    Golay, J.; Kanevski, M.

    2012-04-01

    Environmental monitoring networks (EMN) discreetly measure the intensities of continuous phenomena (e.g. pollution, temperature, etc.). Spatial prediction models, like kriging, are then used for modeling. But, they give rise to smooth representations of phenomena which leads to overestimations or underestimations of extreme values. Moreover, they do not reproduce the spatial variability of the original data and the corresponding uncertainties. When dealing with risk assessment, this is unacceptable, since extreme values must be retrieved and probabilities of exceeding given thresholds must be computed [Kanevski et al., 2009]. In order to overcome these obstacles, geostatistics provides another approach: conditional stochastic simulations. Here, the basic idea is to generate multiple estimates of variable values (e.g. pollution concentration) at every location of interest which are calculated as stochastic realizations of an unknown random function (see, for example, [Kanevski, 2008], where both theoretical concepts and real data case studies are presented in detail). Many algorithms implement this approach. The most widely used in spatial modeling are sequential Gaussian simulations/cosimulations, sequential indicator simulations/cosimulations and direct simulations. In the present study, several algorithms of geostatistical conditional simulations were applied on real data collected from Lake Geneva. The main objectives were to compare their effectiveness in reproducing global statistics (histograms, variograms) and the way they characterize the variability and uncertainty of the contamination patterns. The dataset is composed of 200 measurements of the contamination of the lake sediments by heavy metals (i.e. Cadmium, Mercury, Zinc, Copper, Titanium and Chromium). The results obtained show some differences highlighting that risk assessment can be influenced by the algorithm it relies on. Moreover, hybrid models based on machine learning algorithms and

  17. Geostatistical methods for radiological evaluation and risk analysis of contaminated premises

    International Nuclear Information System (INIS)

    Desnoyers, Y.; Jeannee, N.; Chiles, J.P.; Dubot, D.

    2009-01-01

    Full text: At the end of process equipment dismantling, the complete decontamination of nuclear facilities requires the radiological assessment of residual activity levels of building structures. As stated by the IAEA, 'Segregation and characterization of contaminated materials are the key elements of waste minimization'. From this point of view, the set up of an appropriate evaluation methodology is of primordial importance. The radiological characterization of contaminated premises can be divided into three steps. First, the most exhaustive facility analysis provides historical, functional and qualitative information. Then, a systematic (exhaustive or not) control of the emergent signal is performed by means of in situ measurement methods such as surface control device combined with in situ gamma spectrometry. Besides, in order to assess the contamination depth, samples can be collected from boreholes at several locations within the premises and analyzed. Combined with historical information and emergent signal maps, such data improve and reinforce the preliminary waste zoning. In order to provide reliable estimates while avoiding supplementary investigation costs, there is therefore a crucial need for sampling optimization methods together with appropriate data processing techniques. The relevance of the geostatistical methodology relies on the presence of a spatial continuity for radiological contamination. In this case, geostatistics provides reliable methods for activity estimation, uncertainty quantification and risk analysis, which are essential decision-making tools for decommissioning and dismantling projects of nuclear installations. Besides, the ability of this geostatistical framework to provide answers to several key issues that generally occur during the clean-up preparation phase is discussed: How to optimise the investigation costs? How to deal with data quality issues? How to consistently take into account auxiliary information such as historical

  18. Statistical perspectives on inverse problems

    DEFF Research Database (Denmark)

    Andersen, Kim Emil

    of the interior of an object from electrical boundary measurements. One part of this thesis concerns statistical approaches for solving, possibly non-linear, inverse problems. Thus inverse problems are recasted in a form suitable for statistical inference. In particular, a Bayesian approach for regularisation...... problem is given in terms of probability distributions. Posterior inference is obtained by Markov chain Monte Carlo methods and new, powerful simulation techniques based on e.g. coupled Markov chains and simulated tempering is developed to improve the computational efficiency of the overall simulation......Inverse problems arise in many scientific disciplines and pertain to situations where inference is to be made about a particular phenomenon from indirect measurements. A typical example, arising in diffusion tomography, is the inverse boundary value problem for non-invasive reconstruction...

  19. A Joint Method of Envelope Inversion Combined with Hybrid-domain Full Waveform Inversion

    Science.gov (United States)

    CUI, C.; Hou, W.

    2017-12-01

    Full waveform inversion (FWI) aims to construct high-precision subsurface models by fully using the information in seismic records, including amplitude, travel time, phase and so on. However, high non-linearity and the absence of low frequency information in seismic data lead to the well-known cycle skipping problem and make inversion easily fall into local minima. In addition, those 3D inversion methods that are based on acoustic approximation ignore the elastic effects in real seismic field, and make inversion harder. As a result, the accuracy of final inversion results highly relies on the quality of initial model. In order to improve stability and quality of inversion results, multi-scale inversion that reconstructs subsurface model from low to high frequency are applied. But, the absence of very low frequencies (time domain and inversion in the frequency domain. To accelerate the inversion, we adopt CPU/GPU heterogeneous computing techniques. There were two levels of parallelism. In the first level, the inversion tasks are decomposed and assigned to each computation node by shot number. In the second level, GPU multithreaded programming is used for the computation tasks in each node, including forward modeling, envelope extraction, DFT (discrete Fourier transform) calculation and gradients calculation. Numerical tests demonstrated that the combined envelope inversion + hybrid-domain FWI could obtain much faithful and accurate result than conventional hybrid-domain FWI. The CPU/GPU heterogeneous parallel computation could improve the performance speed.

  20. Spatial Downscaling of TRMM Precipitation Using Geostatistics and Fine Scale Environmental Variables

    Directory of Open Access Journals (Sweden)

    No-Wook Park

    2013-01-01

    Full Text Available A geostatistical downscaling scheme is presented and can generate fine scale precipitation information from coarse scale Tropical Rainfall Measuring Mission (TRMM data by incorporating auxiliary fine scale environmental variables. Within the geostatistical framework, the TRMM precipitation data are first decomposed into trend and residual components. Quantitative relationships between coarse scale TRMM data and environmental variables are then estimated via regression analysis and used to derive trend components at a fine scale. Next, the residual components, which are the differences between the trend components and the original TRMM data, are then downscaled at a target fine scale via area-to-point kriging. The trend and residual components are finally added to generate fine scale precipitation estimates. Stochastic simulation is also applied to the residual components in order to generate multiple alternative realizations and to compute uncertainty measures. From an experiment using a digital elevation model (DEM and normalized difference vegetation index (NDVI, the geostatistical downscaling scheme generated the downscaling results that reflected detailed characteristics with better predictive performance, when compared with downscaling without the environmental variables. Multiple realizations and uncertainty measures from simulation also provided useful information for interpretations and further environmental modeling.

  1. A conceptual sedimentological-geostatistical model of aquifer heterogeneity based on outcrop studies

    International Nuclear Information System (INIS)

    Davis, J.M.

    1994-01-01

    Three outcrop studies were conducted in deposits of different depositional environments. At each site, permeability measurements were obtained with an air-minipermeameter developed as part of this study. In addition, the geological units were mapped with either surveying, photographs, or both. Geostatistical analysis of the permeability data was performed to estimate the characteristics of the probability distribution function and the spatial correlation structure. The information obtained from the geological mapping was then compared with the results of the geostatistical analysis for any relationships that may exist. The main field site was located in the Albuquerque Basin of central New Mexico at an outcrop of the Pliocene-Pleistocene Sierra Ladrones Formation. The second study was conducted on the walls of waste pits in alluvial fan deposits at the Nevada Test Site. The third study was conducted on an outcrop of an eolian deposit (miocene) south of Socorro, New Mexico. The results of the three studies were then used to construct a conceptual model relating depositional environment to geostatistical models of heterogeneity. The model presented is largely qualitative but provides a basis for further hypothesis formulation and testing

  2. A conceptual sedimentological-geostatistical model of aquifer heterogeneity based on outcrop studies

    Energy Technology Data Exchange (ETDEWEB)

    Davis, J.M.

    1994-01-01

    Three outcrop studies were conducted in deposits of different depositional environments. At each site, permeability measurements were obtained with an air-minipermeameter developed as part of this study. In addition, the geological units were mapped with either surveying, photographs, or both. Geostatistical analysis of the permeability data was performed to estimate the characteristics of the probability distribution function and the spatial correlation structure. The information obtained from the geological mapping was then compared with the results of the geostatistical analysis for any relationships that may exist. The main field site was located in the Albuquerque Basin of central New Mexico at an outcrop of the Pliocene-Pleistocene Sierra Ladrones Formation. The second study was conducted on the walls of waste pits in alluvial fan deposits at the Nevada Test Site. The third study was conducted on an outcrop of an eolian deposit (miocene) south of Socorro, New Mexico. The results of the three studies were then used to construct a conceptual model relating depositional environment to geostatistical models of heterogeneity. The model presented is largely qualitative but provides a basis for further hypothesis formulation and testing.

  3. 4th European Conference on Geostatistics for Environmental Applications

    CERN Document Server

    Carrera, Jesus; Gómez-Hernández, José

    2004-01-01

    The fourth edition of the European Conference on Geostatistics for Environmental Applications (geoENV IV) took place in Barcelona, November 27-29, 2002. As a proof that there is an increasing interest in environmental issues in the geostatistical community, the conference attracted over 100 participants, mostly Europeans (up to 10 European countries were represented), but also from other countries in the world. Only 46 contributions, selected out of around 100 submitted papers, were invited to be presented orally during the conference. Additionally 30 authors were invited to present their work in poster format during a special session. All oral and poster contributors were invited to submit their work to be considered for publication in this Kluwer series. All papers underwent a reviewing process, which consisted on two reviewers for oral presentations and one reviewer for posters. The book opens with one keynote paper by Philippe Naveau. It is followed by 40 papers that correspond to those presented orally d...

  4. Inverse atmospheric radiative transfer problems - A nonlinear minimization search method of solution. [aerosol pollution monitoring

    Science.gov (United States)

    Fymat, A. L.

    1976-01-01

    The paper studies the inversion of the radiative transfer equation describing the interaction of electromagnetic radiation with atmospheric aerosols. The interaction can be considered as the propagation in the aerosol medium of two light beams: the direct beam in the line-of-sight attenuated by absorption and scattering, and the diffuse beam arising from scattering into the viewing direction, which propagates more or less in random fashion. The latter beam has single scattering and multiple scattering contributions. In the former case and for single scattering, the problem is reducible to first-kind Fredholm equations, while for multiple scattering it is necessary to invert partial integrodifferential equations. A nonlinear minimization search method, applicable to the solution of both types of problems has been developed, and is applied here to the problem of monitoring aerosol pollution, namely the complex refractive index and size distribution of aerosol particles.

  5. Nonlinear Dynamic Inversion Baseline Control Law: Flight-Test Results for the Full-scale Advanced Systems Testbed F/A-18 Airplane

    Science.gov (United States)

    Miller, Christopher J.

    2011-01-01

    A model reference nonlinear dynamic inversion control law has been developed to provide a baseline controller for research into simple adaptive elements for advanced flight control laws. This controller has been implemented and tested in a hardware-in-the-loop simulation and in flight. The flight results agree well with the simulation predictions and show good handling qualities throughout the tested flight envelope with some noteworthy deficiencies highlighted both by handling qualities metrics and pilot comments. Many design choices and implementation details reflect the requirements placed on the system by the nonlinear flight environment and the desire to keep the system as simple as possible to easily allow the addition of the adaptive elements. The flight-test results and how they compare to the simulation predictions are discussed, along with a discussion about how each element affected pilot opinions. Additionally, aspects of the design that performed better than expected are presented, as well as some simple improvements that will be suggested for follow-on work.

  6. Geostatistical enhancement of european hydrological predictions

    Science.gov (United States)

    Pugliese, Alessio; Castellarin, Attilio; Parajka, Juraj; Arheimer, Berit; Bagli, Stefano; Mazzoli, Paolo; Montanari, Alberto; Blöschl, Günter

    2016-04-01

    Geostatistical Enhancement of European Hydrological Prediction (GEEHP) is a research experiment developed within the EU funded SWITCH-ON project, which proposes to conduct comparative experiments in a virtual laboratory in order to share water-related information and tackle changes in the hydrosphere for operational needs (http://www.water-switch-on.eu). The main objective of GEEHP deals with the prediction of streamflow indices and signatures in ungauged basins at different spatial scales. In particular, among several possible hydrological signatures we focus in our experiment on the prediction of flow-duration curves (FDCs) along the stream-network, which has attracted an increasing scientific attention in the last decades due to the large number of practical and technical applications of the curves (e.g. hydropower potential estimation, riverine habitat suitability and ecological assessments, etc.). We apply a geostatistical procedure based on Top-kriging, which has been recently shown to be particularly reliable and easy-to-use regionalization approach, employing two different type of streamflow data: pan-European E-HYPE simulations (http://hypeweb.smhi.se/europehype) and observed daily streamflow series collected in two pilot study regions, i.e. Tyrol (merging data from Austrian and Italian stream gauging networks) and Sweden. The merger of the two study regions results in a rather large area (~450000 km2) and might be considered as a proxy for a pan-European application of the approach. In a first phase, we implement a bidirectional validation, i.e. E-HYPE catchments are set as training sites to predict FDCs at the same sites where observed data are available, and vice-versa. Such a validation procedure reveals (1) the usability of the proposed approach for predicting the FDCs over the entire river network of interest using alternatively observed data and E-HYPE simulations and (2) the accuracy of E-HYPE-based predictions of FDCs in ungauged sites. In a

  7. Regularized inversion of controlled source and earthquake data

    International Nuclear Information System (INIS)

    Ramachandran, Kumar

    2012-01-01

    Estimation of the seismic velocity structure of the Earth's crust and upper mantle from travel-time data has advanced greatly in recent years. Forward modelling trial-and-error methods have been superseded by tomographic methods which allow more objective analysis of large two-dimensional and three-dimensional refraction and/or reflection data sets. The fundamental purpose of travel-time tomography is to determine the velocity structure of a medium by analysing the time it takes for a wave generated at a source point within the medium to arrive at a distribution of receiver points. Tomographic inversion of first-arrival travel-time data is a nonlinear problem since both the velocity of the medium and ray paths in the medium are unknown. The solution for such a problem is typically obtained by repeated application of linearized inversion. Regularization of the nonlinear problem reduces the ill posedness inherent in the tomographic inversion due to the under-determined nature of the problem and the inconsistencies in the observed data. This paper discusses the theory of regularized inversion for joint inversion of controlled source and earthquake data, and results from synthetic data testing and application to real data. The results obtained from tomographic inversion of synthetic data and real data from the northern Cascadia subduction zone show that the velocity model and hypocentral parameters can be efficiently estimated using this approach. (paper)

  8. Geostatistical analysis of prevailing groundwater conditions and potential solute migration at Elstow, Bedfordshire

    International Nuclear Information System (INIS)

    MacKay, R.; Cooper, T.A.; Porter, J.D.; O'Connell, P.E.; Metcalfe, A.V.

    1988-06-01

    A geostatistical approach is applied in a study of the potential migration of contaminants from a hypothetical waste disposal facility near Elstow, Bedfordshire. A deterministic numerical model of groundwater flow in the Kellaways Sands formation and adjacent layers is coupled with geostatistical simulation of the heterogeneous transmissivity field of this principal formation. A particle tracking technique is used to predict the migration pathways for alternative realisations of flow. Alternative statistical descriptions of the spatial structure of the transmissivity field are implemented and the temporal and spatial distributions of escape of contaminants to the biosphere are investigated. (author)

  9. Estimating Rainfall in Rodrigues by Geostatistics: (A) Theory | Proag ...

    African Journals Online (AJOL)

    This paper introduces the geostatistical method. Originally devised to treat problems that arise when conventional statistical theory is used in estimating changes in ore grade within a mine, it is, however, an abstract theory of statistical behaviour that is applicable to many circumstances in different areas of geology and other ...

  10. Topsoil moisture mapping using geostatistical techniques under different Mediterranean climatic conditions.

    Science.gov (United States)

    Martínez-Murillo, J F; Hueso-González, P; Ruiz-Sinoga, J D

    2017-10-01

    Soil mapping has been considered as an important factor in the widening of Soil Science and giving response to many different environmental questions. Geostatistical techniques, through kriging and co-kriging techniques, have made possible to improve the understanding of eco-geomorphologic variables, e.g., soil moisture. This study is focused on mapping of topsoil moisture using geostatistical techniques under different Mediterranean climatic conditions (humid, dry and semiarid) in three small watersheds and considering topography and soil properties as key factors. A Digital Elevation Model (DEM) with a resolution of 1×1m was derived from a topographical survey as well as soils were sampled to analyzed soil properties controlling topsoil moisture, which was measured during 4-years. Afterwards, some topography attributes were derived from the DEM, the soil properties analyzed in laboratory, and the topsoil moisture was modeled for the entire watersheds applying three geostatistical techniques: i) ordinary kriging; ii) co-kriging considering as co-variate topography attributes; and iii) co-kriging ta considering as co-variates topography attributes and gravel content. The results indicated topsoil moisture was more accurately mapped in the dry and semiarid watersheds when co-kriging procedure was performed. The study is a contribution to improve the efficiency and accuracy of studies about the Mediterranean eco-geomorphologic system and soil hydrology in field conditions. Copyright © 2017 Elsevier B.V. All rights reserved.

  11. Exploring prediction uncertainty of spatial data in geostatistical and machine learning Approaches

    Science.gov (United States)

    Klump, J. F.; Fouedjio, F.

    2017-12-01

    Geostatistical methods such as kriging with external drift as well as machine learning techniques such as quantile regression forest have been intensively used for modelling spatial data. In addition to providing predictions for target variables, both approaches are able to deliver a quantification of the uncertainty associated with the prediction at a target location. Geostatistical approaches are, by essence, adequate for providing such prediction uncertainties and their behaviour is well understood. However, they often require significant data pre-processing and rely on assumptions that are rarely met in practice. Machine learning algorithms such as random forest regression, on the other hand, require less data pre-processing and are non-parametric. This makes the application of machine learning algorithms to geostatistical problems an attractive proposition. The objective of this study is to compare kriging with external drift and quantile regression forest with respect to their ability to deliver reliable prediction uncertainties of spatial data. In our comparison we use both simulated and real world datasets. Apart from classical performance indicators, comparisons make use of accuracy plots, probability interval width plots, and the visual examinations of the uncertainty maps provided by the two approaches. By comparing random forest regression to kriging we found that both methods produced comparable maps of estimated values for our variables of interest. However, the measure of uncertainty provided by random forest seems to be quite different to the measure of uncertainty provided by kriging. In particular, the lack of spatial context can give misleading results in areas without ground truth data. These preliminary results raise questions about assessing the risks associated with decisions based on the predictions from geostatistical and machine learning algorithms in a spatial context, e.g. mineral exploration.

  12. Wave-equation reflection traveltime inversion

    KAUST Repository

    Zhang, Sanzong

    2011-01-01

    The main difficulty with iterative waveform inversion using a gradient optimization method is that it tends to get stuck in local minima associated within the waveform misfit function. This is because the waveform misfit function is highly nonlinear with respect to changes in the velocity model. To reduce this nonlinearity, we present a reflection traveltime tomography method based on the wave equation which enjoys a more quasi-linear relationship between the model and the data. A local crosscorrelation of the windowed downgoing direct wave and the upgoing reflection wave at the image point yields the lag time that maximizes the correlation. This lag time represents the reflection traveltime residual that is back-projected into the earth model to update the velocity in the same way as wave-equation transmission traveltime inversion. No travel-time picking is needed and no high-frequency approximation is assumed. The mathematical derivation and the numerical examples are presented to partly demonstrate its efficiency and robustness. © 2011 Society of Exploration Geophysicists.

  13. Full-waveform inversion using a nonlinearly smoothed wavefield

    KAUST Repository

    Li, Yuanyuan; Choi, Yun Seok; Alkhalifah, Tariq Ali; Li, Zhenchun; Zhang, Kai

    2017-01-01

    width applied to the nonlinear wavefield to naturally adopt the multiscale strategy. Using examples on the Marmousi 2 model, we determine that the proposed FWI helps to generate convergent results without the need for low-frequency information.

  14. Specific storage and hydraulic conductivity tomography through the joint inversion of hydraulic heads and self-potential data

    Science.gov (United States)

    Ahmed, A. Soueid; Jardani, A.; Revil, A.; Dupont, J. P.

    2016-03-01

    Transient hydraulic tomography is used to image the heterogeneous hydraulic conductivity and specific storage fields of shallow aquifers using time series of hydraulic head data. Such ill-posed and non-unique inverse problem can be regularized using some spatial geostatistical characteristic of the two fields. In addition to hydraulic heads changes, the flow of water, during pumping tests, generates an electrical field of electrokinetic nature. These electrical field fluctuations can be passively recorded at the ground surface using a network of non-polarizing electrodes connected to a high impedance (> 10 MOhm) and sensitive (0.1 mV) voltmeter, a method known in geophysics as the self-potential method. We perform a joint inversion of the self-potential and hydraulic head data to image the hydraulic conductivity and specific storage fields. We work on a 3D synthetic confined aquifer and we use the adjoint state method to compute the sensitivities of the hydraulic parameters to the hydraulic head and self-potential data in both steady-state and transient conditions. The inverse problem is solved using the geostatistical quasi-linear algorithm framework of Kitanidis. When the number of piezometers is small, the record of the transient self-potential signals provides useful information to characterize the hydraulic conductivity and specific storage fields. These results show that the self-potential method reveals the heterogeneities of some areas of the aquifer, which could not been captured by the tomography based on the hydraulic heads alone. In our analysis, the improvement on the hydraulic conductivity and specific storage estimations were based on perfect knowledge of electrical resistivity field. This implies that electrical resistivity will need to be jointly inverted with the hydraulic parameters in future studies and the impact of its uncertainty assessed with respect to the final tomograms of the hydraulic parameters.

  15. Monte Carlo aided treatments of the nonlinear inverse PGNAA measurement problem for various continuous on-line applications

    International Nuclear Information System (INIS)

    Gardner, R.P.; Guo, P.; Sood, A.; Mayo, C.W.; Dobbs, C.L.

    1998-01-01

    A review of our work on the application of the PGNAA method as applied to five industrial applications is given. Some introductory material is first given on the importance and use of Monte Carlo simulation in this area, some comments on the place of PGNAA in elemental analysis, and a brief description of the Monte Carlo - Library Least-Squares (MCLLS) approach to the nonlinear inverse PGNAA analysis problem. Then the applications of PGNAA are discussed for: (1) on-line bulk coal analysis, (2) nuclear oil well logging, (3) vitrified waste, (4) the analysis of sodium and aluminium in 'green liquor' in the presence of chlorine, and (5) the conveyor belt sorting of aluminum alloy samples. It is concluded that PGNAA is a rapidly emerging important new technology and measurement approach. (author)

  16. Variational structure of inverse problems in wave propagation and vibration

    Energy Technology Data Exchange (ETDEWEB)

    Berryman, J.G.

    1995-03-01

    Practical algorithms for solving realistic inverse problems may often be viewed as problems in nonlinear programming with the data serving as constraints. Such problems are most easily analyzed when it is possible to segment the solution space into regions that are feasible (satisfying all the known constraints) and infeasible (violating some of the constraints). Then, if the feasible set is convex or at least compact, the solution to the problem will normally lie on the boundary of the feasible set. A nonlinear program may seek the solution by systematically exploring the boundary while satisfying progressively more constraints. Examples of inverse problems in wave propagation (traveltime tomography) and vibration (modal analysis) will be presented to illustrate how the variational structure of these problems may be used to create nonlinear programs using implicit variational constraints.

  17. Validating spatial structure in canopy water content using geostatistics

    Science.gov (United States)

    Sanderson, E. W.; Zhang, M. H.; Ustin, S. L.; Rejmankova, E.; Haxo, R. S.

    1995-01-01

    Heterogeneity in ecological phenomena are scale dependent and affect the hierarchical structure of image data. AVIRIS pixels average reflectance produced by complex absorption and scattering interactions between biogeochemical composition, canopy architecture, view and illumination angles, species distributions, and plant cover as well as other factors. These scales affect validation of pixel reflectance, typically performed by relating pixel spectra to ground measurements acquired at scales of 1m(exp 2) or less (e.g., field spectra, foilage and soil samples, etc.). As image analysis becomes more sophisticated, such as those for detection of canopy chemistry, better validation becomes a critical problem. This paper presents a methodology for bridging between point measurements and pixels using geostatistics. Geostatistics have been extensively used in geological or hydrogeolocial studies but have received little application in ecological studies. The key criteria for kriging estimation is that the phenomena varies in space and that an underlying controlling process produces spatial correlation between the measured data points. Ecological variation meets this requirement because communities vary along environmental gradients like soil moisture, nutrient availability, or topography.

  18. A method of the asymmetric Abel's inversion in plasma diagnosis

    International Nuclear Information System (INIS)

    Matoba, Tohru; Funahashi, Akimasa

    1975-09-01

    In the case of a noncylindrical plasma, axis symmetric components are drawn from observed projected intensities of physical quantities, assuming an asymmetric form. And the radial intensity distribution is determined by Abel's inversion method. The best fitting curve is obtained analytically from measured values by the least-square estimation of nonlinear parameters. The cylindrical symmetric Abel's inversion code ( ABELIC ) and the asymmetric Abel's inversion code ( ABELILSENP 2 ) are described. (auth.)

  19. Full-waveform inversion with reflected waves for 2D VTI media

    KAUST Repository

    Pattnaik, Sonali

    2016-09-06

    Full-waveform inversion in anisotropic media using reflected waves suffers from the strong non-linearity of the objective function and trade-offs between model parameters. Estimating long-wavelength model components by fixing parameter perturbations, referred to as reflection-waveform inversion (RWI), can mitigate nonlinearity-related inversion issues. Here, we extend RWI to acoustic VTI (transversely isotropic with a vertical symmetry axis) media. To minimize trade-offs between the model parameters, we employ a new hierarchical two-stage approach that operates with the P-wave normal-moveout velocity and anisotropy coefficents ζ and η. First, is estimated using a fixed perturbation in ζ, and then we invert for η by fixing the updated perturbation in . The proposed 2D algorithm is tested on a horizontally layered VTI model.

  20. Geostatistical Borehole Image-Based Mapping of Karst-Carbonate Aquifer Pores.

    Science.gov (United States)

    Sukop, Michael C; Cunningham, Kevin J

    2016-03-01

    Quantification of the character and spatial distribution of porosity in carbonate aquifers is important as input into computer models used in the calculation of intrinsic permeability and for next-generation, high-resolution groundwater flow simulations. Digital, optical, borehole-wall image data from three closely spaced boreholes in the karst-carbonate Biscayne aquifer in southeastern Florida are used in geostatistical experiments to assess the capabilities of various methods to create realistic two-dimensional models of vuggy megaporosity and matrix-porosity distribution in the limestone that composes the aquifer. When the borehole image data alone were used as the model training image, multiple-point geostatistics failed to detect the known spatial autocorrelation of vuggy megaporosity and matrix porosity among the three boreholes, which were only 10 m apart. Variogram analysis and subsequent Gaussian simulation produced results that showed a realistic conceptualization of horizontal continuity of strata dominated by vuggy megaporosity and matrix porosity among the three boreholes. © 2015, National Ground Water Association.

  1. A geostatistical methodology to assess the accuracy of unsaturated flow models

    Energy Technology Data Exchange (ETDEWEB)

    Smoot, J.L.; Williams, R.E.

    1996-04-01

    The Pacific Northwest National Laboratory spatiotemporal movement of water injected into (PNNL) has developed a Hydrologic unsaturated sediments at the Hanford Site in Evaluation Methodology (HEM) to assist the Washington State was used to develop a new U.S. Nuclear Regulatory Commission in method for evaluating mathematical model evaluating the potential that infiltrating meteoric predictions. Measured water content data were water will produce leachate at commercial low- interpolated geostatistically to a 16 x 16 x 36 level radioactive waste disposal sites. Two key grid at several time intervals. Then a issues are raised in the HEM: (1) evaluation of mathematical model was used to predict water mathematical models that predict facility content at the same grid locations at the selected performance, and (2) estimation of the times. Node-by-node comparison of the uncertainty associated with these mathematical mathematical model predictions with the model predictions. The technical objective of geostatistically interpolated values was this research is to adapt geostatistical tools conducted. The method facilitates a complete commonly used for model parameter estimation accounting and categorization of model error at to the problem of estimating the spatial every node. The comparison suggests that distribution of the dependent variable to be model results generally are within measurement calculated by the model. To fulfill this error. The worst model error occurs in silt objective, a database describing the lenses and is in excess of measurement error.

  2. A geostatistical methodology to assess the accuracy of unsaturated flow models

    International Nuclear Information System (INIS)

    Smoot, J.L.; Williams, R.E.

    1996-04-01

    The Pacific Northwest National Laboratory spatiotemporal movement of water injected into (PNNL) has developed a Hydrologic unsaturated sediments at the Hanford Site in Evaluation Methodology (HEM) to assist the Washington State was used to develop a new U.S. Nuclear Regulatory Commission in method for evaluating mathematical model evaluating the potential that infiltrating meteoric predictions. Measured water content data were water will produce leachate at commercial low- interpolated geostatistically to a 16 x 16 x 36 level radioactive waste disposal sites. Two key grid at several time intervals. Then a issues are raised in the HEM: (1) evaluation of mathematical model was used to predict water mathematical models that predict facility content at the same grid locations at the selected performance, and (2) estimation of the times. Node-by-node comparison of the uncertainty associated with these mathematical mathematical model predictions with the model predictions. The technical objective of geostatistically interpolated values was this research is to adapt geostatistical tools conducted. The method facilitates a complete commonly used for model parameter estimation accounting and categorization of model error at to the problem of estimating the spatial every node. The comparison suggests that distribution of the dependent variable to be model results generally are within measurement calculated by the model. To fulfill this error. The worst model error occurs in silt objective, a database describing the lenses and is in excess of measurement error

  3. Geostatistical interpolation model selection based on ArcGIS and spatio-temporal variability analysis of groundwater level in piedmont plains, northwest China.

    Science.gov (United States)

    Xiao, Yong; Gu, Xiaomin; Yin, Shiyang; Shao, Jingli; Cui, Yali; Zhang, Qiulan; Niu, Yong

    2016-01-01

    Based on the geo-statistical theory and ArcGIS geo-statistical module, datas of 30 groundwater level observation wells were used to estimate the decline of groundwater level in Beijing piedmont. Seven different interpolation methods (inverse distance weighted interpolation, global polynomial interpolation, local polynomial interpolation, tension spline interpolation, ordinary Kriging interpolation, simple Kriging interpolation and universal Kriging interpolation) were used for interpolating groundwater level between 2001 and 2013. Cross-validation, absolute error and coefficient of determination (R(2)) was applied to evaluate the accuracy of different methods. The result shows that simple Kriging method gave the best fit. The analysis of spatial and temporal variability suggest that the nugget effects from 2001 to 2013 were increasing, which means the spatial correlation weakened gradually under the influence of human activities. The spatial variability in the middle areas of the alluvial-proluvial fan is relatively higher than area in top and bottom. Since the changes of the land use, groundwater level also has a temporal variation, the average decline rate of groundwater level between 2007 and 2013 increases compared with 2001-2006. Urban development and population growth cause over-exploitation of residential and industrial areas. The decline rate of the groundwater level in residential, industrial and river areas is relatively high, while the decreasing of farmland area and development of water-saving irrigation reduce the quantity of water using by agriculture and decline rate of groundwater level in agricultural area is not significant.

  4. Scattering angle base filtering of the inversion gradients

    KAUST Repository

    Alkhalifah, Tariq Ali

    2014-01-01

    Full waveform inversion (FWI) requires a hierarchical approach based on the availability of low frequencies to maneuver the complex nonlinearity associated with the problem of velocity inversion. I develop a model gradient filter to help us access the parts of the gradient more suitable to combat this potential nonlinearity. The filter is based on representing the gradient in the time-lag normalized domain, in which low scattering angles of the gradient update are initially muted. The result are long-wavelength updates controlled by the ray component of the wavefield. In this case, even 10 Hz data can produce near zero wavelength updates suitable for a background correction of the model. Allowing smaller scattering angle to contribute provides higher resolution information to the model.

  5. The Cauchy problem for non-linear Klein-Gordon equations

    International Nuclear Information System (INIS)

    Simon, J.C.H.; Taflin, E.

    1993-01-01

    We consider in R n+1 , n≥2, the non-linear Klein-Gordon equation. We prove for such an equation that there is neighbourhood of zero in a Hilbert space of initial conditions for which the Cauchy problem has global solutions and on which there is asymptotic completeness. The inverse of the wave operator linearizes the non-linear equation. If, moreover, the equation is manifestly Poincare covariant then the non-linear representation of the Poincare-Lie algebra, associated with the non-linear Klein-Gordon equation is integrated to a non-linear representation of the Poincare group on an invariant neighbourhood of zero in the Hilbert space. This representation is linearized by the inverse of the wave operator. The Hilbert space is, in both cases, the closure of the space of the differentiable vectors for the linear representation of the Poincare group, associated with the Klein-Gordon equation, with respect to a norm defined by the representation of the enveloping algebra. (orig.)

  6. Nonlinear transport of accelerator beam phase space

    International Nuclear Information System (INIS)

    Xie Xi; Xia Jiawen

    1995-01-01

    Based on the any order analytical solution of accelerator beam dynamics, the general theory for nonlinear transport of accelerator beam phase space is developed by inverse transformation method. The method is general by itself, and hence can also be applied to the nonlinear transport of various dynamic systems in physics, chemistry and biology

  7. Nonlinear generalization of special relativity

    International Nuclear Information System (INIS)

    Winterberg, F.

    1985-01-01

    In Poincares axiomatic formulation special relativity is a derived consequence of a true Lorentz contraction, for a rod in absolute motion through a substratum. Furthermore, Lorentz had shown that the rod contraction can be understood by an inverse square law interaction and therefore special relativity derived from more fundamental principles. The derivation by Lorentz shows that the root of the divergence problems is the singular inverse square law. By replacing the inverse square law with a regular one through the introduction of a finite length, the author has succeeded in deriving a nonlinear generalization of special relativity which eliminates all infinities. Besides the relative velocities, these nonlinear transformation equations also contain absolute velocities against a substratum, but in the limit of small energies they go over into the linear Lorentz transformations. Depending on the smallness of the fundamental length, departures from special relativity can be observed only at very high energies. The theorem that the velocity of light is the same in all reference systems still holds and likewise the conservation laws for energy and momentum

  8. Geostatistics applied to estimation of uranium bearing ore reserves

    International Nuclear Information System (INIS)

    Urbina Galan, L.I.

    1982-01-01

    A computer assisted method for assessing uranium-bearing ore deposit reserves is analyzed. Determinations of quality-thickness, namely quality by thickness calculations of mineralization, were obtained by means of a mathematical method known as the theory of rational variables for each drill-hole layer. Geostatistical results were derived based on a Fortrand computer program on a DEC 20/40 system. (author)

  9. Effects of applied electromagnetic fields on the linear and nonlinear optical properties in an inverse parabolic quantum well

    International Nuclear Information System (INIS)

    Ungan, F.; Yesilgul, U.; Kasapoglu, E.; Sari, H.; Sökmen, I.

    2012-01-01

    In this present work, we have investigated theoretically the effects of applied electric and magnetic fields on the linear and nonlinear optical properties in a GaAs/Al x Ga 1−x As inverse parabolic quantum well for different Al concentrations at the well center. The Al concentration at the barriers was always x max =0.3. The energy levels and wave functions are calculated within the effective mass approximation and the envelope function approach. The analytical expressions of optical properties are obtained by using the compact density-matrix approach. The linear, third-order nonlinear and total absorption and refractive index changes depending on the Al concentration at the well center are investigated as a function of the incident photon energy for the different values of the applied electric and magnetic fields. The results show that the applied electric and magnetic fields have a great effect on these optical quantities. - Highlights: ► The x c concentration has a great effect on the optical characteristics of these structures. ► The EM fields have a great effect on the optical properties of these structures. ► The total absorption coefficients increased as the electric and magnetic field increases. ► The RICs reduced as the electric and magnetic field increases.

  10. Accelerated Computing in Magnetic Resonance Imaging: Real-Time Imaging Using Nonlinear Inverse Reconstruction

    Directory of Open Access Journals (Sweden)

    Sebastian Schaetz

    2017-01-01

    Full Text Available Purpose. To develop generic optimization strategies for image reconstruction using graphical processing units (GPUs in magnetic resonance imaging (MRI and to exemplarily report on our experience with a highly accelerated implementation of the nonlinear inversion (NLINV algorithm for dynamic MRI with high frame rates. Methods. The NLINV algorithm is optimized and ported to run on a multi-GPU single-node server. The algorithm is mapped to multiple GPUs by decomposing the data domain along the channel dimension. Furthermore, the algorithm is decomposed along the temporal domain by relaxing a temporal regularization constraint, allowing the algorithm to work on multiple frames in parallel. Finally, an autotuning method is presented that is capable of combining different decomposition variants to achieve optimal algorithm performance in different imaging scenarios. Results. The algorithm is successfully ported to a multi-GPU system and allows online image reconstruction with high frame rates. Real-time reconstruction with low latency and frame rates up to 30 frames per second is demonstrated. Conclusion. Novel parallel decomposition methods are presented which are applicable to many iterative algorithms for dynamic MRI. Using these methods to parallelize the NLINV algorithm on multiple GPUs, it is possible to achieve online image reconstruction with high frame rates.

  11. Full waveform inversion based on scattering angle enrichment with application to real dataset

    KAUST Repository

    Wu, Zedong; Alkhalifah, Tariq Ali

    2015-01-01

    Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI). However, the drawback of the existing RWI methods is inability to utilize diving waves and the extra sensitivity

  12. Geostatistical analysis and kriging of Hexachlorocyclohexane residues in topsoil from Tianjin, China

    International Nuclear Information System (INIS)

    Li, B.G.; Cao, J.; Liu, W.X.; Shen, W.R.; Wang, X.J.; Tao, S.

    2006-01-01

    A previously published data set of HCH isomer concentrations in topsoil samples from Tianjin, China, was subjected to geospatial analysis. Semivariograms were calculated and modeled using geostatistical techniques. Parameters of semivariogram models were analyzed and compared for four HCH isomers. Two-dimensional ordinary block kriging was applied to HCH isomers data set for mapping purposes. Dot maps and gray-scaled raster maps of HCH concentrations were presented based on kriging results. The appropriateness of the kriging procedure for mapping purposes was evaluated based on the kriging errors and kriging variances. It was found that ordinary block kriging can be applied to interpolate HCH concentrations in Tianjin topsoil with acceptable accuracy for mapping purposes. - Geostatistical analysis and kriging were applied to HCH concentrations in topsoil of Tianjin, China for mapping purposes

  13. Geostatistical integration and uncertainty in pollutant concentration surface under preferential sampling

    Directory of Open Access Journals (Sweden)

    Laura Grisotto

    2016-04-01

    Full Text Available In this paper the focus is on environmental statistics, with the aim of estimating the concentration surface and related uncertainty of an air pollutant. We used air quality data recorded by a network of monitoring stations within a Bayesian framework to overcome difficulties in accounting for prediction uncertainty and to integrate information provided by deterministic models based on emissions meteorology and chemico-physical characteristics of the atmosphere. Several authors have proposed such integration, but all the proposed approaches rely on representativeness and completeness of existing air pollution monitoring networks. We considered the situation in which the spatial process of interest and the sampling locations are not independent. This is known in the literature as the preferential sampling problem, which if ignored in the analysis, can bias geostatistical inferences. We developed a Bayesian geostatistical model to account for preferential sampling with the main interest in statistical integration and uncertainty. We used PM10 data arising from the air quality network of the Environmental Protection Agency of Lombardy Region (Italy and numerical outputs from the deterministic model. We specified an inhomogeneous Poisson process for the sampling locations intensities and a shared spatial random component model for the dependence between the spatial location of monitors and the pollution surface. We found greater predicted standard deviation differences in areas not properly covered by the air quality network. In conclusion, in this context inferences on prediction uncertainty may be misleading when geostatistical modelling does not take into account preferential sampling.

  14. Forecasting Interest Rates Using Geostatistical Techniques

    Directory of Open Access Journals (Sweden)

    Giuseppe Arbia

    2015-11-01

    Full Text Available Geostatistical spatial models are widely used in many applied fields to forecast data observed on continuous three-dimensional surfaces. We propose to extend their use to finance and, in particular, to forecasting yield curves. We present the results of an empirical application where we apply the proposed method to forecast Euro Zero Rates (2003–2014 using the Ordinary Kriging method based on the anisotropic variogram. Furthermore, a comparison with other recent methods for forecasting yield curves is proposed. The results show that the model is characterized by good levels of predictions’ accuracy and it is competitive with the other forecasting models considered.

  15. Relevance vector machine technique for the inverse scattering problem

    International Nuclear Information System (INIS)

    Wang Fang-Fang; Zhang Ye-Rong

    2012-01-01

    A novel method based on the relevance vector machine (RVM) for the inverse scattering problem is presented in this paper. The nonlinearity and the ill-posedness inherent in this problem are simultaneously considered. The nonlinearity is embodied in the relation between the scattered field and the target property, which can be obtained through the RVM training process. Besides, rather than utilizing regularization, the ill-posed nature of the inversion is naturally accounted for because the RVM can produce a probabilistic output. Simulation results reveal that the proposed RVM-based approach can provide comparative performances in terms of accuracy, convergence, robustness, generalization, and improved performance in terms of sparse property in comparison with the support vector machine (SVM) based approach. (general)

  16. Geostatistical risk estimation at waste disposal sites in the presence of hot spots

    International Nuclear Information System (INIS)

    Komnitsas, Kostas; Modis, Kostas

    2009-01-01

    The present paper aims to estimate risk by using geostatistics at the wider coal mining/waste disposal site of Belkovskaya, Tula region, in Russia. In this area the presence of hot spots causes a spatial trend in the mean value of the random field and a non-Gaussian data distribution. Prior to application of geostatistics, subtraction of trend and appropriate smoothing and transformation of the data into a Gaussian form were carried out; risk maps were then generated for the wider study area in order to assess the probability of exceeding risk thresholds. Finally, the present paper discusses the need for homogenization of soil risk thresholds regarding hazardous elements that will enhance reliability of risk estimation and enable application of appropriate rehabilitation actions in contaminated areas.

  17. On nonlinear periodic drift waves

    International Nuclear Information System (INIS)

    Kauschke, U.; Schlueter, H.

    1990-09-01

    Nonlinear periodic drift waves are investigated on the basis of a simple perturbation scheme for both the amplitude and inverse frequency. The coefficients for the generation of the forced harmonics are derived, a nonlinear dispersion relation is suggested and a criterion for the onset of the modulational instability is obtained. The results are compared with the ones obtained with the help of a standard KBM-treatment. Moreover cnoidal drift waves are suggested and compared to an experimental observation. (orig.)

  18. Geostatistical methods for the integrated information; Metodos geoestadisticos para la integracion de informacion

    Energy Technology Data Exchange (ETDEWEB)

    Cassiraga, E F; Gomez-Hernandez, J J [Departamento de Ingenieria Hidraulica y Medio Ambiente, Universidad Politecnica de Valencia, Valencia (Spain)

    1996-10-01

    The main objective of this report is to describe the different geostatistical techniques to use the geophysical and hydrological parameters. We analyze the characteristics of estimation methods used in others studies.

  19. Assessment of effectiveness of geologic isolation systems: geostatistical modeling of pore velocity

    International Nuclear Information System (INIS)

    Devary, J.L.; Doctor, P.G.

    1981-06-01

    A significant part of evaluating a geologic formation as a nuclear waste repository involves the modeling of contaminant transport in the surrounding media in the event the repository is breached. The commonly used contaminant transport models are deterministic. However, the spatial variability of hydrologic field parameters introduces uncertainties into contaminant transport predictions. This paper discusses the application of geostatistical techniques to the modeling of spatially varying hydrologic field parameters required as input to contaminant transport analyses. Kriging estimation techniques were applied to Hanford Reservation field data to calculate hydraulic conductivity and the ground-water potential gradients. These quantities were statistically combined to estimate the groundwater pore velocity and to characterize the pore velocity estimation error. Combining geostatistical modeling techniques with product error propagation techniques results in an effective stochastic characterization of groundwater pore velocity, a hydrologic parameter required for contaminant transport analyses

  20. Delineating Hydrofacies Spatial Distribution by Integrating Ensemble Data Assimilation and Indicator Geostatistics

    Energy Technology Data Exchange (ETDEWEB)

    Song, Xuehang [Florida State Univ., Tallahassee, FL (United States); Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Chen, Xingyuan [Pacific Northwest National Lab. (PNNL), Richland, WA (United States); Ye, Ming [Florida State Univ., Tallahassee, FL (United States); Dai, Zhenxue [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Hammond, Glenn Edward [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2015-07-01

    This study develops a new framework of facies-based data assimilation for characterizing spatial distribution of hydrofacies and estimating their associated hydraulic properties. This framework couples ensemble data assimilation with transition probability-based geostatistical model via a parameterization based on a level set function. The nature of ensemble data assimilation makes the framework efficient and flexible to be integrated with various types of observation data. The transition probability-based geostatistical model keeps the updated hydrofacies distributions under geological constrains. The framework is illustrated by using a two-dimensional synthetic study that estimates hydrofacies spatial distribution and permeability in each hydrofacies from transient head data. Our results show that the proposed framework can characterize hydrofacies distribution and associated permeability with adequate accuracy even with limited direct measurements of hydrofacies. Our study provides a promising starting point for hydrofacies delineation in complex real problems.

  1. Application of Geostatistical Modelling to Study the Exploration Adequacy of Uniaxial Compressive Strength of Intact Rock alongthe Behesht-Abad Tunnel Route

    Directory of Open Access Journals (Sweden)

    Mohammad Doustmohammadi

    2014-12-01

    Full Text Available Uniaxial compressive strength (UCS is one of the most significant factors on the stability of underground excavation projects. Most of the time, this factor can be obtained by exploratory boreholes evaluation. Due to the large distance between exploratory boreholes in the majority of geotechnical projects, the application of geostatistical methods has increased as an estimator of rock mass properties. The present paper ties the estimation of UCS values of intact rock to the distance between boreholes of the Behesht-Abad tunnel in central Iran, using SGEMS geostatistical program. Variography showed that UCS estimation of intact rock using geostatistical methods is reasonable. The model establishment and validation was done after assessment that the model was trustworthy. Cross validation proved the high accuracy (98% and reliability of the model to estimate uniaxial compressive strength. The UCS values were then estimated along the tunnel axis. Moreover, using geostatistical estimation led to better identification of the pros and cons of geotechnical explorations in each location of tunnel route.

  2. Nonlinear Fourier transform for dual-polarization optical communication system

    DEFF Research Database (Denmark)

    Gaiarin, Simone

    communication is considered an emerging paradigm in fiber-optic communications that could potentially overcome these limitations. It relies on a mathematical technique called “inverse scattering transform” or “nonlinear Fourier transform (NFT)” to exploit the “hidden” linearity of the nonlinear Schrödinger...

  3. Application of a computationally efficient geostatistical approach to characterizing variably spaced water-table data

    International Nuclear Information System (INIS)

    Quinn, J.J.

    1996-01-01

    Geostatistical analysis of hydraulic head data is useful in producing unbiased contour plots of head estimates and relative errors. However, at most sites being characterized, monitoring wells are generally present at different densities, with clusters of wells in some areas and few wells elsewhere. The problem that arises when kriging data at different densities is in achieving adequate resolution of the grid while maintaining computational efficiency and working within software limitations. For the site considered, 113 data points were available over a 14-mi 2 study area, including 57 monitoring wells within an area of concern of 1.5 mi 2 . Variogram analyses of the data indicate a linear model with a negligible nugget effect. The geostatistical package used in the study allows a maximum grid of 100 by 100 cells. Two-dimensional kriging was performed for the entire study area with a 500-ft grid spacing, while the smaller zone was modeled separately with a 100-ft spacing. In this manner, grid cells for the dense area and the sparse area remained small relative to the well separation distances, and the maximum dimensions of the program were not exceeded. The spatial head results for the detailed zone were then nested into the regional output by use of a graphical, object-oriented database that performed the contouring of the geostatistical output. This study benefitted from the two-scale approach and from very fine geostatistical grid spacings relative to typical data separation distances. The combining of the sparse, regional results with those from the finer-resolution area of concern yielded contours that honored the actual data at every measurement location. The method applied in this study can also be used to generate reproducible, unbiased representations of other types of spatial data

  4. Confronting uncertainty in model-based geostatistics using Markov Chain Monte Carlo simulation

    NARCIS (Netherlands)

    Minasny, B.; Vrugt, J.A.; McBratney, A.B.

    2011-01-01

    This paper demonstrates for the first time the use of Markov Chain Monte Carlo (MCMC) simulation for parameter inference in model-based soil geostatistics. We implemented the recently developed DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm to jointly summarize the posterior

  5. Solution of the Cox-Thompson inverse scattering problem using finite set of phase shifts

    CERN Document Server

    Apagyi, B; Scheid, W

    2003-01-01

    A system of nonlinear equations is presented for the solution of the Cox-Thompson inverse scattering problem (1970 J. Math. Phys. 11 805) at fixed energy. From a given finite set of phase shifts for physical angular momenta, the nonlinear equations determine related sets of asymptotic normalization constants and nonphysical (shifted) angular momenta from which all quantities of interest, including the inversion potential itself, can be calculated. As a first application of the method we use input data consisting of a finite set of phase shifts calculated from Woods-Saxon and box potentials representing interactions with diffuse or sharp surfaces, respectively. The results for the inversion potentials, their first moments and asymptotic properties are compared with those provided by the Newton-Sabatier quantum inversion procedure. It is found that in order to achieve inversion potentials of similar quality, the Cox-Thompson method requires a smaller set of phase shifts than the Newton-Sabatier procedure.

  6. Solution of the Cox-Thompson inverse scattering problem using finite set of phase shifts

    International Nuclear Information System (INIS)

    Apagyi, Barnabas; Harman, Zoltan; Scheid, Werner

    2003-01-01

    A system of nonlinear equations is presented for the solution of the Cox-Thompson inverse scattering problem (1970 J. Math. Phys. 11 805) at fixed energy. From a given finite set of phase shifts for physical angular momenta, the nonlinear equations determine related sets of asymptotic normalization constants and nonphysical (shifted) angular momenta from which all quantities of interest, including the inversion potential itself, can be calculated. As a first application of the method we use input data consisting of a finite set of phase shifts calculated from Woods-Saxon and box potentials representing interactions with diffuse or sharp surfaces, respectively. The results for the inversion potentials, their first moments and asymptotic properties are compared with those provided by the Newton-Sabatier quantum inversion procedure. It is found that in order to achieve inversion potentials of similar quality, the Cox-Thompson method requires a smaller set of phase shifts than the Newton-Sabatier procedure

  7. Mercury emissions from coal combustion in Silesia, analysis using geostatistics

    Science.gov (United States)

    Zasina, Damian; Zawadzki, Jaroslaw

    2015-04-01

    Data provided by the UNEP's report on mercury [1] shows that solid fuel combustion in significant source of mercury emission to air. Silesia, located in southwestern Poland, is notably affected by mercury emission due to being one of the most industrialized Polish regions: the place of coal mining, production of metals, stone mining, mineral quarrying and chemical industry. Moreover, Silesia is the region with high population density. People are exposed to severe risk of mercury emitted from both: industrial and domestic sources (i.e. small household furnaces). Small sources have significant contribution to total emission of mercury. Official and statistical analysis, including prepared for international purposes [2] did not provide data about spatial distribution of the mercury emitted to air, however number of analysis on Polish public power and energy sector had been prepared so far [3; 4]. The distribution of locations exposed for mercury emission from small domestic sources is interesting matter merging information from various sources: statistical, economical and environmental. This paper presents geostatistical approach to distibution of mercury emission from coal combustion. Analysed data organized in 2 independent levels: individual, bottom-up approach derived from national emission reporting system [5; 6] and top down - regional data calculated basing on official statistics [7]. Analysis, that will be presented, will include comparison of spatial distributions of mercury emission using data derived from sources mentioned above. Investigation will include three voivodeships of Poland: Lower Silesian, Opole (voivodeship) and Silesian using selected geostatistical methodologies including ordinary kriging [8]. References [1] UNEP. Global Mercury Assessment 2013: Sources, Emissions, Releases and Environmental Transport. UNEP Chemicals Branch, Geneva, Switzerland, 2013. [2] NCEM. Poland's Informative Inventory Report 2014. NCEM at the IEP-NRI, 2014. http

  8. Full waveform inversion for time-distance helioseismology

    International Nuclear Information System (INIS)

    Hanasoge, Shravan M.; Tromp, Jeroen

    2014-01-01

    Inferring interior properties of the Sun from photospheric measurements of the seismic wavefield constitutes the helioseismic inverse problem. Deviations in seismic measurements (such as wave travel times) from their fiducial values estimated for a given model of the solar interior imply that the model is inaccurate. Contemporary inversions in local helioseismology assume that properties of the solar interior are linearly related to measured travel-time deviations. It is widely known, however, that this assumption is invalid for sunspots and active regions and is likely for supergranular flows. Here, we introduce nonlinear optimization, executed iteratively, as a means of inverting for the subsurface structure of large-amplitude perturbations. Defining the penalty functional as the L 2 norm of wave travel-time deviations, we compute the total misfit gradient of this functional with respect to the relevant model parameters at each iteration around the corresponding model. The model is successively improved using either steepest descent, conjugate gradient, or the quasi-Newton limited-memory Broyden-Fletcher-Goldfarb-Shanno algorithm. Performing nonlinear iterations requires privileging pixels (such as those in the near field of the scatterer), a practice that is not compliant with the standard assumption of translational invariance. Measurements for these inversions, although similar in principle to those used in time-distance helioseismology, require some retooling. For the sake of simplicity in illustrating the method, we consider a two-dimensional inverse problem with only a sound-speed perturbation.

  9. Modelling Geomechanical Heterogeneity of Rock Masses Using Direct and Indirect Geostatistical Conditional Simulation Methods

    Science.gov (United States)

    Eivazy, Hesameddin; Esmaieli, Kamran; Jean, Raynald

    2017-12-01

    An accurate characterization and modelling of rock mass geomechanical heterogeneity can lead to more efficient mine planning and design. Using deterministic approaches and random field methods for modelling rock mass heterogeneity is known to be limited in simulating the spatial variation and spatial pattern of the geomechanical properties. Although the applications of geostatistical techniques have demonstrated improvements in modelling the heterogeneity of geomechanical properties, geostatistical estimation methods such as Kriging result in estimates of geomechanical variables that are not fully representative of field observations. This paper reports on the development of 3D models for spatial variability of rock mass geomechanical properties using geostatistical conditional simulation method based on sequential Gaussian simulation. A methodology to simulate the heterogeneity of rock mass quality based on the rock mass rating is proposed and applied to a large open-pit mine in Canada. Using geomechanical core logging data collected from the mine site, a direct and an indirect approach were used to model the spatial variability of rock mass quality. The results of the two modelling approaches were validated against collected field data. The study aims to quantify the risks of pit slope failure and provides a measure of uncertainties in spatial variability of rock mass properties in different areas of the pit.

  10. Nonlinear Multivariate Spline-Based Control Allocation for High-Performance Aircraft

    NARCIS (Netherlands)

    Tol, H.J.; De Visser, C.C.; Van Kampen, E.; Chu, Q.P.

    2014-01-01

    High performance flight control systems based on the nonlinear dynamic inversion (NDI) principle require highly accurate models of aircraft aerodynamics. In general, the accuracy of the internal model determines to what degree the system nonlinearities can be canceled; the more accurate the model,

  11. On inverse problem of calculus of variations

    Energy Technology Data Exchange (ETDEWEB)

    Tao, Z-L [College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044 (China)], E-mail: zaolingt@nuist.edu.cn

    2008-02-15

    Using the semi-inverse method proposed by Ji-Huan He, variational principles are established for some nonlinear equations arising in physics, including the (p, 2p)-mZK equation, Klein-Gordon equation, sine-Gordon equation, Liouville equation, Dodd- Bullough-Mikhailov equation, and Tzitzeica-Dodd-Bullough equation.

  12. The attitude inversion method of geostationary satellites based on unscented particle filter

    Science.gov (United States)

    Du, Xiaoping; Wang, Yang; Hu, Heng; Gou, Ruixin; Liu, Hao

    2018-04-01

    The attitude information of geostationary satellites is difficult to be obtained since they are presented in non-resolved images on the ground observation equipment in space object surveillance. In this paper, an attitude inversion method for geostationary satellite based on Unscented Particle Filter (UPF) and ground photometric data is presented. The inversion algorithm based on UPF is proposed aiming at the strong non-linear feature in the photometric data inversion for satellite attitude, which combines the advantage of Unscented Kalman Filter (UKF) and Particle Filter (PF). This update method improves the particle selection based on the idea of UKF to redesign the importance density function. Moreover, it uses the RMS-UKF to partially correct the prediction covariance matrix, which improves the applicability of the attitude inversion method in view of UKF and the particle degradation and dilution of the attitude inversion method based on PF. This paper describes the main principles and steps of algorithm in detail, correctness, accuracy, stability and applicability of the method are verified by simulation experiment and scaling experiment in the end. The results show that the proposed method can effectively solve the problem of particle degradation and depletion in the attitude inversion method on account of PF, and the problem that UKF is not suitable for the strong non-linear attitude inversion. However, the inversion accuracy is obviously superior to UKF and PF, in addition, in the case of the inversion with large attitude error that can inverse the attitude with small particles and high precision.

  13. Preliminary evaluation of uranium deposits. A geostatistical study of drilling density in Wyoming solution fronts

    International Nuclear Information System (INIS)

    Sandefur, R.L.; Grant, D.C.

    1976-01-01

    Studies of a roll-front uranium deposit in Shirley Basin Wyoming indicate that preliminary evaluation of the reserve potential of an ore body is possible with less drilling than currently practiced in industry. Estimating ore reserves from sparse drilling is difficult because most reserve calculation techniques do not give the accuracy of the estimate. A study of several deposits with a variety of drilling densities shows that geostatistics consistently provides a method of assessing the accuracy of an ore reserve estimate. Geostatistics provides the geologist with an additional descriptive technique - one which is valuable in the economic assessment of a uranium deposit. Closely spaced drilling on past properties provides both geological and geometric insight into the occurrence of uranium in roll-front type deposits. Just as the geological insight assists in locating new ore bodies and siting preferential drill locations, the geometric insight can be applied mathematically to evaluate the accuracy of a new ore reserve estimate. By expressing the geometry in numerical terms, geostatistics extracts important geological characteristics and uses this information to aid in describing the unknown characteristics of a property. (author)

  14. Electron dose map inversion based on several algorithms

    International Nuclear Information System (INIS)

    Li Gui; Zheng Huaqing; Wu Yican; Fds Team

    2010-01-01

    The reconstruction to the electron dose map in radiation therapy was investigated by constructing the inversion model of electron dose map with different algorithms. The inversion model of electron dose map based on nonlinear programming was used, and this model was applied the penetration dose map to invert the total space one. The realization of this inversion model was by several inversion algorithms. The test results with seven samples show that except the NMinimize algorithm, which worked for just one sample, with great error,though,all the inversion algorithms could be realized to our inversion model rapidly and accurately. The Levenberg-Marquardt algorithm, having the greatest accuracy and speed, could be considered as the first choice in electron dose map inversion.Further tests show that more error would be created when the data close to the electron range was used (tail error). The tail error might be caused by the approximation of mean energy spectra, and this should be considered to improve the method. The time-saving and accurate algorithms could be used to achieve real-time dose map inversion. By selecting the best inversion algorithm, the clinical need in real-time dose verification can be satisfied. (authors)

  15. Conditioning the full-waveform inversion gradient to welcome anisotropy

    KAUST Repository

    Alkhalifah, Tariq Ali

    2015-01-01

    Multiparameter full-waveform inversion (FWI) suffers from complex nonlinearity in the objective function, compounded by the eventual trade-off between the model parameters. A hierarchical approach based on frequency and arrival time data decimation

  16. Integration of GIS, Geostatistics, and 3-D Technology to Assess the Spatial Distribution of Soil Moisture

    Science.gov (United States)

    Betts, M.; Tsegaye, T.; Tadesse, W.; Coleman, T. L.; Fahsi, A.

    1998-01-01

    The spatial and temporal distribution of near surface soil moisture is of fundamental importance to many physical, biological, biogeochemical, and hydrological processes. However, knowledge of these space-time dynamics and the processes which control them remains unclear. The integration of geographic information systems (GIS) and geostatistics together promise a simple mechanism to evaluate and display the spatial and temporal distribution of this vital hydrologic and physical variable. Therefore, this research demonstrates the use of geostatistics and GIS to predict and display soil moisture distribution under vegetated and non-vegetated plots. The research was conducted at the Winfred Thomas Agricultural Experiment Station (WTAES), Hazel Green, Alabama. Soil moisture measurement were done on a 10 by 10 m grid from tall fescue grass (GR), alfalfa (AA), bare rough (BR), and bare smooth (BS) plots. Results indicated that variance associated with soil moisture was higher for vegetated plots than non-vegetated plots. The presence of vegetation in general contributed to the spatial variability of soil moisture. Integration of geostatistics and GIS can improve the productivity of farm lands and the precision of farming.

  17. Geostatistical analyses and hazard assessment on soil lead in Silvermines area, Ireland

    International Nuclear Information System (INIS)

    McGrath, David; Zhang Chaosheng; Carton, Owen T.

    2004-01-01

    Spatial distribution and hazard assessment of soil lead in the mining site of Silvermines, Ireland, were investigated using statistics, geostatistics and geographic information system (GIS) techniques. Positively skewed distribution and possible outlying values of Pb and other heavy metals were observed. Box-Cox transformation was applied in order to achieve normality in the data set and to reduce the effect of outliers. Geostatistical analyses were carried out, including calculation of experimental variograms and model fitting. The ordinary point kriging estimates of Pb concentration were mapped. Kriging standard deviations were regarded as the standard deviations of the interpolated pixel values, and a second map was produced, that quantified the probability of Pb concentration higher than a threshold value of 1000 mg/kg. These maps provide valuable information for hazard assessment and for decision support. - A probability map was produced that was useful for hazard assessment and decision support

  18. Geostatistical analyses and hazard assessment on soil lead in Silvermines area, Ireland

    Energy Technology Data Exchange (ETDEWEB)

    McGrath, David; Zhang Chaosheng; Carton, Owen T

    2004-01-01

    Spatial distribution and hazard assessment of soil lead in the mining site of Silvermines, Ireland, were investigated using statistics, geostatistics and geographic information system (GIS) techniques. Positively skewed distribution and possible outlying values of Pb and other heavy metals were observed. Box-Cox transformation was applied in order to achieve normality in the data set and to reduce the effect of outliers. Geostatistical analyses were carried out, including calculation of experimental variograms and model fitting. The ordinary point kriging estimates of Pb concentration were mapped. Kriging standard deviations were regarded as the standard deviations of the interpolated pixel values, and a second map was produced, that quantified the probability of Pb concentration higher than a threshold value of 1000 mg/kg. These maps provide valuable information for hazard assessment and for decision support. - A probability map was produced that was useful for hazard assessment and decision support.

  19. Two-point versus multiple-point geostatistics: the ability of geostatistical methods to capture complex geobodies and their facies associations—an application to a channelized carbonate reservoir, southwest Iran

    International Nuclear Information System (INIS)

    Hashemi, Seyyedhossein; Javaherian, Abdolrahim; Ataee-pour, Majid; Khoshdel, Hossein

    2014-01-01

    Facies models try to explain facies architectures which have a primary control on the subsurface heterogeneities and the fluid flow characteristics of a given reservoir. In the process of facies modeling, geostatistical methods are implemented to integrate different sources of data into a consistent model. The facies models should describe facies interactions; the shape and geometry of the geobodies as they occur in reality. Two distinct categories of geostatistical techniques are two-point and multiple-point (geo) statistics (MPS). In this study, both of the aforementioned categories were applied to generate facies models. A sequential indicator simulation (SIS) and a truncated Gaussian simulation (TGS) represented two-point geostatistical methods, and a single normal equation simulation (SNESIM) selected as an MPS simulation representative. The dataset from an extremely channelized carbonate reservoir located in southwest Iran was applied to these algorithms to analyze their performance in reproducing complex curvilinear geobodies. The SNESIM algorithm needs consistent training images (TI) in which all possible facies architectures that are present in the area are included. The TI model was founded on the data acquired from modern occurrences. These analogies delivered vital information about the possible channel geometries and facies classes that are typically present in those similar environments. The MPS results were conditioned to both soft and hard data. Soft facies probabilities were acquired from a neural network workflow. In this workflow, seismic-derived attributes were implemented as the input data. Furthermore, MPS realizations were conditioned to hard data to guarantee the exact positioning and continuity of the channel bodies. A geobody extraction workflow was implemented to extract the most certain parts of the channel bodies from the seismic data. These extracted parts of the channel bodies were applied to the simulation workflow as hard data

  20. Geostatistical Investigations of Displacements on the Basis of Data from the Geodetic Monitoring of a Hydrotechnical Object

    Science.gov (United States)

    Namysłowska-Wilczyńska, Barbara; Wynalek, Janusz

    2017-12-01

    ) were obtained for selected years (1995 and 2007), taking the ground height 136 m a.s.l. into calculation. To calculate raster maps of Z* interpolated values, methods of quick interpolation were also used, such as the technique of the inverse distance squares, a linear model of kriging, a spline kriging, which made the recognition of the general background of displacements possible, without the accuracy assessment of Z* value estimation, i.e., the value of σk. These maps are also related to 1995 and 2007 and the elevation. As a result of applying these techniques, clear boundaries of subsiding areas, upthrusting and also horizontal displacements on the examined hydrotechnical object were marked out, which can be interpreted as areas of local deformations of the object, important for the safety of the construction. The effect of geostatistical research conducted, including the structural analysis, semivariograms modeling, estimating the displacements of the hydrotechnical object, are rich cartographic characteristic (semivariograms, raster maps, block diagrams), which present the spatial visualization of the conducted various analyses of the monitored displacements. The prepared geostatistical model (3D) of displacement variability (analysed within the area of the dam, during its operating period and including its height) will be useful not only in the correct assessment of displacements and deformations, but it will also make it possible to forecast these phenomena, which is crucial when the operating safety of such constructions is taken into account.

  1. Frequency-domain waveform inversion using the unwrapped phase

    KAUST Repository

    Choi, Yun Seok

    2011-01-01

    Phase wrapping in the frequency-domain (or cycle skipping in the time-domain) is the major cause of the local minima problem in the waveform inversion. The unwrapped phase has the potential to provide us with a robust and reliable waveform inversion, with reduced local minima. We propose a waveform inversion algorithm using the unwrapped phase objective function in the frequency-domain. The unwrapped phase, or what we call the instantaneous traveltime, is given by the imaginary part of dividing the derivative of the wavefield with respect to the angular frequency by the wavefield itself. As a result, the objective function is given a traveltime-like function, which allows us to smooth it and reduce its nonlinearity. The gradient of the objective function is computed using the back-propagation algorithm based on the adjoint-state technique. We apply both our waveform inversion algorithm using the unwrapped phase and the conventional waveform inversion and show that our inversion algorithm gives better convergence to the true model than the conventional waveform inversion. © 2011 Society of Exploration Geophysicists.

  2. Evaluation of geostatistical parameters based on well tests; Estimation de parametres geostatistiques a partir de tests de puits

    Energy Technology Data Exchange (ETDEWEB)

    Gauthier, Y.

    1997-10-20

    Geostatistical tools are increasingly used to model permeability fields in subsurface reservoirs, which are considered as a particular random variable development depending of several geostatistical parameters such as variance and correlation length. The first part of the thesis is devoted to the study of relations existing between the transient well pressure (the well test) and the stochastic permeability field, using the apparent permeability concept.The well test performs a moving permeability average over larger and larger volume with increasing time. In the second part, the geostatistical parameters are evaluated using well test data; a Bayesian framework is used and parameters are estimated using the maximum likelihood principle by maximizing the well test data probability density function with respect to these parameters. This method, involving a well test fast evaluation, provides an estimation of the correlation length and the variance over different realizations of a two-dimensional permeability field

  3. Convergence of Chahine's nonlinear relaxation inversion method used for limb viewing remote sensing

    Science.gov (United States)

    Chu, W. P.

    1985-01-01

    The application of Chahine's (1970) inversion technique to remote sensing problems utilizing the limb viewing geometry is discussed. The problem considered here involves occultation-type measurements and limb radiance-type measurements from either spacecraft or balloon platforms. The kernel matrix of the inversion problem is either an upper or lower triangular matrix. It is demonstrated that the Chahine inversion technique always converges, provided the diagonal elements of the kernel matrix are nonzero.

  4. The Volterra's integral equation theory for accelerator single-freedom nonlinear components

    International Nuclear Information System (INIS)

    Wang Sheng; Xie Xi

    1996-01-01

    The Volterra's integral equation equivalent to the dynamic equation of accelerator single-freedom nonlinear components is given, starting from which the transport operator of accelerator single-freedom nonlinear components and its inverse transport operator are obtained. Therefore, another algorithm for the expert system of the beam transport operator of accelerator single-freedom nonlinear components is developed

  5. Solving probabilistic inverse problems rapidly with prior samples

    NARCIS (Netherlands)

    Käufl, Paul; Valentine, Andrew P.; de Wit, Ralph W.; Trampert, Jeannot

    2016-01-01

    Owing to the increasing availability of computational resources, in recent years the probabilistic solution of non-linear, geophysical inverse problems by means of sampling methods has become increasingly feasible. Nevertheless, we still face situations in which a Monte Carlo approach is not

  6. Robust 1D inversion and analysis of helicopter electromagnetic (HEM) data

    DEFF Research Database (Denmark)

    Tølbøll, R.J.; Christensen, N.B.

    2006-01-01

    but can resolve layer boundary to a depth of more than 100 m. Modeling experiments also show that the effect of altimeter errors on the inversion results is serious. We suggest a new interpretation scheme for HEM data founded solely on full nonlinear 1D inversion and providing layered-earth models...... supported by datamisfit parameters and a quantitative model-parameter analysis. The backbone of the scheme is the removal of cultural coupling effects followed by a multilayer inversion that in turn provides reliable starting models for a subsequent few-layer inversion. A new procedure for correlation...

  7. Neural network based adaptive control for nonlinear dynamic regimes

    Science.gov (United States)

    Shin, Yoonghyun

    Adaptive control designs using neural networks (NNs) based on dynamic inversion are investigated for aerospace vehicles which are operated at highly nonlinear dynamic regimes. NNs play a key role as the principal element of adaptation to approximately cancel the effect of inversion error, which subsequently improves robustness to parametric uncertainty and unmodeled dynamics in nonlinear regimes. An adaptive control scheme previously named 'composite model reference adaptive control' is further developed so that it can be applied to multi-input multi-output output feedback dynamic inversion. It can have adaptive elements in both the dynamic compensator (linear controller) part and/or in the conventional adaptive controller part, also utilizing state estimation information for NN adaptation. This methodology has more flexibility and thus hopefully greater potential than conventional adaptive designs for adaptive flight control in highly nonlinear flight regimes. The stability of the control system is proved through Lyapunov theorems, and validated with simulations. The control designs in this thesis also include the use of 'pseudo-control hedging' techniques which are introduced to prevent the NNs from attempting to adapt to various actuation nonlinearities such as actuator position and rate saturations. Control allocation is introduced for the case of redundant control effectors including thrust vectoring nozzles. A thorough comparison study of conventional and NN-based adaptive designs for a system under a limit cycle, wing-rock, is included in this research, and the NN-based adaptive control designs demonstrate their performances for two highly maneuverable aerial vehicles, NASA F-15 ACTIVE and FQM-117B unmanned aerial vehicle (UAV), operated under various nonlinearities and uncertainties.

  8. Spatial analysis of groundwater levels using Fuzzy Logic and geostatistical tools

    Science.gov (United States)

    Theodoridou, P. G.; Varouchakis, E. A.; Karatzas, G. P.

    2017-12-01

    The spatial variability evaluation of the water table of an aquifer provides useful information in water resources management plans. Geostatistical methods are often employed to map the free surface of an aquifer. In geostatistical analysis using Kriging techniques the selection of the optimal variogram is very important for the optimal method performance. This work compares three different criteria to assess the theoretical variogram that fits to the experimental one: the Least Squares Sum method, the Akaike Information Criterion and the Cressie's Indicator. Moreover, variable distance metrics such as the Euclidean, Minkowski, Manhattan, Canberra and Bray-Curtis are applied to calculate the distance between the observation and the prediction points, that affects both the variogram calculation and the Kriging estimator. A Fuzzy Logic System is then applied to define the appropriate neighbors for each estimation point used in the Kriging algorithm. The two criteria used during the Fuzzy Logic process are the distance between observation and estimation points and the groundwater level value at each observation point. The proposed techniques are applied to a data set of 250 hydraulic head measurements distributed over an alluvial aquifer. The analysis showed that the Power-law variogram model and Manhattan distance metric within ordinary kriging provide the best results when the comprehensive geostatistical analysis process is applied. On the other hand, the Fuzzy Logic approach leads to a Gaussian variogram model and significantly improves the estimation performance. The two different variogram models can be explained in terms of a fractional Brownian motion approach and of aquifer behavior at local scale. Finally, maps of hydraulic head spatial variability and of predictions uncertainty are constructed for the area with the two different approaches comparing their advantages and drawbacks.

  9. Applicability of geostatistical procedures for the evaluation of hydrogeological parameters of a fractured aquifer in the Ronneburg mine district

    International Nuclear Information System (INIS)

    Grasshoff, C.; Schetelig, K.; Tomschi, H.

    1998-01-01

    The following paper demonstrates, how a geostatistical approach can help interpolating hydrogeological parameters over a certain area. The basic elements developed by G. Matheron in the sixties are represented as the preconditions and assumptions, which provide the best results of the estimation. The variogram as the most important tool in geostatistics offers the opportunity to describe the correlating behaviour of a regionalized variable. Some kriging procedures are briefly introduced, which provide under varying circumstances estimating of non-measured values with the theoretical variogram-model. In the Ronneburg mine district 108 screened drill-holes could provide coefficients of hydraulic conductivity. These were interpolated with ordinary kriging over the whole investigation area. An error calculation was performed, which could prove the accuracy of the estimation. Short prospects point out some difficulties handling with geostatistic procedures and make suggestions for further investigations. (orig.) [de

  10. Inverse scattering problems with multi-frequencies

    International Nuclear Information System (INIS)

    Bao, Gang; Li, Peijun; Lin, Junshan; Triki, Faouzi

    2015-01-01

    This paper is concerned with computational approaches and mathematical analysis for solving inverse scattering problems in the frequency domain. The problems arise in a diverse set of scientific areas with significant industrial, medical, and military applications. In addition to nonlinearity, there are two common difficulties associated with the inverse problems: ill-posedness and limited resolution (diffraction limit). Due to the diffraction limit, for a given frequency, only a low spatial frequency part of the desired parameter can be observed from measurements in the far field. The main idea developed here is that if the reconstruction is restricted to only the observable part, then the inversion will become stable. The challenging task is how to design stable numerical methods for solving these inverse scattering problems inspired by the diffraction limit. Recently, novel recursive linearization based algorithms have been presented in an attempt to answer the above question. These methods require multi-frequency scattering data and proceed via a continuation procedure with respect to the frequency from low to high. The objective of this paper is to give a brief review of these methods, their error estimates, and the related mathematical analysis. More attention is paid to the inverse medium and inverse source problems. Numerical experiments are included to illustrate the effectiveness of these methods. (topical review)

  11. Redesigning rain gauges network in Johor using geostatistics and simulated annealing

    International Nuclear Information System (INIS)

    Aziz, Mohd Khairul Bazli Mohd; Yusof, Fadhilah; Daud, Zalina Mohd; Yusop, Zulkifli; Kasno, Mohammad Afif

    2015-01-01

    Recently, many rainfall network design techniques have been developed, discussed and compared by many researchers. Present day hydrological studies require higher levels of accuracy from collected data. In numerous basins, the rain gauge stations are located without clear scientific understanding. In this study, an attempt is made to redesign rain gauge network for Johor, Malaysia in order to meet the required level of accuracy preset by rainfall data users. The existing network of 84 rain gauges in Johor is optimized and redesigned into a new locations by using rainfall, humidity, solar radiation, temperature and wind speed data collected during the monsoon season (November - February) of 1975 until 2008. This study used the combination of geostatistics method (variance-reduction method) and simulated annealing as the algorithm of optimization during the redesigned proses. The result shows that the new rain gauge location provides minimum value of estimated variance. This shows that the combination of geostatistics method (variance-reduction method) and simulated annealing is successful in the development of the new optimum rain gauge system

  12. Redesigning rain gauges network in Johor using geostatistics and simulated annealing

    Science.gov (United States)

    Aziz, Mohd Khairul Bazli Mohd; Yusof, Fadhilah; Daud, Zalina Mohd; Yusop, Zulkifli; Kasno, Mohammad Afif

    2015-02-01

    Recently, many rainfall network design techniques have been developed, discussed and compared by many researchers. Present day hydrological studies require higher levels of accuracy from collected data. In numerous basins, the rain gauge stations are located without clear scientific understanding. In this study, an attempt is made to redesign rain gauge network for Johor, Malaysia in order to meet the required level of accuracy preset by rainfall data users. The existing network of 84 rain gauges in Johor is optimized and redesigned into a new locations by using rainfall, humidity, solar radiation, temperature and wind speed data collected during the monsoon season (November - February) of 1975 until 2008. This study used the combination of geostatistics method (variance-reduction method) and simulated annealing as the algorithm of optimization during the redesigned proses. The result shows that the new rain gauge location provides minimum value of estimated variance. This shows that the combination of geostatistics method (variance-reduction method) and simulated annealing is successful in the development of the new optimum rain gauge system.

  13. Redesigning rain gauges network in Johor using geostatistics and simulated annealing

    Energy Technology Data Exchange (ETDEWEB)

    Aziz, Mohd Khairul Bazli Mohd, E-mail: mkbazli@yahoo.com [Centre of Preparatory and General Studies, TATI University College, 24000 Kemaman, Terengganu, Malaysia and Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor (Malaysia); Yusof, Fadhilah, E-mail: fadhilahy@utm.my [Department of Mathematical Sciences, Faculty of Science, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor (Malaysia); Daud, Zalina Mohd, E-mail: zalina@ic.utm.my [UTM Razak School of Engineering and Advanced Technology, Universiti Teknologi Malaysia, UTM KL, 54100 Kuala Lumpur (Malaysia); Yusop, Zulkifli, E-mail: zulyusop@utm.my [Institute of Environmental and Water Resource Management (IPASA), Faculty of Civil Engineering, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor (Malaysia); Kasno, Mohammad Afif, E-mail: mafifkasno@gmail.com [Malaysia - Japan International Institute of Technology (MJIIT), Universiti Teknologi Malaysia, UTM KL, 54100 Kuala Lumpur (Malaysia)

    2015-02-03

    Recently, many rainfall network design techniques have been developed, discussed and compared by many researchers. Present day hydrological studies require higher levels of accuracy from collected data. In numerous basins, the rain gauge stations are located without clear scientific understanding. In this study, an attempt is made to redesign rain gauge network for Johor, Malaysia in order to meet the required level of accuracy preset by rainfall data users. The existing network of 84 rain gauges in Johor is optimized and redesigned into a new locations by using rainfall, humidity, solar radiation, temperature and wind speed data collected during the monsoon season (November - February) of 1975 until 2008. This study used the combination of geostatistics method (variance-reduction method) and simulated annealing as the algorithm of optimization during the redesigned proses. The result shows that the new rain gauge location provides minimum value of estimated variance. This shows that the combination of geostatistics method (variance-reduction method) and simulated annealing is successful in the development of the new optimum rain gauge system.

  14. Experimental validation of GADRAS's coupled neutron-photon inverse radiation transport solver

    International Nuclear Information System (INIS)

    Mattingly, John K.; Mitchell, Dean James; Harding, Lee T.

    2010-01-01

    Sandia National Laboratories has developed an inverse radiation transport solver that applies nonlinear regression to coupled neutron-photon deterministic transport models. The inverse solver uses nonlinear regression to fit a radiation transport model to gamma spectrometry and neutron multiplicity counting measurements. The subject of this paper is the experimental validation of that solver. This paper describes a series of experiments conducted with a 4.5 kg sphere of α-phase, weapons-grade plutonium. The source was measured bare and reflected by high-density polyethylene (HDPE) spherical shells with total thicknesses between 1.27 and 15.24 cm. Neutron and photon emissions from the source were measured using three instruments: a gross neutron counter, a portable neutron multiplicity counter, and a high-resolution gamma spectrometer. These measurements were used as input to the inverse radiation transport solver to evaluate the solver's ability to correctly infer the configuration of the source from its measured radiation signatures.

  15. Bayesian Geostatistical Modeling of Malaria Indicator Survey Data in Angola

    Science.gov (United States)

    Gosoniu, Laura; Veta, Andre Mia; Vounatsou, Penelope

    2010-01-01

    The 2006–2007 Angola Malaria Indicator Survey (AMIS) is the first nationally representative household survey in the country assessing coverage of the key malaria control interventions and measuring malaria-related burden among children under 5 years of age. In this paper, the Angolan MIS data were analyzed to produce the first smooth map of parasitaemia prevalence based on contemporary nationwide empirical data in the country. Bayesian geostatistical models were fitted to assess the effect of interventions after adjusting for environmental, climatic and socio-economic factors. Non-linear relationships between parasitaemia risk and environmental predictors were modeled by categorizing the covariates and by employing two non-parametric approaches, the B-splines and the P-splines. The results of the model validation showed that the categorical model was able to better capture the relationship between parasitaemia prevalence and the environmental factors. Model fit and prediction were handled within a Bayesian framework using Markov chain Monte Carlo (MCMC) simulations. Combining estimates of parasitaemia prevalence with the number of children under we obtained estimates of the number of infected children in the country. The population-adjusted prevalence ranges from in Namibe province to in Malanje province. The odds of parasitaemia in children living in a household with at least ITNs per person was by 41% lower (CI: 14%, 60%) than in those with fewer ITNs. The estimates of the number of parasitaemic children produced in this paper are important for planning and implementing malaria control interventions and for monitoring the impact of prevention and control activities. PMID:20351775

  16. Nonlinear waves and weak turbulence

    CERN Document Server

    Zakharov, V E

    1997-01-01

    This book is a collection of papers on dynamical and statistical theory of nonlinear wave propagation in dispersive conservative media. Emphasis is on waves on the surface of an ideal fluid and on Rossby waves in the atmosphere. Although the book deals mainly with weakly nonlinear waves, it is more than simply a description of standard perturbation techniques. The goal is to show that the theory of weakly interacting waves is naturally related to such areas of mathematics as Diophantine equations, differential geometry of waves, Poincaré normal forms, and the inverse scattering method.

  17. Towards adjoint-based inversion of time-dependent mantle convection with nonlinear viscosity

    Science.gov (United States)

    Li, Dunzhu; Gurnis, Michael; Stadler, Georg

    2017-04-01

    We develop and study an adjoint-based inversion method for the simultaneous recovery of initial temperature conditions and viscosity parameters in time-dependent mantle convection from the current mantle temperature and historic plate motion. Based on a realistic rheological model with temperature-dependent and strain-rate-dependent viscosity, we formulate the inversion as a PDE-constrained optimization problem. The objective functional includes the misfit of surface velocity (plate motion) history, the misfit of the current mantle temperature, and a regularization for the uncertain initial condition. The gradient of this functional with respect to the initial temperature and the uncertain viscosity parameters is computed by solving the adjoint of the mantle convection equations. This gradient is used in a pre-conditioned quasi-Newton minimization algorithm. We study the prospects and limitations of the inversion, as well as the computational performance of the method using two synthetic problems, a sinking cylinder and a realistic subduction model. The subduction model is characterized by the migration of a ridge toward a trench whereby both plate motions and subduction evolve. The results demonstrate: (1) for known viscosity parameters, the initial temperature can be well recovered, as in previous initial condition-only inversions where the effective viscosity was given; (2) for known initial temperature, viscosity parameters can be recovered accurately, despite the existence of trade-offs due to ill-conditioning; (3) for the joint inversion of initial condition and viscosity parameters, initial condition and effective viscosity can be reasonably recovered, but the high dimension of the parameter space and the resulting ill-posedness may limit recovery of viscosity parameters.

  18. Topics in nonlinear wave theory with applications

    International Nuclear Information System (INIS)

    Tracy, E.R.

    1984-01-01

    Selected topics in nonlinear wave theory are discussed, and applications to the study of modulational instabilities are presented. A historical survey is given of topics relating to solitons and modulational problems. A method is then presented for generating exact periodic and quasi-periodic solutions to several nonlinear wave equations, which have important physical applications. The method is then specialized for the purposes of studying the modulational instability of a plane wave solution of the nonlinear Schroedinger equation, an equation with general applicability in one-dimensional modulational problems. Some numerical results obtained in conjunction with the analytic study are presented. The analytic approach explains the recurrence phenomena seen in the numerical studies, and the numerical work of other authors. The method of solution (related to the inverse scattering method) is then analyzed within the context of Hamiltonian dynamics where it is shown that the method can be viewed as simply a pair of canonical transformations. The Abel Transformation, which appears here and in the work of other authors, is shown to be a special form of Liouville's transformation to action-angle variables. The construction of closed form solutions of these nonlinear wave equations, via the solution of Jacobi's inversion problem, is surveyed briefly

  19. Stochastic forward and inverse groundwater flow and solute transport modeling

    NARCIS (Netherlands)

    Janssen, G.M.C.M.

    2008-01-01

    Keywords: calibration, inverse modeling, stochastic modeling, nonlinear biodegradation, stochastic-convective, advective-dispersive, travel time, network design, non-Gaussian distribution, multimodal distribution, representers

    This thesis offers three new approaches that contribute

  20. Adaptive dynamic inversion robust control for BTT missile based on wavelet neural network

    Science.gov (United States)

    Li, Chuanfeng; Wang, Yongji; Deng, Zhixiang; Wu, Hao

    2009-10-01

    A new nonlinear control strategy incorporated the dynamic inversion method with wavelet neural networks is presented for the nonlinear coupling system of Bank-to-Turn(BTT) missile in reentry phase. The basic control law is designed by using the dynamic inversion feedback linearization method, and the online learning wavelet neural network is used to compensate the inversion error due to aerodynamic parameter errors, modeling imprecise and external disturbance in view of the time-frequency localization properties of wavelet transform. Weights adjusting laws are derived according to Lyapunov stability theory, which can guarantee the boundedness of all signals in the whole system. Furthermore, robust stability of the closed-loop system under this tracking law is proved. Finally, the six degree-of-freedom(6DOF) simulation results have shown that the attitude angles can track the anticipant command precisely under the circumstances of existing external disturbance and in the presence of parameter uncertainty. It means that the dependence on model by dynamic inversion method is reduced and the robustness of control system is enhanced by using wavelet neural network(WNN) to reconstruct inversion error on-line.

  1. Geostatistical radar-raingauge combination with nonparametric correlograms: methodological considerations and application in Switzerland

    Science.gov (United States)

    Schiemann, R.; Erdin, R.; Willi, M.; Frei, C.; Berenguer, M.; Sempere-Torres, D.

    2011-05-01

    Modelling spatial covariance is an essential part of all geostatistical methods. Traditionally, parametric semivariogram models are fit from available data. More recently, it has been suggested to use nonparametric correlograms obtained from spatially complete data fields. Here, both estimation techniques are compared. Nonparametric correlograms are shown to have a substantial negative bias. Nonetheless, when combined with the sample variance of the spatial field under consideration, they yield an estimate of the semivariogram that is unbiased for small lag distances. This justifies the use of this estimation technique in geostatistical applications. Various formulations of geostatistical combination (Kriging) methods are used here for the construction of hourly precipitation grids for Switzerland based on data from a sparse realtime network of raingauges and from a spatially complete radar composite. Two variants of Ordinary Kriging (OK) are used to interpolate the sparse gauge observations. In both OK variants, the radar data are only used to determine the semivariogram model. One variant relies on a traditional parametric semivariogram estimate, whereas the other variant uses the nonparametric correlogram. The variants are tested for three cases and the impact of the semivariogram model on the Kriging prediction is illustrated. For the three test cases, the method using nonparametric correlograms performs equally well or better than the traditional method, and at the same time offers great practical advantages. Furthermore, two variants of Kriging with external drift (KED) are tested, both of which use the radar data to estimate nonparametric correlograms, and as the external drift variable. The first KED variant has been used previously for geostatistical radar-raingauge merging in Catalonia (Spain). The second variant is newly proposed here and is an extension of the first. Both variants are evaluated for the three test cases as well as an extended evaluation

  2. A geostatistical estimation of zinc grade in bore-core samples

    International Nuclear Information System (INIS)

    Starzec, A.

    1987-01-01

    Possibilities and preliminary results of geostatistical interpretation of the XRF determination of zinc in bore-core samples are considered. For the spherical model of the variogram the estimation variance of grade in a disk-shape sample (estimated from the grade on the circumference sample) is calculated. Variograms of zinc grade in core samples are presented and examples of the grade estimation are discussed. 4 refs., 7 figs., 1 tab. (author)

  3. Geostatistical simulations for radon indoor with a nested model including the housing factor.

    Science.gov (United States)

    Cafaro, C; Giovani, C; Garavaglia, M

    2016-01-01

    The radon prone areas definition is matter of many researches in radioecology, since radon is considered a leading cause of lung tumours, therefore the authorities ask for support to develop an appropriate sanitary prevention strategy. In this paper, we use geostatistical tools to elaborate a definition accounting for some of the available information about the dwellings. Co-kriging is the proper interpolator used in geostatistics to refine the predictions by using external covariates. In advance, co-kriging is not guaranteed to improve significantly the results obtained by applying the common lognormal kriging. Here, instead, such multivariate approach leads to reduce the cross-validation residual variance to an extent which is deemed as satisfying. Furthermore, with the application of Monte Carlo simulations, the paradigm provides a more conservative radon prone areas definition than the one previously made by lognormal kriging. Copyright © 2015 Elsevier Ltd. All rights reserved.

  4. Geostatistical Spatio-Time model of crime in el Salvador: Structural and Predictive Analysis

    Directory of Open Access Journals (Sweden)

    Welman Rosa Alvarado

    2011-07-01

    Full Text Available Today, to study a geospatial and spatio-temporal phenomena requires searching statistical tools that enable the analysis of the dependency of space, time and interactions. The science that studies this kind of subjects is the Geoestatics which the goal is to predict spatial phenomenon. This science is considered the base for modeling phenomena that involves interactions between space and time. In the past 10 years, the Geostatistic had seen a great development in areas like the geology, soils, remote sensing, epidemiology, agriculture, ecology, economy, etc. In this research, the geostatistic had been apply to build a predictive map about crime in El Salvador; for that the variability of space and time together is studied to generate crime scenarios: crime hot spots are determined, crime vulnerable groups are identified, to improve political decisions and facilitate to decision makers about the insecurity in the country.

  5. MARE2DEM: a 2-D inversion code for controlled-source electromagnetic and magnetotelluric data

    Science.gov (United States)

    Key, Kerry

    2016-10-01

    This work presents MARE2DEM, a freely available code for 2-D anisotropic inversion of magnetotelluric (MT) data and frequency-domain controlled-source electromagnetic (CSEM) data from onshore and offshore surveys. MARE2DEM parametrizes the inverse model using a grid of arbitrarily shaped polygons, where unstructured triangular or quadrilateral grids are typically used due to their ease of construction. Unstructured grids provide significantly more geometric flexibility and parameter efficiency than the structured rectangular grids commonly used by most other inversion codes. Transmitter and receiver components located on topographic slopes can be tilted parallel to the boundary so that the simulated electromagnetic fields accurately reproduce the real survey geometry. The forward solution is implemented with a goal-oriented adaptive finite-element method that automatically generates and refines unstructured triangular element grids that conform to the inversion parameter grid, ensuring accurate responses as the model conductivity changes. This dual-grid approach is significantly more efficient than the conventional use of a single grid for both the forward and inverse meshes since the more detailed finite-element meshes required for accurate responses do not increase the memory requirements of the inverse problem. Forward solutions are computed in parallel with a highly efficient scaling by partitioning the data into smaller independent modeling tasks consisting of subsets of the input frequencies, transmitters and receivers. Non-linear inversion is carried out with a new Occam inversion approach that requires fewer forward calls. Dense matrix operations are optimized for memory and parallel scalability using the ScaLAPACK parallel library. Free parameters can be bounded using a new non-linear transformation that leaves the transformed parameters nearly the same as the original parameters within the bounds, thereby reducing non-linear smoothing effects. Data

  6. Adaptive Inverse Optimal Control for Rehabilitation Robot Systems Using Actor-Critic Algorithm

    Directory of Open Access Journals (Sweden)

    Fancheng Meng

    2014-01-01

    Full Text Available The higher goal of rehabilitation robot is to aid a person to achieve a desired functional task (e.g., tracking trajectory based on assisted-as-needed principle. To this goal, a new adaptive inverse optimal hybrid control (AHC combining inverse optimal control and actor-critic learning is proposed. Specifically, an uncertain nonlinear rehabilitation robot model is firstly developed that includes human motor behavior dynamics. Then, based on this model, an open-loop error system is formed; thereafter, an inverse optimal control input is designed to minimize the cost functional and a NN-based actor-critic feedforward signal is responsible for the nonlinear dynamic part contaminated by uncertainties. Finally, the AHC controller is proven (through a Lyapunov-based stability analysis to yield a global uniformly ultimately bounded stability result, and the resulting cost functional is meaningful. Simulation and experiment on rehabilitation robot demonstrate the effectiveness of the proposed control scheme.

  7. Approximate 2D inversion of airborne TEM data

    DEFF Research Database (Denmark)

    Christensen, N.B.; Wolfgram, Peter

    2006-01-01

    We propose an approximate two-dimensional inversion procedure for transient electromagnetic data. The method is a two-stage procedure, where data are first inverted with 1D multi-layer models. The 1D model section is then considered as data for the next inversion stage that produces the 2D model...... section. For moving platform data there is translational invariance and the second part of the inversion becomes a deconvolution. The convolution kernels are computed by perturbing one model element in an otherwise homogeneous 2D section and calculating full nonlinear responses. These responses...... are then inverted with 1D models to produce a 1D model section. This section is the convolution kernel for the deconvolution. Within its limitations, the approximate 2D inversion performs well. Theoretical modeling shows that it delivers model sections that are a definite improvement over 1D model sections...

  8. A Resampling-Based Stochastic Approximation Method for Analysis of Large Geostatistical Data

    KAUST Repository

    Liang, Faming

    2013-03-01

    The Gaussian geostatistical model has been widely used in modeling of spatial data. However, it is challenging to computationally implement this method because it requires the inversion of a large covariance matrix, particularly when there is a large number of observations. This article proposes a resampling-based stochastic approximation method to address this challenge. At each iteration of the proposed method, a small subsample is drawn from the full dataset, and then the current estimate of the parameters is updated accordingly under the framework of stochastic approximation. Since the proposed method makes use of only a small proportion of the data at each iteration, it avoids inverting large covariance matrices and thus is scalable to large datasets. The proposed method also leads to a general parameter estimation approach, maximum mean log-likelihood estimation, which includes the popular maximum (log)-likelihood estimation (MLE) approach as a special case and is expected to play an important role in analyzing large datasets. Under mild conditions, it is shown that the estimator resulting from the proposed method converges in probability to a set of parameter values of equivalent Gaussian probability measures, and that the estimator is asymptotically normally distributed. To the best of the authors\\' knowledge, the present study is the first one on asymptotic normality under infill asymptotics for general covariance functions. The proposed method is illustrated with large datasets, both simulated and real. Supplementary materials for this article are available online. © 2013 American Statistical Association.

  9. Nonlinear silicon photonics

    Science.gov (United States)

    Tsia, Kevin K.; Jalali, Bahram

    2010-05-01

    An intriguing optical property of silicon is that it exhibits a large third-order optical nonlinearity, with orders-ofmagnitude larger than that of silica glass in the telecommunication band. This allows efficient nonlinear optical interaction at relatively low power levels in a small footprint. Indeed, we have witnessed a stunning progress in harnessing the Raman and Kerr effects in silicon as the mechanisms for enabling chip-scale optical amplification, lasing, and wavelength conversion - functions that until recently were perceived to be beyond the reach of silicon. With all the continuous efforts developing novel techniques, nonlinear silicon photonics is expected to be able to reach even beyond the prior achievements. Instead of providing a comprehensive overview of this field, this manuscript highlights a number of new branches of nonlinear silicon photonics, which have not been fully recognized in the past. In particular, they are two-photon photovoltaic effect, mid-wave infrared (MWIR) silicon photonics, broadband Raman effects, inverse Raman scattering, and periodically-poled silicon (PePSi). These novel effects and techniques could create a new paradigm for silicon photonics and extend its utility beyond the traditionally anticipated applications.

  10. Image processing with a cellular nonlinear network

    International Nuclear Information System (INIS)

    Morfu, S.

    2005-01-01

    A cellular nonlinear network (CNN) based on uncoupled nonlinear oscillators is proposed for image processing purposes. It is shown theoretically and numerically that the contrast of an image loaded at the nodes of the CNN is strongly enhanced, even if this one is initially weak. An image inversion can be also obtained without reconfiguration of the network whereas a gray levels extraction can be performed with an additional threshold filtering. Lastly, an electronic implementation of this CNN is presented

  11. Geostatistical and GIS analysis of the spatial variability of alluvial gold content in Ngoura-Colomines area, Eastern Cameroon: Implications for the exploration of primary gold deposit

    Science.gov (United States)

    Takodjou Wambo, Jonas Didero; Ganno, Sylvestre; Djonthu Lahe, Yannick Sthopira; Kouankap Nono, Gus Djibril; Fossi, Donald Hermann; Tchouatcha, Milan Stafford; Nzenti, Jean Paul

    2018-06-01

    Linear and nonlinear geostatistic is commonly used in ore grade estimation and seldom used in Geographical Information System (GIS) technology. In this study, we suggest an approach based on geostatistic linear ordinary kriging (OK) and Geographical Information System (GIS) techniques to investigate the spatial distribution of alluvial gold content, mineralized and gangue layers thicknesses from 73 pits at the Ngoura-Colomines area with the aim to determine controlling factors for the spatial distribution of mineralization and delineate the most prospective area for primary gold mineralization. Gold content varies between 0.1 and 4.6 g/m3 and has been broadly grouped into three statistical classes. These classes have been spatially subdivided into nine zones using ordinary kriging model based on physical and topographical characteristics. Both mineralized and barren layer thicknesses show randomly spatial distribution, and there is no correlation between these parameters and the gold content. This approach has shown that the Ngoura-Colomines area is located in a large shear zone compatible with the Riedel fault system composed of P and P‧ fractures oriented NE-SW and NNE-SSW respectively; E-W trending R fractures and R‧ fractures with NW-SE trends that could have contributed significantly to the establishment of this gold mineralization. The combined OK model and GIS analysis have led to the delineation of Colomines, Tissongo, Madubal and Boutou villages as the most prospective areas for the exploration of primary gold deposit in the study area.

  12. Asymptotic inverse periods of reflected reactors above prompt critical

    International Nuclear Information System (INIS)

    Spriggs, G.D.; Busch, R.D.

    1995-01-01

    It is commonly assumed that the kinetic behavior of reflected and unreflected reactors is identical. In particular, it is often accepted that a given reactivity change in either type of system will result in an identical asymptotic inverse period. This is generally true for reactivities below prompt critical. For reactivities above prompt critical, however, the asymptotic inverse period can vary in a highly nonlinear fashion with system reactivity depending on the reflector return fraction, the neutron lifetime in the core, and the neutron lifetime in the reflector

  13. A Comparison of Traditional, Step-Path, and Geostatistical Techniques in the Stability Analysis of a Large Open Pit

    Science.gov (United States)

    Mayer, J. M.; Stead, D.

    2017-04-01

    With the increased drive towards deeper and more complex mine designs, geotechnical engineers are often forced to reconsider traditional deterministic design techniques in favour of probabilistic methods. These alternative techniques allow for the direct quantification of uncertainties within a risk and/or decision analysis framework. However, conventional probabilistic practices typically discretize geological materials into discrete, homogeneous domains, with attributes defined by spatially constant random variables, despite the fact that geological media display inherent heterogeneous spatial characteristics. This research directly simulates this phenomenon using a geostatistical approach, known as sequential Gaussian simulation. The method utilizes the variogram which imposes a degree of controlled spatial heterogeneity on the system. Simulations are constrained using data from the Ok Tedi mine site in Papua New Guinea and designed to randomly vary the geological strength index and uniaxial compressive strength using Monte Carlo techniques. Results suggest that conventional probabilistic techniques have a fundamental limitation compared to geostatistical approaches, as they fail to account for the spatial dependencies inherent to geotechnical datasets. This can result in erroneous model predictions, which are overly conservative when compared to the geostatistical results.

  14. Multivariate analysis and geostatistics of the fertility of a humic rhodic hapludox under coffee cultivation

    Directory of Open Access Journals (Sweden)

    Samuel de Assis Silva

    2012-04-01

    Full Text Available The spatial variability of soil and plant properties exerts great influence on the yeld of agricultural crops. This study analyzed the spatial variability of the fertility of a Humic Rhodic Hapludox with Arabic coffee, using principal component analysis, cluster analysis and geostatistics in combination. The experiment was carried out in an area under Coffea arabica L., variety Catucai 20/15 - 479. The soil was sampled at a depth 0.20 m, at 50 points of a sampling grid. The following chemical properties were determined: P, K+, Ca2+, Mg2+, Na+, S, Al3+, pH, H + Al, SB, t, T, V, m, OM, Na saturation index (SSI, remaining phosphorus (P-rem, and micronutrients (Zn, Fe, Mn, Cu and B. The data were analyzed with descriptive statistics, followed by principal component and cluster analyses. Geostatistics were used to check and quantify the degree of spatial dependence of properties, represented by principal components. The principal component analysis allowed a dimensional reduction of the problem, providing interpretable components, with little information loss. Despite the characteristic information loss of principal component analysis, the combination of this technique with geostatistical analysis was efficient for the quantification and determination of the structure of spatial dependence of soil fertility. In general, the availability of soil mineral nutrients was low and the levels of acidity and exchangeable Al were high.

  15. Geostatistics: a common link between medical geography, mathematical geology, and medical geology.

    Science.gov (United States)

    Goovaerts, P

    2014-08-01

    Since its development in the mining industry, geostatistics has emerged as the primary tool for spatial data analysis in various fields, ranging from earth and atmospheric sciences to agriculture, soil science, remote sensing, and more recently environmental exposure assessment. In the last few years, these tools have been tailored to the field of medical geography or spatial epidemiology, which is concerned with the study of spatial patterns of disease incidence and mortality and the identification of potential 'causes' of disease, such as environmental exposure, diet and unhealthy behaviours, economic or socio-demographic factors. On the other hand, medical geology is an emerging interdisciplinary scientific field studying the relationship between natural geological factors and their effects on human and animal health. This paper provides an introduction to the field of medical geology with an overview of geostatistical methods available for the analysis of geological and health data. Key concepts are illustrated using the mapping of groundwater arsenic concentration across eleven Michigan counties and the exploration of its relationship to the incidence of prostate cancer at the township level.

  16. Geostatistical prediction of microbial water quality throughout a stream network using meteorology, land cover, and spatiotemporal autocorrelation.

    Science.gov (United States)

    Holcomb, David Andrew; Messier, Kyle P; Serre, Marc L; Rowny, Jakob G; Stewart, Jill R

    2018-06-11

    Predictive modeling is promising as an inexpensive tool to assess water quality. We developed geostatistical predictive models of microbial water quality that empirically modelled spatiotemporal autocorrelation in measured fecal coliform (FC) bacteria concentrations to improve prediction. We compared five geostatistical models featuring different autocorrelation structures, fit to 676 observations from 19 locations in North Carolina's Jordan Lake watershed using meteorological and land cover predictor variables. Though stream distance metrics (with and without flow-weighting) failed to improve prediction over the Euclidean distance metric, incorporating temporal autocorrelation substantially improved prediction over the space-only models. We predicted FC throughout the stream network daily for one year, designating locations "impaired", "unimpaired", or "unassessed" if the probability of exceeding the state standard was >90%, 10% but <90%, respectively. We could assign impairment status to more of the stream network on days any FC were measured, suggesting frequent sample-based monitoring remains necessary, though implementing spatiotemporal predictive models may reduce the number of concurrent sampling locations required to adequately assess water quality. Together, these results suggest that prioritizing sampling at different times and conditions using geographically sparse monitoring networks is adequate to build robust and informative geostatistical models of water quality impairment.

  17. Nonlinear optical studies of organic monolayers

    International Nuclear Information System (INIS)

    Shen, Y.R.

    1988-02-01

    Second-order nonlinear optical effects are forbidden in a medium with inversion symmetry, but are necessarily allowed at a surface where the inversion summary is broken. They are often sufficiently strong so that a submonolayer perturbation of the surface can be readily detected. They can therefore be used as effective tools to study monolayers adsorbed at various interfaces. We discuss here a number of recent experiments in which optical second harmonic generation (SHG) and sum-frequency generation (SFG) are employed to probe and characterize organic monolayers. 15 refs., 5 figs

  18. Full-waveform inversion with reflected waves for 2D VTI media

    KAUST Repository

    Pattnaik, Sonali; Tsvankin, Ilya; Wang, Hui; Alkhalifah, Tariq

    2016-01-01

    Full-waveform inversion in anisotropic media using reflected waves suffers from the strong non-linearity of the objective function and trade-offs between model parameters. Estimating long-wavelength model components by fixing parameter perturbations

  19. Angle-domain Migration Velocity Analysis using Wave-equation Reflection Traveltime Inversion

    KAUST Repository

    Zhang, Sanzong

    2012-11-04

    The main difficulty with an iterative waveform inversion is that it tends to get stuck in a local minima associated with the waveform misfit function. This is because the waveform misfit function is highly non-linear with respect to changes in the velocity model. To reduce this nonlinearity, we present a reflection traveltime tomography method based on the wave equation which enjoys a more quasi-linear relationship between the model and the data. A local crosscorrelation of the windowed downgoing direct wave and the upgoing reflection wave at the image point yields the lag time that maximizes the correlation. This lag time represents the reflection traveltime residual that is back-projected into the earth model to update the velocity in the same way as wave-equation transmission traveltime inversion. The residual movemout analysis in the angle-domain common image gathers provides a robust estimate of the depth residual which is converted to the reflection traveltime residual for the velocity inversion. We present numerical examples to demonstrate its efficiency in inverting seismic data for complex velocity model.

  20. Optimal design of sampling and mapping schemes in the radiometric exploration of Chipilapa, El Salvador (Geo-statistics)

    International Nuclear Information System (INIS)

    Balcazar G, M.; Flores R, J.H.

    1992-01-01

    As part of the knowledge about the radiometric surface exploration, carried out in the geothermal field of Chipilapa, El Salvador, its were considered the geo-statistical parameters starting from the calculated variogram of the field data, being that the maxim distance of correlation of the samples in 'radon' in the different observation addresses (N-S, E-W, N W-S E, N E-S W), it was of 121 mts for the monitoring grill in future prospectus in the same area. Being derived of it an optimization (minimum cost) in the spacing of the field samples by means of geo-statistical techniques, without losing the detection of the anomaly. (Author)

  1. Can Geostatistical Models Represent Nature's Variability? An Analysis Using Flume Experiments

    Science.gov (United States)

    Scheidt, C.; Fernandes, A. M.; Paola, C.; Caers, J.

    2015-12-01

    The lack of understanding in the Earth's geological and physical processes governing sediment deposition render subsurface modeling subject to large uncertainty. Geostatistics is often used to model uncertainty because of its capability to stochastically generate spatially varying realizations of the subsurface. These methods can generate a range of realizations of a given pattern - but how representative are these of the full natural variability? And how can we identify the minimum set of images that represent this natural variability? Here we use this minimum set to define the geostatistical prior model: a set of training images that represent the range of patterns generated by autogenic variability in the sedimentary environment under study. The proper definition of the prior model is essential in capturing the variability of the depositional patterns. This work starts with a set of overhead images from an experimental basin that showed ongoing autogenic variability. We use the images to analyze the essential characteristics of this suite of patterns. In particular, our goal is to define a prior model (a minimal set of selected training images) such that geostatistical algorithms, when applied to this set, can reproduce the full measured variability. A necessary prerequisite is to define a measure of variability. In this study, we measure variability using a dissimilarity distance between the images. The distance indicates whether two snapshots contain similar depositional patterns. To reproduce the variability in the images, we apply an MPS algorithm to the set of selected snapshots of the sedimentary basin that serve as training images. The training images are chosen from among the initial set by using the distance measure to ensure that only dissimilar images are chosen. Preliminary investigations show that MPS can reproduce fairly accurately the natural variability of the experimental depositional system. Furthermore, the selected training images provide

  2. Extreme Nonlinear Optics An Introduction

    CERN Document Server

    Wegener, Martin

    2005-01-01

    Following the birth of the laser in 1960, the field of "nonlinear optics" rapidly emerged. Today, laser intensities and pulse durations are readily available, for which the concepts and approximations of traditional nonlinear optics no longer apply. In this regime of "extreme nonlinear optics," a large variety of novel and unusual effects arise, for example frequency doubling in inversion symmetric materials or high-harmonic generation in gases, which can lead to attosecond electromagnetic pulses or pulse trains. Other examples of "extreme nonlinear optics" cover diverse areas such as solid-state physics, atomic physics, relativistic free electrons in a vacuum and even the vacuum itself. This book starts with an introduction to the field based primarily on extensions of two famous textbook examples, namely the Lorentz oscillator model and the Drude model. Here the level of sophistication should be accessible to any undergraduate physics student. Many graphical illustrations and examples are given. The followi...

  3. Application of optical deformation analysis system on wedge splitting test and its inverse analysis

    DEFF Research Database (Denmark)

    Skocek, Jan; Stang, Henrik

    2010-01-01

    . Results of the inverse analysis are compared with traditional inverse analysis based on clip gauge data. Then the optically measured crack profile and crack tip position are compared with predictions done by the non-linear hinge model and a finite element analysis. It is shown that the inverse analysis...... based on the optically measured data can provide material parameters of the fictitious crack model matching favorably those obtained by classical inverse analysis based on the clip gauge data. Further advantages of using of the optical deformation analysis lie in identification of such effects...

  4. Seismic forecast using geostatistics

    International Nuclear Information System (INIS)

    Grecu, Valeriu; Mateiciuc, Doru

    2007-01-01

    The main idea of this research direction consists in the special way of constructing a new type of mathematical function as being a correlation between a computed statistical quantity and another physical quantity. This type of function called 'position function' was taken over by the authors of this study in the field of seismology with the hope of solving - at least partially - the difficult problem of seismic forecast. The geostatistic method of analysis focuses on the process of energy accumulation in a given seismic area, completing this analysis by a so-called loading function. This function - in fact a temporal function - describes the process of energy accumulation during a seismic cycle from a given seismic area. It was possible to discover a law of evolution of the seismic cycles that was materialized in a so-called characteristic function. This special function will help us to forecast the magnitude and the occurrence moment of the largest earthquake in the analysed area. Since 2000, the authors have been evolving to a new stage of testing: real - time analysis, in order to verify the quality of the method. There were five large earthquakes forecasts. (authors)

  5. High-resolution inverse Raman and resonant-wave-mixing spectroscopy

    Energy Technology Data Exchange (ETDEWEB)

    Rahn, L.A. [Sandia National Laboratories, Livermore, CA (United States)

    1993-12-01

    These research activities consist of high-resolution inverse Raman spectroscopy (IRS) and resonant wave-mixing spectroscopy to support the development of nonlinear-optical techniques for temperature and concentration measurements in combustion research. Objectives of this work include development of spectral models of important molecular species needed to perform coherent anti-Stokes Raman spectroscopy (CARS) measurements and the investigation of new nonlinear-optical processes as potential diagnostic techniques. Some of the techniques being investigated include frequency-degenerate and nearly frequency-degenerate resonant four-wave-mixing (DFWM and NDFWM), and resonant multi-wave mixing (RMWM).

  6. A new algorithm combining geostatistics with the surrogate data approach to increase the accuracy of comparisons of point radiation measurements with cloud measurements

    Science.gov (United States)

    Venema, V. K. C.; Lindau, R.; Varnai, T.; Simmer, C.

    2009-04-01

    Two main groups of statistical methods used in the Earth sciences are geostatistics and stochastic modelling. Geostatistical methods, such as various kriging algorithms, aim at estimating the mean value for every point as well as possible. In case of sparse measurements, such fields have less variability at small scales and a narrower distribution as the true field. This can lead to biases if a nonlinear process is simulated on such a kriged field. Stochastic modelling aims at reproducing the structure of the data. One of the stochastic modelling methods, the so-called surrogate data approach, replicates the value distribution and power spectrum of a certain data set. However, while stochastic methods reproduce the statistical properties of the data, the location of the measurement is not considered. Because radiative transfer through clouds is a highly nonlinear process it is essential to model the distribution (e.g. of optical depth, extinction, liquid water content or liquid water path) accurately as well as the correlations in the cloud field because of horizontal photon transport. This explains the success of surrogate cloud fields for use in 3D radiative transfer studies. However, up to now we could only achieve good results for the radiative properties averaged over the field, but not for a radiation measurement located at a certain position. Therefore we have developed a new algorithm that combines the accuracy of stochastic (surrogate) modelling with the positioning capabilities of kriging. In this way, we can automatically profit from the large geostatistical literature and software. The algorithm is tested on cloud fields from large eddy simulations (LES). On these clouds a measurement is simulated. From the pseudo-measurement we estimated the distribution and power spectrum. Furthermore, the pseudo-measurement is kriged to a field the size of the final surrogate cloud. The distribution, spectrum and the kriged field are the inputs to the algorithm. This

  7. On the evolution equations, solvable through the inverse scattering method

    International Nuclear Information System (INIS)

    Gerdjikov, V.S.; Khristov, E.Kh.

    1979-01-01

    The nonlinear evolution equations (NLEE), related to the one-parameter family of Dirac operators are considered in a uniform manner. The class of NLEE solvable through the inverse scatterina method and their conservation laws are described. The description of the hierarchy of Hamiltonian structures and the proof of complete integrability of the NLEE is presented. The class of Baecklund transformations for these NLEE is derived. The general formulae are illustrated by two important examples: the nonlinear Schroedinger equation and the sine-Gordon equation

  8. ANNIT - An Efficient Inversion Algorithm based on Prediction Principles

    Science.gov (United States)

    Růžek, B.; Kolář, P.

    2009-04-01

    Solution of inverse problems represents meaningful job in geophysics. The amount of data is continuously increasing, methods of modeling are being improved and the computer facilities are also advancing great technical progress. Therefore the development of new and efficient algorithms and computer codes for both forward and inverse modeling is still up to date. ANNIT is contributing to this stream since it is a tool for efficient solution of a set of non-linear equations. Typical geophysical problems are based on parametric approach. The system is characterized by a vector of parameters p, the response of the system is characterized by a vector of data d. The forward problem is usually represented by unique mapping F(p)=d. The inverse problem is much more complex and the inverse mapping p=G(d) is available in an analytical or closed form only exceptionally and generally it may not exist at all. Technically, both forward and inverse mapping F and G are sets of non-linear equations. ANNIT solves such situation as follows: (i) joint subspaces {pD, pM} of original data and model spaces D, M, resp. are searched for, within which the forward mapping F is sufficiently smooth that the inverse mapping G does exist, (ii) numerical approximation of G in subspaces {pD, pM} is found, (iii) candidate solution is predicted by using this numerical approximation. ANNIT is working in an iterative way in cycles. The subspaces {pD, pM} are searched for by generating suitable populations of individuals (models) covering data and model spaces. The approximation of the inverse mapping is made by using three methods: (a) linear regression, (b) Radial Basis Function Network technique, (c) linear prediction (also known as "Kriging"). The ANNIT algorithm has built in also an archive of already evaluated models. Archive models are re-used in a suitable way and thus the number of forward evaluations is minimized. ANNIT is now implemented both in MATLAB and SCILAB. Numerical tests show good

  9. Time-domain induced polarization - an analysis of Cole-Cole parameter resolution and correlation using Markov Chain Monte Carlo inversion

    Science.gov (United States)

    Madsen, Line Meldgaard; Fiandaca, Gianluca; Auken, Esben; Christiansen, Anders Vest

    2017-12-01

    The application of time-domain induced polarization (TDIP) is increasing with advances in acquisition techniques, data processing and spectral inversion schemes. An inversion of TDIP data for the spectral Cole-Cole parameters is a non-linear problem, but by applying a 1-D Markov Chain Monte Carlo (MCMC) inversion algorithm, a full non-linear uncertainty analysis of the parameters and the parameter correlations can be accessed. This is essential to understand to what degree the spectral Cole-Cole parameters can be resolved from TDIP data. MCMC inversions of synthetic TDIP data, which show bell-shaped probability distributions with a single maximum, show that the Cole-Cole parameters can be resolved from TDIP data if an acquisition range above two decades in time is applied. Linear correlations between the Cole-Cole parameters are observed and by decreasing the acquisitions ranges, the correlations increase and become non-linear. It is further investigated how waveform and parameter values influence the resolution of the Cole-Cole parameters. A limiting factor is the value of the frequency exponent, C. As C decreases, the resolution of all the Cole-Cole parameters decreases and the results become increasingly non-linear. While the values of the time constant, τ, must be in the acquisition range to resolve the parameters well, the choice between a 50 per cent and a 100 per cent duty cycle for the current injection does not have an influence on the parameter resolution. The limits of resolution and linearity are also studied in a comparison between the MCMC and a linearized gradient-based inversion approach. The two methods are consistent for resolved models, but the linearized approach tends to underestimate the uncertainties for poorly resolved parameters due to the corresponding non-linear features. Finally, an MCMC inversion of 1-D field data verifies that spectral Cole-Cole parameters can also be resolved from TD field measurements.

  10. A comprehensive inversion approach for feedforward compensation of piezoactuator system at high frequency

    Science.gov (United States)

    Tian, Lizhi; Xiong, Zhenhua; Wu, Jianhua; Ding, Han

    2016-09-01

    Motion control of the piezoactuator system over broadband frequencies is limited due to its inherent hysteresis and system dynamics. One of the suggested ways is to use feedforward controller to linearize the input-output relationship of the piezoactuator system. Although there have been many feedforward approaches, it is still a challenge to develop feedforward controller for the piezoactuator system at high frequency. Hence, this paper presents a comprehensive inversion approach in consideration of the coupling of hysteresis and dynamics. In this work, the influence of dynamics compensation on the input-output relationship of the piezoactuator system is investigated first. With system dynamics compensation, the input-output relationship of the piezoactuator system will be further represented as rate-dependent nonlinearity due to the inevitable dynamics compensation error, especially at high frequency. Base on this result, the feedforward controller composed by a cascade of linear dynamics inversion and rate-dependent nonlinearity inversion is developed. Then, the system identification of the comprehensive inversion approach is proposed. Finally, experimental results show that the proposed approach can improve the performance on tracking of both periodic and non-periodic trajectories at medium and high frequency compared with the conventional feedforward approaches.

  11. A perturbation expansion for the nonlinear Schroedinger equation with application to the influence of nonlinear Landau damping

    International Nuclear Information System (INIS)

    Weiland, J.; Ichikawa, Y.H.; Wilhelmsson, H.

    1977-12-01

    The Bogoliubov-Mitropolsky perturbation method has been applied to the study of a perturbation on soliton solutions to the nonlinear Schroedinger equation. The results are compared to those of Karpman and Maslov using the inverse scattering method and to those by Ott and Sudan on the KdV equation. (auth.)

  12. Technology demonstration: geostatistical and hydrologic analysis of salt areas. Assessment of effectiveness of geologic isolation systems

    International Nuclear Information System (INIS)

    Doctor, P.G.; Oberlander, P.L.; Rice, W.A.; Devary, J.L.; Nelson, R.W.; Tucker, P.E.

    1982-09-01

    The Office of Nuclear Waste Isolation (ONWI) requested Pacific Northwest Laboratory (PNL) to: (1) use geostatistical analyses to evaluate the adequacy of hydrologic data from three salt regions, each of which contains a potential nuclear waste repository site; and (2) demonstrate a methodology that allows quantification of the value of additional data collection. The three regions examined are the Paradox Basin in Utah, the Permian Basin in Texas, and the Mississippi Study Area. Additional and new data became available to ONWI during and following these analyses; therefore, this report must be considered a methodology demonstration here would apply as illustrated had the complete data sets been available. A combination of geostatistical and hydrologic analyses was used for this demonstration. Geostatistical analyses provided an optimal estimate of the potentiometric surface from the available data, a measure of the uncertainty of that estimate, and a means for selecting and evaluating the location of future data. The hydrologic analyses included the calculation of transmissivities, flow paths, travel times, and ground-water flow rates from hypothetical repository sites. Simulation techniques were used to evaluate the effect of optimally located future data on the potentiometric surface, flow lines, travel times, and flow rates. Data availability, quality, quantity, and conformance with model assumptions differed in each of the salt areas. Report highlights for the three locations are given

  13. A projected back-tracking line-search for constrained interactive inverse kinematics

    DEFF Research Database (Denmark)

    Engell-Nørregård, Morten Pol; Erleben, Kenny

    2011-01-01

    Inverse kinematics is the problem of manipulating the pose of an articulated figure in order to achieve a desired goal disregarding inertia and forces. One can approach the problem as a non-linear optimization problem or as non-linear equation solving. The former approach is superior in its...... of joint limits in an interactive solver. This makes it possible to compute the pose in each frame without the discontinuities exhibited by existing key frame animation techniques....

  14. Collision-free inverse kinematics of the redundant seven link manipulator used in a cucumber harvesting robot

    NARCIS (Netherlands)

    Henten, van E.J.; Schenk, E.J.J.; Willigenburg, van L.G.; Meuleman, J.; Barreiro, P.

    2010-01-01

    The paper presents results of research on an inverse kinematics algorithm that has been used in a functional model of a cucumber-harvesting robot consisting of a redundant P6R manipulator. Within a first generic approach, the inverse kinematics problem was reformulated as a non-linear programming

  15. Geostatistical Analysis of Mesoscale Spatial Variability and Error in SeaWiFS and MODIS/Aqua Global Ocean Color Data

    Science.gov (United States)

    Glover, David M.; Doney, Scott C.; Oestreich, William K.; Tullo, Alisdair W.

    2018-01-01

    Mesoscale (10-300 km, weeks to months) physical variability strongly modulates the structure and dynamics of planktonic marine ecosystems via both turbulent advection and environmental impacts upon biological rates. Using structure function analysis (geostatistics), we quantify the mesoscale biological signals within global 13 year SeaWiFS (1998-2010) and 8 year MODIS/Aqua (2003-2010) chlorophyll a ocean color data (Level-3, 9 km resolution). We present geographical distributions, seasonality, and interannual variability of key geostatistical parameters: unresolved variability or noise, resolved variability, and spatial range. Resolved variability is nearly identical for both instruments, indicating that geostatistical techniques isolate a robust measure of biophysical mesoscale variability largely independent of measurement platform. In contrast, unresolved variability in MODIS/Aqua is substantially lower than in SeaWiFS, especially in oligotrophic waters where previous analysis identified a problem for the SeaWiFS instrument likely due to sensor noise characteristics. Both records exhibit a statistically significant relationship between resolved mesoscale variability and the low-pass filtered chlorophyll field horizontal gradient magnitude, consistent with physical stirring acting on large-scale gradient as an important factor supporting observed mesoscale variability. Comparable horizontal length scales for variability are found from tracer-based scaling arguments and geostatistical decorrelation. Regional variations between these length scales may reflect scale dependence of biological mechanisms that also create variability directly at the mesoscale, for example, enhanced net phytoplankton growth in coastal and frontal upwelling and convective mixing regions. Global estimates of mesoscale biophysical variability provide an improved basis for evaluating higher resolution, coupled ecosystem-ocean general circulation models, and data assimilation.

  16. Non-linear Imaging using an Experimental Synthetic Aperture Real Time Ultrasound Scanner

    DEFF Research Database (Denmark)

    Rasmussen, Joachim; Du, Yigang; Jensen, Jørgen Arendt

    2011-01-01

    This paper presents the first non-linear B-mode image of a wire phantom using pulse inversion attained via an experimental synthetic aperture real-time ultrasound scanner (SARUS). The purpose of this study is to implement and validate non-linear imaging on SARUS for the further development of new...... non-linear techniques. This study presents non-linear and linear B-mode images attained via SARUS and an existing ultrasound system as well as a Field II simulation. The non-linear image shows an improved spatial resolution and lower full width half max and -20 dB resolution values compared to linear...

  17. Nonlinear model predictive control theory and algorithms

    CERN Document Server

    Grüne, Lars

    2017-01-01

    This book offers readers a thorough and rigorous introduction to nonlinear model predictive control (NMPC) for discrete-time and sampled-data systems. NMPC schemes with and without stabilizing terminal constraints are detailed, and intuitive examples illustrate the performance of different NMPC variants. NMPC is interpreted as an approximation of infinite-horizon optimal control so that important properties like closed-loop stability, inverse optimality and suboptimality can be derived in a uniform manner. These results are complemented by discussions of feasibility and robustness. An introduction to nonlinear optimal control algorithms yields essential insights into how the nonlinear optimization routine—the core of any nonlinear model predictive controller—works. Accompanying software in MATLAB® and C++ (downloadable from extras.springer.com/), together with an explanatory appendix in the book itself, enables readers to perform computer experiments exploring the possibilities and limitations of NMPC. T...

  18. Integrability of a system of two nonlinear Schroedinger equations

    International Nuclear Information System (INIS)

    Zhukhunashvili, V.Z.

    1989-01-01

    In recent years the inverse scattering method has achieved significant successes in the integration of nonlinear models that arise in different branches of physics. However, its region of applicability is still restricted, i.e., not all nonlinear models can be integrated. In view of the great mathematical difficulties that arise in integration, it is clearly worth testing a model for integrability before turning to integration. Such a possibility is provided by the Zakharov-Schulman method. The question of the integrability of a system of two nonlinear Schroedinger equations is resolved. It is shown that the previously known cases exhaust all integrable variants

  19. Sparse contrast-source inversion using linear-shrinkage-enhanced inexact Newton method

    KAUST Repository

    Desmal, Abdulla

    2014-07-01

    A contrast-source inversion scheme is proposed for microwave imaging of domains with sparse content. The scheme uses inexact Newton and linear shrinkage methods to account for the nonlinearity and ill-posedness of the electromagnetic inverse scattering problem, respectively. Thresholded shrinkage iterations are accelerated using a preconditioning technique. Additionally, during Newton iterations, the weight of the penalty term is reduced consistently with the quadratic convergence of the Newton method to increase accuracy and efficiency. Numerical results demonstrate the applicability of the proposed method.

  20. Sparse contrast-source inversion using linear-shrinkage-enhanced inexact Newton method

    KAUST Repository

    Desmal, Abdulla; Bagci, Hakan

    2014-01-01

    A contrast-source inversion scheme is proposed for microwave imaging of domains with sparse content. The scheme uses inexact Newton and linear shrinkage methods to account for the nonlinearity and ill-posedness of the electromagnetic inverse scattering problem, respectively. Thresholded shrinkage iterations are accelerated using a preconditioning technique. Additionally, during Newton iterations, the weight of the penalty term is reduced consistently with the quadratic convergence of the Newton method to increase accuracy and efficiency. Numerical results demonstrate the applicability of the proposed method.

  1. Workflows for Full Waveform Inversions

    Science.gov (United States)

    Boehm, Christian; Krischer, Lion; Afanasiev, Michael; van Driel, Martin; May, Dave A.; Rietmann, Max; Fichtner, Andreas

    2017-04-01

    Despite many theoretical advances and the increasing availability of high-performance computing clusters, full seismic waveform inversions still face considerable challenges regarding data and workflow management. While the community has access to solvers which can harness modern heterogeneous computing architectures, the computational bottleneck has fallen to these often manpower-bounded issues that need to be overcome to facilitate further progress. Modern inversions involve huge amounts of data and require a tight integration between numerical PDE solvers, data acquisition and processing systems, nonlinear optimization libraries, and job orchestration frameworks. To this end we created a set of libraries and applications revolving around Salvus (http://salvus.io), a novel software package designed to solve large-scale full waveform inverse problems. This presentation focuses on solving passive source seismic full waveform inversions from local to global scales with Salvus. We discuss (i) design choices for the aforementioned components required for full waveform modeling and inversion, (ii) their implementation in the Salvus framework, and (iii) how it is all tied together by a usable workflow system. We combine state-of-the-art algorithms ranging from high-order finite-element solutions of the wave equation to quasi-Newton optimization algorithms using trust-region methods that can handle inexact derivatives. All is steered by an automated interactive graph-based workflow framework capable of orchestrating all necessary pieces. This naturally facilitates the creation of new Earth models and hopefully sparks new scientific insights. Additionally, and even more importantly, it enhances reproducibility and reliability of the final results.

  2. Research Note: Full-waveform inversion of the unwrapped phase of a model

    KAUST Repository

    Alkhalifah, Tariq Ali

    2013-12-06

    Reflections in seismic data induce serious non-linearity in the objective function of full- waveform inversion. Thus, without a good initial velocity model that can produce reflections within a half cycle of the frequency used in the inversion, convergence to a solution becomes difficult. As a result, we tend to invert for refracted events and damp reflections in data. Reflection induced non-linearity stems from cycle skipping between the imprint of the true model in observed data and the predicted model in synthesized data. Inverting for the phase of the model allows us to address this problem by avoiding the source of non-linearity, the phase wrapping phenomena. Most of the information related to the location (or depths) of interfaces is embedded in the phase component of a model, mainly influenced by the background model, while the velocity-contrast information (responsible for the reflection energy) is mainly embedded in the amplitude component. In combination with unwrapping the phase of data, which mitigates the non-linearity introduced by the source function, I develop a framework to invert for the unwrapped phase of a model, represented by the instantaneous depth, using the unwrapped phase of the data. The resulting gradient function provides a mechanism to non-linearly update the velocity model by applying mainly phase shifts to the model. In using the instantaneous depth as a model parameter, we keep track of the model properties unfazed by the wrapping phenomena. © 2013 European Association of Geoscientists & Engineers.

  3. Humanoid Walking Robot: Modeling, Inverse Dynamics, and Gain Scheduling Control

    Directory of Open Access Journals (Sweden)

    Elvedin Kljuno

    2010-01-01

    Full Text Available This article presents reference-model-based control design for a 10 degree-of-freedom bipedal walking robot, using nonlinear gain scheduling. The main goal is to show concentrated mass models can be used for prediction of the required joint torques for a bipedal walking robot. Relatively complicated architecture, high DOF, and balancing requirements make the control task of these robots difficult. Although linear control techniques can be used to control bipedal robots, nonlinear control is necessary for better performance. The emphasis of this work is to show that the reference model can be a bipedal walking model with concentrated mass at the center of gravity, which removes the problems related to design of a pseudo-inverse system. Another significance of this approach is the reduced calculation requirements due to the simplified procedure of nominal joint torques calculation. Kinematic and dynamic analysis is discussed including results for joint torques and ground force necessary to implement a prescribed walking motion. This analysis is accompanied by a comparison with experimental data. An inverse plant and a tracking error linearization-based controller design approach is described. We propose a novel combination of a nonlinear gain scheduling with a concentrated mass model for the MIMO bipedal robot system.

  4. A Novel Approach of Understanding and Incorporating Error of Chemical Transport Models into a Geostatistical Framework

    Science.gov (United States)

    Reyes, J.; Vizuete, W.; Serre, M. L.; Xu, Y.

    2015-12-01

    The EPA employs a vast monitoring network to measure ambient PM2.5 concentrations across the United States with one of its goals being to quantify exposure within the population. However, there are several areas of the country with sparse monitoring spatially and temporally. One means to fill in these monitoring gaps is to use PM2.5 modeled estimates from Chemical Transport Models (CTMs) specifically the Community Multi-scale Air Quality (CMAQ) model. CMAQ is able to provide complete spatial coverage but is subject to systematic and random error due to model uncertainty. Due to the deterministic nature of CMAQ, often these uncertainties are not quantified. Much effort is employed to quantify the efficacy of these models through different metrics of model performance. Currently evaluation is specific to only locations with observed data. Multiyear studies across the United States are challenging because the error and model performance of CMAQ are not uniform over such large space/time domains. Error changes regionally and temporally. Because of the complex mix of species that constitute PM2.5, CMAQ error is also a function of increasing PM2.5 concentration. To address this issue we introduce a model performance evaluation for PM2.5 CMAQ that is regionalized and non-linear. This model performance evaluation leads to error quantification for each CMAQ grid. Areas and time periods of error being better qualified. The regionalized error correction approach is non-linear and is therefore more flexible at characterizing model performance than approaches that rely on linearity assumptions and assume homoscedasticity of CMAQ predictions errors. Corrected CMAQ data are then incorporated into the modern geostatistical framework of Bayesian Maximum Entropy (BME). Through cross validation it is shown that incorporating error-corrected CMAQ data leads to more accurate estimates than just using observed data by themselves.

  5. Spin-current emission governed by nonlinear spin dynamics.

    Science.gov (United States)

    Tashiro, Takaharu; Matsuura, Saki; Nomura, Akiyo; Watanabe, Shun; Kang, Keehoon; Sirringhaus, Henning; Ando, Kazuya

    2015-10-16

    Coupling between conduction electrons and localized magnetization is responsible for a variety of phenomena in spintronic devices. This coupling enables to generate spin currents from dynamical magnetization. Due to the nonlinearity of magnetization dynamics, the spin-current emission through the dynamical spin-exchange coupling offers a route for nonlinear generation of spin currents. Here, we demonstrate spin-current emission governed by nonlinear magnetization dynamics in a metal/magnetic insulator bilayer. The spin-current emission from the magnetic insulator is probed by the inverse spin Hall effect, which demonstrates nontrivial temperature and excitation power dependences of the voltage generation. The experimental results reveal that nonlinear magnetization dynamics and enhanced spin-current emission due to magnon scatterings are triggered by decreasing temperature. This result illustrates the crucial role of the nonlinear magnon interactions in the spin-current emission driven by dynamical magnetization, or nonequilibrium magnons, from magnetic insulators.

  6. Modelling and inversion of local magnetic anomalies

    International Nuclear Information System (INIS)

    Quesnel, Y; Langlais, B; Sotin, C; Galdéano, A

    2008-01-01

    We present a method—named as MILMA for modelling and inversion of local magnetic anomalies—that combines forward and inverse modelling of aeromagnetic data to characterize both magnetization properties and location of unconstrained local sources. Parameters of simple-shape magnetized bodies (cylinder, prism or sphere) are first adjusted by trial and error to predict the signal. Their parameters provide a priori information for inversion of the measurements. Here, a generalized nonlinear approach with a least-squares criterion is adopted to seek the best parameters of the sphere (dipole). This inversion step allows the model to be more objectively adjusted to fit the magnetic signal. The validity of the MILMA method is demonstrated through synthetic and real cases using aeromagnetic measurements. Tests with synthetic data reveal accurate results in terms of depth source, whatever be the number of sources. The MILMA method is then used with real measurements to constrain the properties of the magnetized units of the Champtoceaux complex (France). The resulting parameters correlate with the crustal structure and properties revealed by other geological and geophysical surveys in the same area. The MILMA method can therefore be used to investigate the properties of poorly constrained lithospheric magnetized sources

  7. Power-Law Radon-Transformed Superimposed Inverse Filter Synthetic Discriminant Correlator for Facial Recognition

    National Research Council Canada - National Science Library

    Haji-saeed, Bahareh; Khoury, Jed; Woods, Charles L; Kierstead, John

    2008-01-01

    ...) for facial recognition is proposed. In order to avoid spectral overlap and nonlinear crosstalk, superposition of rotationally variant sets of inverse filter Fourier-transformed Radon-processed templates is used to generate the SDF...

  8. On the connection between the inverse transform method and the exact quantum eigenstates

    International Nuclear Information System (INIS)

    Honerkamp, J.; Weber, P.; Wiesler, A.

    1979-01-01

    The 'inverse scattering transformation', which has been used to solve certain nonlinear field theories classically, is discussed in the context of the quantized version of these theories. In particular the non-linear Schroedinger equation and the massive Thirring model are considered. It is found that certain Jost functions of the associated scattering problem lead already, in quantizing the theory, to creation operators for the exact eigenstates of the corresponding Hamiltonians. (Auth.)

  9. Incorporating modelled subglacial hydrology into inversions for basal drag

    Directory of Open Access Journals (Sweden)

    C. P. Koziol

    2017-12-01

    Full Text Available A key challenge in modelling coupled ice-flow–subglacial hydrology is initializing the state and parameters of the system. We address this problem by presenting a workflow for initializing these values at the start of a summer melt season. The workflow depends on running a subglacial hydrology model for the winter season, when the system is not forced by meltwater inputs, and ice velocities can be assumed constant. Key parameters of the winter run of the subglacial hydrology model are determined from an initial inversion for basal drag using a linear sliding law. The state of the subglacial hydrology model at the end of winter is incorporated into an inversion of basal drag using a non-linear sliding law which is a function of water pressure. We demonstrate this procedure in the Russell Glacier area and compare the output of the linear sliding law with two non-linear sliding laws. Additionally, we compare the modelled winter hydrological state to radar observations and find that it is in line with summer rather than winter observations.

  10. Robust, nonlinear, high angle-of-attack control design for a supermaneuverable vehicle

    Science.gov (United States)

    Adams, Richard J.

    1993-01-01

    High angle-of-attack flight control laws are developed for a supermaneuverable fighter aircraft. The methods of dynamic inversion and structured singular value synthesis are combined into an approach which addresses both the nonlinearity and robustness problems of flight at extreme operating conditions. The primary purpose of the dynamic inversion control elements is to linearize the vehicle response across the flight envelope. Structured singular value synthesis is used to design a dynamic controller which provides robust tracking to pilot commands. The resulting control system achieves desired flying qualities and guarantees a large margin of robustness to uncertainties for high angle-of-attack flight conditions. The results of linear simulation and structured singular value stability analysis are presented to demonstrate satisfaction of the design criteria. High fidelity nonlinear simulation results show that the combined dynamics inversion/structured singular value synthesis control law achieves a high level of performance in a realistic environment.

  11. Implementation of non-linear filters for iterative penalized maximum likelihood image reconstruction

    International Nuclear Information System (INIS)

    Liang, Z.; Gilland, D.; Jaszczak, R.; Coleman, R.

    1990-01-01

    In this paper, the authors report on the implementation of six edge-preserving, noise-smoothing, non-linear filters applied in image space for iterative penalized maximum-likelihood (ML) SPECT image reconstruction. The non-linear smoothing filters implemented were the median filter, the E 6 filter, the sigma filter, the edge-line filter, the gradient-inverse filter, and the 3-point edge filter with gradient-inverse filter, and the 3-point edge filter with gradient-inverse weight. A 3 x 3 window was used for all these filters. The best image obtained, by viewing the profiles through the image in terms of noise-smoothing, edge-sharpening, and contrast, was the one smoothed with the 3-point edge filter. The computation time for the smoothing was less than 1% of one iteration, and the memory space for the smoothing was negligible. These images were compared with the results obtained using Bayesian analysis

  12. Solving Large Scale Nonlinear Eigenvalue Problem in Next-Generation Accelerator Design

    Energy Technology Data Exchange (ETDEWEB)

    Liao, Ben-Shan; Bai, Zhaojun; /UC, Davis; Lee, Lie-Quan; Ko, Kwok; /SLAC

    2006-09-28

    A number of numerical methods, including inverse iteration, method of successive linear problem and nonlinear Arnoldi algorithm, are studied in this paper to solve a large scale nonlinear eigenvalue problem arising from finite element analysis of resonant frequencies and external Q{sub e} values of a waveguide loaded cavity in the next-generation accelerator design. They present a nonlinear Rayleigh-Ritz iterative projection algorithm, NRRIT in short and demonstrate that it is the most promising approach for a model scale cavity design. The NRRIT algorithm is an extension of the nonlinear Arnoldi algorithm due to Voss. Computational challenges of solving such a nonlinear eigenvalue problem for a full scale cavity design are outlined.

  13. Alternating minimisation for glottal inverse filtering

    International Nuclear Information System (INIS)

    Bleyer, Ismael Rodrigo; Lybeck, Lasse; Auvinen, Harri; Siltanen, Samuli; Airaksinen, Manu; Alku, Paavo

    2017-01-01

    A new method is proposed for solving the glottal inverse filtering (GIF) problem. The goal of GIF is to separate an acoustical speech signal into two parts: the glottal airflow excitation and the vocal tract filter. To recover such information one has to deal with a blind deconvolution problem. This ill-posed inverse problem is solved under a deterministic setting, considering unknowns on both sides of the underlying operator equation. A stable reconstruction is obtained using a double regularization strategy, alternating between fixing either the glottal source signal or the vocal tract filter. This enables not only splitting the nonlinear and nonconvex problem into two linear and convex problems, but also allows the use of the best parameters and constraints to recover each variable at a time. This new technique, called alternating minimization glottal inverse filtering (AM-GIF), is compared with two other approaches: Markov chain Monte Carlo glottal inverse filtering (MCMC-GIF), and iterative adaptive inverse filtering (IAIF), using synthetic speech signals. The recent MCMC-GIF has good reconstruction quality but high computational cost. The state-of-the-art IAIF method is computationally fast but its accuracy deteriorates, particularly for speech signals of high fundamental frequency ( F 0). The results show the competitive performance of the new method: With high F 0, the reconstruction quality is better than that of IAIF and close to MCMC-GIF while reducing the computational complexity by two orders of magnitude. (paper)

  14. Time-domain incomplete Gauss-Newton full-waveform inversion of Gulf of Mexico data

    KAUST Repository

    AlTheyab, Abdullah

    2013-09-22

    We apply the incomplete Gauss-Newton full-waveform inversion (TDIGN-FWI) to Gulf of Mexico (GOM) data in the space-time domain. In our application, iterative least-squares reverse-time migration (LSRTM) is used to estimate the model update at each non-linear iteration, and the number of LSRTM iterations is progressively increased after each non-linear iteration. With this method, model updating along deep reflection wavepaths are automatically enhanced, which in turn improves imaging below the reach of diving-waves. The forward and adjoint operators are implemented in the space-time domain to simultaneously invert the data over a range of frequencies. A multiscale approach is used where higher frequencies are down-weighted significantly at early iterations, and gradually included in the inversion. Synthetic data results demonstrate the effectiveness of reconstructing both the high- and low-wavenumber features in the model without relying on diving waves in the inversion. Results with Gulf of Mexico field data show a significantly improved migration image in both the shallow and deep sections.

  15. Use of geostatistics on broiler production for evaluation of different minimum ventilation systems during brooding phase

    Directory of Open Access Journals (Sweden)

    Thayla Morandi Ridolfi de Carvalho

    2012-01-01

    Full Text Available The objective of this research was to evaluate different minimum ventilation systems, in relation to air quality and thermal comfort using geostatistics in brooding phase. The minimum ventilation systems were: Blue House I: exhaust fans + curtain management (end of the building; Blue House II: exhaust fans + side curtain management; and Dark House: exhaust fans + flag. The climate variables evaluated were: dry bulb temperature, relative humidity, air velocity, carbon dioxide and ammonia concentration, during winter time, at 9 a.m., in 80 equidistant points in brooding area. Data were evaluated by geostatistic technique. The results indicate that Wider broiler houses (above 15.0 m width present the greatest ammonia and humidity concentration. Blue House II present the best results in relation to air quality. However, none of the studied broiler houses present an ideal thermal comfort.

  16. SPARSE ELECTROMAGNETIC IMAGING USING NONLINEAR LANDWEBER ITERATIONS

    KAUST Repository

    Desmal, Abdulla

    2015-07-29

    A scheme for efficiently solving the nonlinear electromagnetic inverse scattering problem on sparse investigation domains is described. The proposed scheme reconstructs the (complex) dielectric permittivity of an investigation domain from fields measured away from the domain itself. Least-squares data misfit between the computed scattered fields, which are expressed as a nonlinear function of the permittivity, and the measured fields is constrained by the L0/L1-norm of the solution. The resulting minimization problem is solved using nonlinear Landweber iterations, where at each iteration a thresholding function is applied to enforce the sparseness-promoting L0/L1-norm constraint. The thresholded nonlinear Landweber iterations are applied to several two-dimensional problems, where the ``measured\\'\\' fields are synthetically generated or obtained from actual experiments. These numerical experiments demonstrate the accuracy, efficiency, and applicability of the proposed scheme in reconstructing sparse profiles with high permittivity values.

  17. Deep fracturing of granite bodies. Literature survey, geostructural and geostatistic investigations

    International Nuclear Information System (INIS)

    Bles, J.L.; Blanchin, R.

    1986-01-01

    This report deals with investigations about deep fracturing of granite bodies, which were performed within two cost-sharing contracts between the Commission of the European Communities, the Commissariat a l'Energie Atomique and the Bureau de Recherches Geologiques et Minieres. The aim of this work was to study the evolution of fracturing in granite from the surface to larger depths, so that guidelines can be identified in order to extrapolate, at depth, the data obtained from surface investigations. These guidelines could eventually be used for feasibility studies about radioactive waste disposal. The results of structural and geostatistic investigations about the St. Sylvestre granite, as well as the literature survey about fractures encountered in two long Alpine galleries (Mont-Blanc tunnel and Arc-Isere water gallery), in the 1000 m deep borehole at Auriat, and in the Bassies granite body (Pyrenees) are presented. These results show that, for radioactive waste disposal feasibility studies: 1. The deep state of fracturing in a granite body can be estimated from results obtained at the surface; 2. Studying only the large fault network would be insufficient, both for surface investigations and for studies in deep boreholes and/or in underground galleries; 3. It is necessary to study orientations and frequencies of small fractures, so that structural mapping and statistical/geostatistical methods can be used in order to identify zones of higher and lower fracturing

  18. Sparse Nonlinear Electromagnetic Imaging Accelerated With Projected Steepest Descent Algorithm

    KAUST Repository

    Desmal, Abdulla

    2017-04-03

    An efficient electromagnetic inversion scheme for imaging sparse 3-D domains is proposed. The scheme achieves its efficiency and accuracy by integrating two concepts. First, the nonlinear optimization problem is constrained using L₀ or L₁-norm of the solution as the penalty term to alleviate the ill-posedness of the inverse problem. The resulting Tikhonov minimization problem is solved using nonlinear Landweber iterations (NLW). Second, the efficiency of the NLW is significantly increased using a steepest descent algorithm. The algorithm uses a projection operator to enforce the sparsity constraint by thresholding the solution at every iteration. Thresholding level and iteration step are selected carefully to increase the efficiency without sacrificing the convergence of the algorithm. Numerical results demonstrate the efficiency and accuracy of the proposed imaging scheme in reconstructing sparse 3-D dielectric profiles.

  19. Non-perturbational surface-wave inversion: A Dix-type relation for surface waves

    Science.gov (United States)

    Haney, Matt; Tsai, Victor C.

    2015-01-01

    We extend the approach underlying the well-known Dix equation in reflection seismology to surface waves. Within the context of surface wave inversion, the Dix-type relation we derive for surface waves allows accurate depth profiles of shear-wave velocity to be constructed directly from phase velocity data, in contrast to perturbational methods. The depth profiles can subsequently be used as an initial model for nonlinear inversion. We provide examples of the Dix-type relation for under-parameterized and over-parameterized cases. In the under-parameterized case, we use the theory to estimate crustal thickness, crustal shear-wave velocity, and mantle shear-wave velocity across the Western U.S. from phase velocity maps measured at 8-, 20-, and 40-s periods. By adopting a thin-layer formalism and an over-parameterized model, we show how a regularized inversion based on the Dix-type relation yields smooth depth profiles of shear-wave velocity. In the process, we quantitatively demonstrate the depth sensitivity of surface-wave phase velocity as a function of frequency and the accuracy of the Dix-type relation. We apply the over-parameterized approach to a near-surface data set within the frequency band from 5 to 40 Hz and find overall agreement between the inverted model and the result of full nonlinear inversion.

  20. Volcanic source inversion using a genetic algorithm and an elastic-gravitational layered earth model for magmatic intrusions

    Science.gov (United States)

    Tiampo, K. F.; Fernández, J.; Jentzsch, G.; Charco, M.; Rundle, J. B.

    2004-11-01

    Here we present an inversion methodology using the combination of a genetic algorithm (GA) inversion program, and an elastic-gravitational earth model to determine the parameters of a volcanic intrusion. Results from the integration of the elastic-gravitational model, a suite of FORTRAN 77 programs developed to compute the displacements due to volcanic loading, with the GA inversion code, written in the C programming language, are presented. These codes allow for the calculation of displacements (horizontal and vertical), tilt, vertical strain and potential and gravity changes on the surface of an elastic-gravitational layered Earth model due to the magmatic intrusion. We detail the appropriate methodology for examining the sensitivity of the model to variation in the constituent parameters using the GA, and present, for the first time, a Monte Carlo technique for evaluating the propagation of error through the GA inversion process. One application example is given at Mayon volcano, Philippines, for the inversion program, the sensitivity analysis, and the error evaluation. The integration of the GA with the complex elastic-gravitational model is a blueprint for an efficient nonlinear inversion methodology and its implementation into an effective tool for the evaluation of parameter sensitivity. Finally, the extension of this inversion algorithm and the error assessment methodology has important implications to the modeling and data assimilation of a number of other nonlinear applications in the field of geosciences.

  1. Bayesian inversion using a geologically realistic and discrete model space

    Science.gov (United States)

    Jaeggli, C.; Julien, S.; Renard, P.

    2017-12-01

    Since the early days of groundwater modeling, inverse methods play a crucial role. Many research and engineering groups aim to infer extensive knowledge of aquifer parameters from a sparse set of observations. Despite decades of dedicated research on this topic, there are still several major issues to be solved. In the hydrogeological framework, one is often confronted with underground structures that present very sharp contrasts of geophysical properties. In particular, subsoil structures such as karst conduits, channels, faults, or lenses, strongly influence groundwater flow and transport behavior of the underground. For this reason it can be essential to identify their location and shape very precisely. Unfortunately, when inverse methods are specially trained to consider such complex features, their computation effort often becomes unaffordably high. The following work is an attempt to solve this dilemma. We present a new method that is, in some sense, a compromise between the ergodicity of Markov chain Monte Carlo (McMC) methods and the efficient handling of data by the ensemble based Kalmann filters. The realistic and complex random fields are generated by a Multiple-Point Statistics (MPS) tool. Nonetheless, it is applicable with any conditional geostatistical simulation tool. Furthermore, the algorithm is independent of any parametrization what becomes most important when two parametric systems are equivalent (permeability and resistivity, speed and slowness, etc.). When compared to two existing McMC schemes, the computational effort was divided by a factor of 12.

  2. Unwrapped phase inversion with an exponential damping

    KAUST Repository

    Choi, Yun Seok

    2015-07-28

    Full-waveform inversion (FWI) suffers from the phase wrapping (cycle skipping) problem when the frequency of data is not low enough. Unless we obtain a good initial velocity model, the phase wrapping problem in FWI causes a result corresponding to a local minimum, usually far away from the true solution, especially at depth. Thus, we have developed an inversion algorithm based on a space-domain unwrapped phase, and we also used exponential damping to mitigate the nonlinearity associated with the reflections. We construct the 2D phase residual map, which usually contains the wrapping discontinuities, especially if the model is complex and the frequency is high. We then unwrap the phase map and remove these cycle-based jumps. However, if the phase map has several residues, the unwrapping process becomes very complicated. We apply a strong exponential damping to the wavefield to eliminate much of the residues in the phase map, thus making the unwrapping process simple. We finally invert the unwrapped phases using the back-propagation algorithm to calculate the gradient. We progressively reduce the damping factor to obtain a high-resolution image. Numerical examples determined that the unwrapped phase inversion with a strong exponential damping generated convergent long-wavelength updates without low-frequency information. This model can be used as a good starting model for a subsequent inversion with a reduced damping, eventually leading to conventional waveform inversion.

  3. Ore reserve evalution, through geostatistical methods, in sector C-09, Pocos de Caldas, MG-Brazil

    International Nuclear Information System (INIS)

    Guerra, P.A.G.; Censi, A.C.; Marques, J.P.M.; Huijbregts, Ch.

    1978-01-01

    In sector C-09, Pocos de Caldas in the state of Minas Gerais, geostatistical techniques have been used to evaluate the tonnage of U 3 O 8 and associated minerals and to delimit ore from sterile areas. The calculation of reserve was based on borehole information including the results of chemical and/or radiometric analysis. Two-and three dimensional evalutions were made following the existing geological models. Initially, the evaluation was based on chemical analysis using the more classical geostatistical technique of kriging. This was followed by a second evaluation using the more recent technique of co-kriging which permited the incorporation of radiometric information in the calculations. The correlation between ore grade and radiometric was studied using the method of cross-covariance. Following restrictions imposed by mining considerations, a probabilistic selection was made of blocks of appropriate dimensions so as to evaluate the grade tonnage curve for each panel. (Author) [pt

  4. Robust 1D inversion and analysis of helicopter electromagnetic (HEM) data

    DEFF Research Database (Denmark)

    Tølbøll, R.J.; Christensen, N.B.

    2006-01-01

    but can resolve layer boundary to a depth of more than 100 m. Modeling experiments also show that the effect of altimeter errors on the inversion results is serious. We suggest a new interpretation scheme for HEM data founded solely on full nonlinear 1D inversion and providing layered-earth models...... of test flights were performed using a frequency-domain, helicopter-borne electromagnetic (HEM) system. We perform a theoretical examination of the resolution capabilities of the applied system. Quantitative model parameter analyses show that the system only weakly resolves conductive, near-surface layers...... supported by datamisfit parameters and a quantitative model-parameter analysis. The backbone of the scheme is the removal of cultural coupling effects followed by a multilayer inversion that in turn provides reliable starting models for a subsequent few-layer inversion. A new procedure for correlation...

  5. Linear and nonlinear intersubband optical absorption in a disk-shaped quantum dot with a parabolic potential plus an inverse squared potential in a static magnetic field

    Energy Technology Data Exchange (ETDEWEB)

    Liu Guanghui [Department of Physics, College of Physics and Electronic Engineering, Guangzhou University, Guangzhou 510006 (China); Guo Kangxian, E-mail: axguo@sohu.com [Department of Physics, College of Physics and Electronic Engineering, Guangzhou University, Guangzhou 510006 (China); Wang Chao [Institute of Public Administration, Guangzhou University, Guangzhou 510006 (China)

    2012-06-15

    The linear and nonlinear optical absorption in a disk-shaped quantum dot (DSQD) with parabolic potential plus an inverse squared potential in the presence of a static magnetic field are theoretically investigated within the framework of the compact-density-matrix approach and iterative method. The energy levels and the wave functions of an electron in the DSQD are obtained by using the effective mass approximation. Numerical calculations are presented for typical GaAs/AlAs DSQD. It is found that the optical absorption coefficients are strongly affected not only by a static magnetic field, but also by the strength of external field, the confinement frequency and the incident optical intensity.

  6. Linear and nonlinear intersubband optical absorption in a disk-shaped quantum dot with a parabolic potential plus an inverse squared potential in a static magnetic field

    International Nuclear Information System (INIS)

    Liu Guanghui; Guo Kangxian; Wang Chao

    2012-01-01

    The linear and nonlinear optical absorption in a disk-shaped quantum dot (DSQD) with parabolic potential plus an inverse squared potential in the presence of a static magnetic field are theoretically investigated within the framework of the compact-density-matrix approach and iterative method. The energy levels and the wave functions of an electron in the DSQD are obtained by using the effective mass approximation. Numerical calculations are presented for typical GaAs/AlAs DSQD. It is found that the optical absorption coefficients are strongly affected not only by a static magnetic field, but also by the strength of external field, the confinement frequency and the incident optical intensity.

  7. An inverse problem strategy based on forward model evaluations: Gradient-based optimization without adjoint solves

    Energy Technology Data Exchange (ETDEWEB)

    Aguilo Valentin, Miguel Alejandro [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

    2016-07-01

    This study presents a new nonlinear programming formulation for the solution of inverse problems. First, a general inverse problem formulation based on the compliance error functional is presented. The proposed error functional enables the computation of the Lagrange multipliers, and thus the first order derivative information, at the expense of just one model evaluation. Therefore, the calculation of the Lagrange multipliers does not require the solution of the computationally intensive adjoint problem. This leads to significant speedups for large-scale, gradient-based inverse problems.

  8. A Note on the Semi-Inverse Method and a Variational Principle for the Generalized KdV-mKdV Equation

    Directory of Open Access Journals (Sweden)

    Li Yao

    2013-01-01

    Full Text Available Ji-Huan He systematically studied the inverse problem of calculus of variations. This note reveals that the semi-inverse method also works for a generalized KdV-mKdV equation with nonlinear terms of any orders.

  9. Trimming and procrastination as inversion techniques

    Science.gov (United States)

    Backus, George E.

    1996-12-01

    By examining the processes of truncating and approximating the model space (trimming it), and by committing to neither the objectivist nor the subjectivist interpretation of probability (procrastinating), we construct a formal scheme for solving linear and non-linear geophysical inverse problems. The necessary prior information about the correct model xE can be either a collection of inequalities or a probability measure describing where xE was likely to be in the model space X before the data vector y0 was measured. The results of the inversion are (1) a vector z0 that estimates some numerical properties zE of xE; (2) an estimate of the error δz = z0 - zE. As y0 is finite dimensional, so is z0, and hence in principle inversion cannot describe all of xE. The error δz is studied under successively more specialized assumptions about the inverse problem, culminating in a complete analysis of the linear inverse problem with a prior quadratic bound on xE. Our formalism appears to encompass and provide error estimates for many of the inversion schemes current in geomagnetism, and would be equally applicable in geodesy and seismology if adequate prior information were available there. As an idealized example we study the magnetic field at the core-mantle boundary, using satellite measurements of field elements at sites assumed to be almost uniformly distributed on a single spherical surface. Magnetospheric currents are neglected and the crustal field is idealized as a random process with rotationally invariant statistics. We find that an appropriate data compression diagonalizes the variance matrix of the crustal signal and permits an analytic trimming of the idealized problem.

  10. A Geostatistical Approach to Indoor Surface Sampling Strategies

    DEFF Research Database (Denmark)

    Schneider, Thomas; Petersen, Ole Holm; Nielsen, Allan Aasbjerg

    1990-01-01

    Particulate surface contamination is of concern in production industries such as food processing, aerospace, electronics and semiconductor manufacturing. There is also an increased awareness that surface contamination should be monitored in industrial hygiene surveys. A conceptual and theoretical...... framework for designing sampling strategies is thus developed. The distribution and spatial correlation of surface contamination can be characterized using concepts from geostatistical science, where spatial applications of statistics is most developed. The theory is summarized and particulate surface...... contamination, sampled from small areas on a table, have been used to illustrate the method. First, the spatial correlation is modelled and the parameters estimated from the data. Next, it is shown how the contamination at positions not measured can be estimated with kriging, a minimum mean square error method...

  11. Implementation and testing of a multivariate inverse radiation transport solver

    International Nuclear Information System (INIS)

    Mattingly, John; Mitchell, Dean J.

    2012-01-01

    Detection, identification, and characterization of special nuclear materials (SNM) all face the same basic challenge: to varying degrees, each must infer the presence, composition, and configuration of the SNM by analyzing a set of measured radiation signatures. Solutions to this problem implement inverse radiation transport methods. Given a set of measured radiation signatures, inverse radiation transport estimates properties of the source terms and transport media that are consistent with those signatures. This paper describes one implementation of a multivariate inverse radiation transport solver. The solver simultaneously analyzes gamma spectrometry and neutron multiplicity measurements to fit a one-dimensional radiation transport model with variable layer thicknesses using nonlinear regression. The solver's essential components are described, and its performance is illustrated by application to benchmark experiments conducted with plutonium metal. - Highlights: ► Inverse problems, specifically applied to identifying and characterizing radiation sources . ► Radiation transport. ► Analysis of gamma spectroscopy and neutron multiplicity counting measurements. ► Experimental testing of the inverse solver against measurements of plutonium.

  12. Nonlinear electron transport in magnetized laser plasmas

    International Nuclear Information System (INIS)

    Kho, T.H.; Haines, M.G.

    1986-01-01

    Electron transport in a magnetized plasma heated by inverse bremsstrahlung is studied numerically using a nonlinear Fokker--Planck model with self-consistent E and B fields. The numerical scheme is described. Nonlocal transport is found to alter many of the transport coefficients derived from linear transport theory, in particular, the Nernst and Righi--Leduc effects, in addition to the perpendicular heat flux q/sub perpendicular/, are substantially reduced near critical surface. The magnetic field, however, remains strongly coupled to the nonlinear q/sub perpendicular/ and, as has been found in hydrosimulations, convective amplification of the magnetic field occurs in the overdense plasma

  13. Nonlinear Multivariate Spline-Based Control Allocation for High-Performance Aircraft

    OpenAIRE

    Tol, H.J.; De Visser, C.C.; Van Kampen, E.; Chu, Q.P.

    2014-01-01

    High performance flight control systems based on the nonlinear dynamic inversion (NDI) principle require highly accurate models of aircraft aerodynamics. In general, the accuracy of the internal model determines to what degree the system nonlinearities can be canceled; the more accurate the model, the better the cancellation, and with that, the higher the performance of the controller. In this paper a new control system is presented that combines NDI with multivariate simplex spline based con...

  14. Geostatistical simulations for radon indoor with a nested model including the housing factor

    International Nuclear Information System (INIS)

    Cafaro, C.; Giovani, C.; Garavaglia, M.

    2016-01-01

    The radon prone areas definition is matter of many researches in radioecology, since radon is considered a leading cause of lung tumours, therefore the authorities ask for support to develop an appropriate sanitary prevention strategy. In this paper, we use geostatistical tools to elaborate a definition accounting for some of the available information about the dwellings. Co-kriging is the proper interpolator used in geostatistics to refine the predictions by using external covariates. In advance, co-kriging is not guaranteed to improve significantly the results obtained by applying the common lognormal kriging. Here, instead, such multivariate approach leads to reduce the cross-validation residual variance to an extent which is deemed as satisfying. Furthermore, with the application of Monte Carlo simulations, the paradigm provides a more conservative radon prone areas definition than the one previously made by lognormal kriging. - Highlights: • The housing class is inserted into co-kriging via an indicator function. • Inserting the housing classes in a co-kriging improves predictions. • The housing class has a structured component in space. • A nested model is implemented into the multigaussian algorithm. • A collection of risk maps is merged into one to create RPA.

  15. Minimization of required model runs in the Random Mixing approach to inverse groundwater flow and transport modeling

    Science.gov (United States)

    Hoerning, Sebastian; Bardossy, Andras; du Plessis, Jaco

    2017-04-01

    Most geostatistical inverse groundwater flow and transport modelling approaches utilize a numerical solver to minimize the discrepancy between observed and simulated hydraulic heads and/or hydraulic concentration values. The optimization procedure often requires many model runs, which for complex models lead to long run times. Random Mixing is a promising new geostatistical technique for inverse modelling. The method is an extension of the gradual deformation approach. It works by finding a field which preserves the covariance structure and maintains observed hydraulic conductivities. This field is perturbed by mixing it with new fields that fulfill the homogeneous conditions. This mixing is expressed as an optimization problem which aims to minimize the difference between the observed and simulated hydraulic heads and/or concentration values. To preserve the spatial structure, the mixing weights must lie on the unit hyper-sphere. We present a modification to the Random Mixing algorithm which significantly reduces the number of model runs required. The approach involves taking n equally spaced points on the unit circle as weights for mixing conditional random fields. Each of these mixtures provides a solution to the forward model at the conditioning locations. For each of the locations the solutions are then interpolated around the circle to provide solutions for additional mixing weights at very low computational cost. The interpolated solutions are used to search for a mixture which maximally reduces the objective function. This is in contrast to other approaches which evaluate the objective function for the n mixtures and then interpolate the obtained values. Keeping the mixture on the unit circle makes it easy to generate equidistant sampling points in the space; however, this means that only two fields are mixed at a time. Once the optimal mixture for two fields has been found, they are combined to form the input to the next iteration of the algorithm. This

  16. Sparse Reconstruction Schemes for Nonlinear Electromagnetic Imaging

    KAUST Repository

    Desmal, Abdulla

    2016-03-01

    Electromagnetic imaging is the problem of determining material properties from scattered fields measured away from the domain under investigation. Solving this inverse problem is a challenging task because (i) it is ill-posed due to the presence of (smoothing) integral operators used in the representation of scattered fields in terms of material properties, and scattered fields are obtained at a finite set of points through noisy measurements; and (ii) it is nonlinear simply due the fact that scattered fields are nonlinear functions of the material properties. The work described in this thesis tackles the ill-posedness of the electromagnetic imaging problem using sparsity-based regularization techniques, which assume that the scatterer(s) occupy only a small fraction of the investigation domain. More specifically, four novel imaging methods are formulated and implemented. (i) Sparsity-regularized Born iterative method iteratively linearizes the nonlinear inverse scattering problem and each linear problem is regularized using an improved iterative shrinkage algorithm enforcing the sparsity constraint. (ii) Sparsity-regularized nonlinear inexact Newton method calls for the solution of a linear system involving the Frechet derivative matrix of the forward scattering operator at every iteration step. For faster convergence, the solution of this matrix system is regularized under the sparsity constraint and preconditioned by leveling the matrix singular values. (iii) Sparsity-regularized nonlinear Tikhonov method directly solves the nonlinear minimization problem using Landweber iterations, where a thresholding function is applied at every iteration step to enforce the sparsity constraint. (iv) This last scheme is accelerated using a projected steepest descent method when it is applied to three-dimensional investigation domains. Projection replaces the thresholding operation and enforces the sparsity constraint. Numerical experiments, which are carried out using

  17. Nonlinear Hamiltonian systems

    DEFF Research Database (Denmark)

    Jørgensen, Michael Finn

    1995-01-01

    It is generally very difficult to solve nonlinear systems, and such systems often possess chaotic solutions. In the rare event that a system is completely solvable, it is said to integrable. Such systems never have chaotic solutions. Using the Inverse Scattering Transform Method (ISTM) two...... particular configurations of the Discrete Self-Trapping (DST) system are shown to be completely solvable. One of these systems includes the Toda lattice in a certain limit. An explicit integration is carried through for this Near-Toda lattice. The Near-Toda lattice is then generalized to include singular...

  18. Evaluation of stationary and non-stationary geostatistical models for inferring hydraulic conductivity values at Aespoe

    International Nuclear Information System (INIS)

    La Pointe, P.R.

    1994-11-01

    This report describes the comparison of stationary and non-stationary geostatistical models for the purpose of inferring block-scale hydraulic conductivity values from packer tests at Aespoe. The comparison between models is made through the evaluation of cross-validation statistics for three experimental designs. The first experiment consisted of a 'Delete-1' test previously used at Finnsjoen. The second test consisted of 'Delete-10%' and the third test was a 'Delete-50%' test. Preliminary data analysis showed that the 3 m and 30 m packer test data can be treated as a sample from a single population for the purposes of geostatistical analyses. Analysis of the 3 m data does not indicate that there are any systematic statistical changes with depth, rock type, fracture zone vs non-fracture zone or other mappable factor. Directional variograms are ambiguous to interpret due to the clustered nature of the data, but do not show any obvious anisotropy that should be accounted for in geostatistical analysis. Stationary analysis suggested that there exists a sizeable spatially uncorrelated component ('Nugget Effect') in the 3 m data, on the order of 60% of the observed variance for the various models fitted. Four different nested models were automatically fit to the data. Results for all models in terms of cross-validation statistics were very similar for the first set of validation tests. Non-stationary analysis established that both the order of drift and the order of the intrinsic random functions is low. This study also suggests that conventional cross-validation studies and automatic variogram fitting are not necessarily evaluating how well a model will infer block scale hydraulic conductivity values. 20 refs, 20 figs, 14 tabs

  19. Quantum osp-invariant non-linear Schroedinger equation

    International Nuclear Information System (INIS)

    Kulish, P.P.

    1985-04-01

    The generalizations of the non-linear Schroedinger equation (NS) associated with the orthosymplectic superalgebras are formulated. The simplest osp(1/2)-NS model is solved by the quantum inverse scattering method on a finite interval under periodic boundary conditions as well as on the wholeline in the case of a finite number of excitations. (author)

  20. A Neural Network Combined Inverse Controller for a Two-Rear-Wheel Independently Driven Electric Vehicle

    Directory of Open Access Journals (Sweden)

    Duo Zhang

    2014-07-01

    Full Text Available Vehicle active safety control is attracting ever increasing attention in the attempt to improve the stability and the maneuverability of electric vehicles. In this paper, a neural network combined inverse (NNCI controller is proposed, incorporating the merits of left-inversion and right-inversion. As the left-inversion soft-sensor can estimate the sideslip angle, while the right-inversion is utilized to decouple control. Then, the proposed NNCI controller not only linearizes and decouples the original nonlinear system, but also directly obtains immeasurable state feedback in constructing the right-inversion. Hence, the proposed controller is very practical in engineering applications. The proposed system is co-simulated based on the vehicle simulation package CarSim in connection with Matlab/Simulink. The results verify the effectiveness of the proposed control strategy.

  1. Analog fault diagnosis by inverse problem technique

    KAUST Repository

    Ahmed, Rania F.

    2011-12-01

    A novel algorithm for detecting soft faults in linear analog circuits based on the inverse problem concept is proposed. The proposed approach utilizes optimization techniques with the aid of sensitivity analysis. The main contribution of this work is to apply the inverse problem technique to estimate the actual parameter values of the tested circuit and so, to detect and diagnose single fault in analog circuits. The validation of the algorithm is illustrated through applying it to Sallen-Key second order band pass filter and the results show that the detecting percentage efficiency was 100% and also, the maximum error percentage of estimating the parameter values is 0.7%. This technique can be applied to any other linear circuit and it also can be extended to be applied to non-linear circuits. © 2011 IEEE.

  2. Spatial distribution of Munida intermedia and M. sarsi (crustacea: Anomura) on the Galician continental shelf (NW Spain): Application of geostatistical analysis

    Science.gov (United States)

    Freire, J.; González-Gurriarán, E.; Olaso, I.

    1992-12-01

    Geostatistical methodology was used to analyse spatial structure and distribution of the epibenthic crustaceans Munida intermedia and M. sarsi within sets of data which had been collected during three survey cruises carried out on the Galician continental shelf (1983 and 1984). This study investigates the feasibility of using geostatistics for data collected according to traditional methods and of enhancing such methodology. The experimental variograms were calculated (pooled variance minus spatial covariance between samples taken one pair at a time vs. distance) and fitted to a 'spherical' model. The spatial structure model was used to estimate the abundance and distribution of the populations studied using the technique of kriging. The species display spatial structures, which are well marked during high density periods and in some areas (especially northern shelf). Geostatistical analysis allows identification of the density gradients in space as well as the patch grain along the continental shelf of 16-25 km diameter for M. intermedia and 12-20 km for M. sarsi. Patches of both species have a consistent location throughout the different cruises. As in other geographical areas, M. intermedia and M. sarsi usually appear at depths ranging from 200 to 500 m, with the highest densities in the continental shelf area located between Fisterra and Estaca de Bares. Althouh sampling was not originally designed specifically for geostatistics, this assay provides a measurement of spatial covariance, and shows variograms with variable structure depending on population density and geographical area. These ideas are useful in improving the design of future sampling cruises.

  3. Evaluation of spatial variability of metal bioavailability in soils using geostatistics

    DEFF Research Database (Denmark)

    Owsianiak, Mikolaj; Hauschild, Michael Zwicky; Rosenbaum, Ralph K.

    2012-01-01

    Soil properties show signifficant spatial variability at local, regional and continental scales. This is a challenge for life cycle impact assessment (LCIA) of metals, because fate, bioavailability and effect factors are controlled by environmental chemistry and can vary orders of magnitude...... is performed using ArcGIS Geostatistical Analyst. Results show that BFs of copper span a range of 6 orders of magnitude, and have signifficant spatial variability at local and continental scales. The model nugget variance is signifficantly higher than zero, suggesting the presence of spatial variability...

  4. The role of geostatistics in medical geology

    Science.gov (United States)

    Goovaerts, Pierre

    2014-05-01

    Since its development in the mining industry, geostatistics has emerged as the primary tool for spatial data analysis in various fields, ranging from earth and atmospheric sciences, to agriculture, soil science, remote sensing, and more recently environmental exposure assessment. In the last few years, these tools have been tailored to the field of medical geography or spatial epidemiology, which is concerned with the study of spatial patterns of disease incidence and mortality and the identification of potential 'causes' of disease, such as environmental exposure, diet and unhealthy behaviors, economic or socio-demographic factors. On the other hand, medical geology is an emerging interdisciplinary scientific field studying the relationship between natural geological factors and their effects on human and animal health. This paper provides an introduction to the field of medical geology with an overview of geostatistical methods available for the analysis of geological and health data. Key concepts are illustrated using the mapping of groundwater arsenic concentrations across eleven Michigan counties and the exploration of its relationship to the incidence of prostate cancer at the township level. Arsenic in drinking-water is a major problem and has received much attention because of the large human population exposed and the extremely high concentrations (e.g. 600 to 700 μg/L) recorded in many instances. Few studies have however assessed the risks associated with exposure to low levels of arsenic (say water in the United States. In the Michigan thumb region, arsenopyrite (up to 7% As by weight) has been identified in the bedrock of the Marshall Sandstone aquifer, one of the region's most productive aquifers. Epidemiologic studies have suggested a possible associationbetween exposure to inorganic arsenic and prostate cancer mortality, including a study of populations residing in Utah. The information available for the present ecological study (i.e. analysis of

  5. Aircraft automatic-flight-control system with inversion of the model in the feed-forward path using a Newton-Raphson technique for the inversion

    Science.gov (United States)

    Smith, G. A.; Meyer, G.; Nordstrom, M.

    1986-01-01

    A new automatic flight control system concept suitable for aircraft with highly nonlinear aerodynamic and propulsion characteristics and which must operate over a wide flight envelope was investigated. This exact model follower inverts a complete nonlinear model of the aircraft as part of the feed-forward path. The inversion is accomplished by a Newton-Raphson trim of the model at each digital computer cycle time of 0.05 seconds. The combination of the inverse model and the actual aircraft in the feed-forward path alloys the translational and rotational regulators in the feedback path to be easily designed by linear methods. An explanation of the model inversion procedure is presented. An extensive set of simulation data for essentially the full flight envelope for a vertical attitude takeoff and landing aircraft (VATOL) is presented. These data demonstrate the successful, smooth, and precise control that can be achieved with this concept. The trajectory includes conventional flight from 200 to 900 ft/sec with path accelerations and decelerations, altitude changes of over 6000 ft and 2g and 3g turns. Vertical attitude maneuvering as a tail sitter along all axes is demonstrated. A transition trajectory from 200 ft/sec in conventional flight to stationary hover in the vertical attitude includes satisfactory operation through lift-cure slope reversal as attitude goes from horizontal to vertical at constant altitude. A vertical attitude takeoff from stationary hover to conventional flight is also demonstrated.

  6. Formal solutions of inverse scattering problems. III

    International Nuclear Information System (INIS)

    Prosser, R.T.

    1980-01-01

    The formal solutions of certain three-dimensional inverse scattering problems presented in papers I and II of this series [J. Math. Phys. 10, 1819 (1969); 17 1175 (1976)] are obtained here as fixed points of a certain nonlinear mapping acting on a suitable Banach space of integral kernels. When the scattering data are sufficiently restricted, this mapping is shown to be a contraction, thereby establishing the existence, uniqueness, and continuous dependence on the data of these formal solutions

  7. Born reflection kernel analysis and wave-equation reflection traveltime inversion in elastic media

    KAUST Repository

    Wang, Tengfei

    2017-08-17

    Elastic reflection waveform inversion (ERWI) utilize the reflections to update the low and intermediate wavenumbers in the deeper part of model. However, ERWI suffers from the cycle-skipping problem due to the objective function of waveform residual. Since traveltime information relates to the background model more linearly, we use the traveltime residuals as objective function to update background velocity model using wave equation reflected traveltime inversion (WERTI). The reflection kernel analysis shows that mode decomposition can suppress the artifacts in gradient calculation. We design a two-step inversion strategy, in which PP reflections are firstly used to invert P wave velocity (Vp), followed by S wave velocity (Vs) inversion with PS reflections. P/S separation of multi-component seismograms and spatial wave mode decomposition can reduce the nonlinearity of inversion effectively by selecting suitable P or S wave subsets for hierarchical inversion. Numerical example of Sigsbee2A model validates the effectiveness of the algorithms and strategies for elastic WERTI (E-WERTI).

  8. Geostatistical uncertainty of assessing air quality using high-spatial-resolution lichen data: A health study in the urban area of Sines, Portugal.

    Science.gov (United States)

    Ribeiro, Manuel C; Pinho, P; Branquinho, C; Llop, Esteve; Pereira, Maria J

    2016-08-15

    In most studies correlating health outcomes with air pollution, personal exposure assignments are based on measurements collected at air-quality monitoring stations not coinciding with health data locations. In such cases, interpolators are needed to predict air quality in unsampled locations and to assign personal exposures. Moreover, a measure of the spatial uncertainty of exposures should be incorporated, especially in urban areas where concentrations vary at short distances due to changes in land use and pollution intensity. These studies are limited by the lack of literature comparing exposure uncertainty derived from distinct spatial interpolators. Here, we addressed these issues with two interpolation methods: regression Kriging (RK) and ordinary Kriging (OK). These methods were used to generate air-quality simulations with a geostatistical algorithm. For each method, the geostatistical uncertainty was drawn from generalized linear model (GLM) analysis. We analyzed the association between air quality and birth weight. Personal health data (n=227) and exposure data were collected in Sines (Portugal) during 2007-2010. Because air-quality monitoring stations in the city do not offer high-spatial-resolution measurements (n=1), we used lichen data as an ecological indicator of air quality (n=83). We found no significant difference in the fit of GLMs with any of the geostatistical methods. With RK, however, the models tended to fit better more often and worse less often. Moreover, the geostatistical uncertainty results showed a marginally higher mean and precision with RK. Combined with lichen data and land-use data of high spatial resolution, RK is a more effective geostatistical method for relating health outcomes with air quality in urban areas. This is particularly important in small cities, which generally do not have expensive air-quality monitoring stations with high spatial resolution. Further, alternative ways of linking human activities with their

  9. Hand-Eye Calibration and Inverse Kinematics of Robot Arm using Neural Network

    DEFF Research Database (Denmark)

    Wu, Haiyan; Tizzano, Walter; Andersen, Thomas Timm

    2013-01-01

    Traditional technologies for solving hand-eye calibration and inverse kinematics are cumbersome and time consuming due to the high nonlinearity in the models. An alternative to the traditional approaches is the articial neural network inspired by the remarkable abilities of the animals in dierent...

  10. Numerical modeling of Harmonic Imaging and Pulse Inversion fields

    Science.gov (United States)

    Humphrey, Victor F.; Duncan, Tracy M.; Duck, Francis

    2003-10-01

    Tissue Harmonic Imaging (THI) and Pulse Inversion (PI) Harmonic Imaging exploit the harmonics generated as a result of nonlinear propagation through tissue to improve the performance of imaging systems. A 3D finite difference model, that solves the KZK equation in the frequency domain, is used to investigate the finite amplitude fields produced by rectangular transducers driven with short pulses and their inverses, in water and homogeneous tissue. This enables the characteristic of the fields and the effective PI field to be calculated. The suppression of the fundamental field in PI is monitored, and the suppression of side lobes and a reduction in the effective beamwidth for each field are calculated. In addition, the differences between the pulse and inverse pulse spectra resulting from the use of very short pulses are noted, and the differences in the location of the fundamental and second harmonic spectral peaks observed.

  11. Controllability of nonlinear delay oscillating systems

    Directory of Open Access Journals (Sweden)

    Chengbin Liang

    2017-05-01

    Full Text Available In this paper, we study the controllability of a system governed by second order delay differential equations. We introduce a delay Gramian matrix involving the delayed matrix sine, which is used to establish sufficient and necessary conditions of controllability for the linear problem. In addition, we also construct a specific control function for controllability. For the nonlinear problem, we construct a control function and transfer the controllability problem to a fixed point problem for a suitable operator. We give a sufficient condition to guarantee the nonlinear delay system is controllable. Two examples are given to illustrate our theoretical results by calculating a specific control function and inverse of a delay Gramian matrix.

  12. Relative sensitivity of depth discrimination for ankle inversion and plantar flexion movements.

    Science.gov (United States)

    Black, Georgia; Waddington, Gordon; Adams, Roger

    2014-02-01

    25 participants (20 women, 5 men) were tested for sensitivity in discrimination between sets of six movements centered on 8 degrees, 11 degrees, and 14 degrees, and separated by 0.3 degrees. Both inversion and plantar flexion movements were tested. Discrimination of the extent of inversion movement was observed to decline linearly with increasing depth; however, for plantar flexion, the discrimination function for movement extent was found to be non-linear. The relatively better discrimination of plantar flexion movements than inversion movements at around 11 degrees from horizontal is interpreted as an effect arising from differential amounts of practice through use, because this position is associated with the plantar flexion movement made in normal walking. The fact that plantar flexion movements are discriminated better than inversion at one region but not others argues against accounts of superior proprioceptive sensitivity for plantar flexion compared to inversion that are based on general properties of plantar flexion such as the number of muscle fibres on stretch.

  13. Extraction of Spin-Orbit Interactions from Phase Shifts via Inversion

    International Nuclear Information System (INIS)

    Lun, D.R.; Buckman, S.J.

    1997-01-01

    An exact inversion procedure for obtaining the central and spin-orbit potential from phase shifts at fixed energy is described. The method, based on Sabatier interpolation formulas, reduces the nonlinear problem to linear-algebraic equations. We have tested the method with a Woods-Saxon potential with a strong spin-orbit component. copyright 1997 The American Physical Society

  14. Theory of nonlinear interaction of particles and waves in an inverse plasma maser. Part 1

    International Nuclear Information System (INIS)

    Krivitsky, V.S.; Vladimirov, S.V.

    1991-01-01

    An expression is obtained for the collision integral describing the simultaneous interaction of plasma particles with resonant and non-resonant waves. It is shown that this collision integral is determined by two processes: a 'direct' nonlinear interaction of particles and waves, and the influence of the non-stationary of the system. The expression for the nonlinear collision integral is found to be quite different from the expression for a quasi-linear collision integral; in particular, the nonlinear integral contains higher-order derivatives of the distribution function with respect to momentum than the quasi-linear one. (author)

  15. Joint inversion of hydraulic head and self-potential data associated with harmonic pumping tests

    Science.gov (United States)

    Soueid Ahmed, A.; Jardani, A.; Revil, A.; Dupont, J. P.

    2016-09-01

    Harmonic pumping tests consist in stimulating an aquifer by the means of hydraulic stimulations at some discrete frequencies. The inverse problem consisting in retrieving the hydraulic properties is inherently ill posed and is usually underdetermined when considering the number of well head data available in field conditions. To better constrain this inverse problem, we add self-potential data recorded at the ground surface to the head data. The self-potential method is a passive geophysical method. Its signals are generated by the groundwater flow through an electrokinetic coupling. We showed using a 3-D saturated unconfined synthetic aquifer that the self-potential method significantly improves the results of the harmonic hydraulic tomography. The hydroelectric forward problem is obtained by solving first the Richards equation, describing the groundwater flow, and then using the result in an electrical Poisson equation describing the self-potential problem. The joint inversion problem is solved using a reduction model based on the principal component geostatistical approach. In this method, the large prior covariance matrix is truncated and replaced by its low-rank approximation, allowing thus for notable computational time and storage savings. Three test cases are studied, to assess the validity of our approach. In the first test, we show that when the number of harmonic stimulations is low, combining the harmonic hydraulic and self-potential data does not improve the inversion results. In the second test where enough harmonic stimulations are performed, a significant improvement of the hydraulic parameters is observed. In the last synthetic test, we show that the electrical conductivity field required to invert the self-potential data can be determined with enough accuracy using an electrical resistivity tomography survey using the same electrodes configuration as used for the self-potential investigation.

  16. Three-dimensional gravity modeling and focusing inversion using rectangular meshes.

    Energy Technology Data Exchange (ETDEWEB)

    Commer, M.

    2011-03-01

    Rectangular grid cells are commonly used for the geophysical modeling of gravity anomalies, owing to their flexibility in constructing complex models. The straightforward handling of cubic cells in gravity inversion algorithms allows for a flexible imposition of model regularization constraints, which are generally essential in the inversion of static potential field data. The first part of this paper provides a review of commonly used expressions for calculating the gravity of a right polygonal prism, both for gravity and gradiometry, where the formulas of Plouff and Forsberg are adapted. The formulas can be cast into general forms practical for implementation. In the second part, a weighting scheme for resolution enhancement at depth is presented. Modelling the earth using highly digitized meshes, depth weighting schemes are typically applied to the model objective functional, subject to minimizing the data misfit. The scheme proposed here involves a non-linear conjugate gradient inversion scheme with a weighting function applied to the non-linear conjugate gradient scheme's gradient vector of the objective functional. The low depth resolution due to the quick decay of the gravity kernel functions is counteracted by suppressing the search directions in the parameter space that would lead to near-surface concentrations of gravity anomalies. Further, a density parameter transformation function enabling the imposition of lower and upper bounding constraints is employed. Using synthetic data from models of varying complexity and a field data set, it is demonstrated that, given an adequate depth weighting function, the gravity inversion in the transform space can recover geologically meaningful models requiring a minimum of prior information and user interaction.

  17. Modeling and inverse feedforward control for conducting polymer actuators with hysteresis

    International Nuclear Information System (INIS)

    Wang, Xiangjiang; Alici, Gursel; Tan, Xiaobo

    2014-01-01

    Conducting polymer actuators are biocompatible with a small footprint, and operate in air or liquid media under low actuation voltages. This makes them excellent actuators for macro- and micro-manipulation devices, however, their positioning ability or accuracy is adversely affected by their hysteresis non-linearity under open-loop control strategies. In this paper, we establish a hysteresis model for conducting polymer actuators, based on a rate-independent hysteresis model known as the Duhem model. The hysteresis model is experimentally identified and integrated with the linear dynamics of the actuator. This combined model is inverted to control the displacement of the tri-layer actuators considered in this study, without using any external feedback. The inversion requires an inverse hysteresis model which was experimentally identified using an inverse neural network model. Experimental results show that the position tracking errors are reduced by more than 50% when the hysteresis inverse model is incorporated into an inversion-based feedforward controller, indicating the potential of the proposed method in enabling wider use of such smart actuators. (paper)

  18. Spatially localized, temporally quasiperiodic, discrete nonlinear excitations

    International Nuclear Information System (INIS)

    Cai, D.; Bishop, A.R.; Gronbech-Jensen, N.

    1995-01-01

    In contrast to the commonly discussed discrete breather, which is a spatially localized, time-periodic solution, we present an exact solution of a discrete nonlinear Schroedinger breather which is a spatially localized, temporally quasiperiodic nonlinear coherent excitation. This breather is a multiple-soliton solution in the sense of the inverse scattering transform. A discrete breather of multiple frequencies is conceptually important in studies of nonlinear lattice systems. We point out that, for this breather, the incommensurability of its frequencies is a discrete lattice effect and these frequencies become commensurate in the continuum limit. To understand the dynamical properties of the breather, we also discuss its stability and its behavior in the presence of an external potential. Finally, we indicate how to obtain an exact N-soliton breather as a discrete generalization of the continuum multiple-soliton solution

  19. Stokes profile analysis and vector magnetic fields. I. Inversion of photospheric lines

    International Nuclear Information System (INIS)

    Skumanich, A.; Lites, B.W.

    1987-01-01

    Improvements are proposed for the Auer et al. (1977) method for the analytic inversion of Stokes profiles via nonlinear least squares. The introduction of additional physics into the Mueller absorption matrix (by including damping wings and magnetooptical birefringence, and by decoupling the intensity profile from the three-vector polarization profile in the analysis) is found to result in a more robust inversion method, providing more reliable and accurate estimates of sunspot vector magnetic fields without significant loss of economy. The method is applied to sunspot observations obtained with the High Altitude Observatory polarimeter. 29 references

  20. Multi-year Estimates of Methane Fluxes in Alaska from an Atmospheric Inverse Model

    Science.gov (United States)

    Miller, S. M.; Commane, R.; Chang, R. Y. W.; Miller, C. E.; Michalak, A. M.; Dinardo, S. J.; Dlugokencky, E. J.; Hartery, S.; Karion, A.; Lindaas, J.; Sweeney, C.; Wofsy, S. C.

    2015-12-01

    We estimate methane fluxes across Alaska over a multi-year period using observations from a three-year aircraft campaign, the Carbon Arctic Reservoirs Vulnerability Experiment (CARVE). Existing estimates of methane from Alaska and other Arctic regions disagree in both magnitude and distribution, and before the CARVE campaign, atmospheric observations in the region were sparse. We combine these observations with an atmospheric particle trajectory model and a geostatistical inversion to estimate surface fluxes at the model grid scale. We first use this framework to estimate the spatial distribution of methane fluxes across the state. We find the largest fluxes in the south-east and North Slope regions of Alaska. This distribution is consistent with several estimates of wetland extent but contrasts with the distribution in most existing flux models. These flux models concentrate methane in warmer or more southerly regions of Alaska compared to the estimate presented here. This result suggests a discrepancy in how existing bottom-up models translate wetland area into methane fluxes across the state. We next use the inversion framework to explore inter-annual variability in regional-scale methane fluxes for 2012-2014. We examine the extent to which this variability correlates with weather or other environmental conditions. These results indicate the possible sensitivity of wetland fluxes to near-term variability in climate.

  1. Nonlinear and anisotropic polarization rotation in two-dimensional Dirac materials

    Science.gov (United States)

    Singh, Ashutosh; Ghosh, Saikat; Agarwal, Amit

    2018-05-01

    We predict nonlinear optical polarization rotation in two-dimensional massless Dirac systems including graphene and 8-P m m n borophene. When illuminated, a continuous-wave optical field leads to a nonlinear steady state of photoexcited carriers in the medium. The photoexcited population inversion and the interband coherence give rise to a finite transverse optical conductivity σx y(ω ) . This in turn leads to definitive signatures in associated Kerr and Faraday polarization rotation, which are measurable in a realistic experimental scenario.

  2. From nonlinear Schroedinger hierarchy to some (2+1)-dimensional nonlinear pseudodifferential equations

    International Nuclear Information System (INIS)

    Yang Xiao; Du Dianlou

    2010-01-01

    The Poisson structure on C N xR N is introduced to give the Hamiltonian system associated with a spectral problem which yields the nonlinear Schroedinger (NLS) hierarchy. The Hamiltonian system is proven to be Liouville integrable. Some (2+1)-dimensional equations including NLS equation, Kadomtesev-Petviashvili I (KPI) equation, coupled KPI equation, and modified Kadomtesev-Petviashvili (mKP) equation, are decomposed into Hamilton flows via the NLS hierarchy. The algebraic curve, Abel-Jacobi coordinates, and Riemann-Jacobi inversion are used to obtain the algebrogeometric solutions of these equations.

  3. Recovery of material parameters of soft hyperelastic tissue by an inverse spectral technique

    KAUST Repository

    Gou, Kun

    2012-07-01

    An inverse spectral method is developed for recovering a spatially inhomogeneous shear modulus for soft tissue. The study is motivated by a novel use of the intravascular ultrasound technique to image arteries. The arterial wall is idealized as a nonlinear isotropic cylindrical hyperelastic body. A boundary value problem is formulated for the response of the arterial wall within a specific class of quasistatic deformations reflective of the response due to imposed blood pressure. Subsequently, a boundary value problem is developed via an asymptotic construction modeling intravascular ultrasound interrogation which generates small amplitude, high frequency time harmonic vibrations superimposed on the static finite deformation. This leads to a system of second order ordinary Sturm-Liouville boundary value problems that are then employed to reconstruct the shear modulus through a nonlinear inverse spectral technique. Numerical examples are demonstrated to show the viability of the method. © 2012 Elsevier Ltd. All rights reserved.

  4. Linearized versus non-linear inverse methods for seismic localization of underground sources

    DEFF Research Database (Denmark)

    Oh, Geok Lian; Jacobsen, Finn

    2013-01-01

    The problem of localization of underground sources from seismic measurements detected by several geophones located on the ground surface is addressed. Two main approaches to the solution of the problem are considered: a beamforming approach that is derived from the linearized inversion problem, a...

  5. Downscaling remotely sensed imagery using area-to-point cokriging and multiple-point geostatistical simulation

    Science.gov (United States)

    Tang, Yunwei; Atkinson, Peter M.; Zhang, Jingxiong

    2015-03-01

    A cross-scale data integration method was developed and tested based on the theory of geostatistics and multiple-point geostatistics (MPG). The goal was to downscale remotely sensed images while retaining spatial structure by integrating images at different spatial resolutions. During the process of downscaling, a rich spatial correlation model in the form of a training image was incorporated to facilitate reproduction of similar local patterns in the simulated images. Area-to-point cokriging (ATPCK) was used as locally varying mean (LVM) (i.e., soft data) to deal with the change of support problem (COSP) for cross-scale integration, which MPG cannot achieve alone. Several pairs of spectral bands of remotely sensed images were tested for integration within different cross-scale case studies. The experiment shows that MPG can restore the spatial structure of the image at a fine spatial resolution given the training image and conditioning data. The super-resolution image can be predicted using the proposed method, which cannot be realised using most data integration methods. The results show that ATPCK-MPG approach can achieve greater accuracy than methods which do not account for the change of support issue.

  6. The inverse problem for Schwinger pair production

    Directory of Open Access Journals (Sweden)

    F. Hebenstreit

    2016-02-01

    Full Text Available The production of electron–positron pairs in time-dependent electric fields (Schwinger mechanism depends non-linearly on the applied field profile. Accordingly, the resulting momentum spectrum is extremely sensitive to small variations of the field parameters. Owing to this non-linear dependence it is so far unpredictable how to choose a field configuration such that a predetermined momentum distribution is generated. We show that quantum kinetic theory along with optimal control theory can be used to approximately solve this inverse problem for Schwinger pair production. We exemplify this by studying the superposition of a small number of harmonic components resulting in predetermined signatures in the asymptotic momentum spectrum. In the long run, our results could facilitate the observation of this yet unobserved pair production mechanism in quantum electrodynamics by providing suggestions for tailored field configurations.

  7. Predictable nonlinear dynamics: Advances and limitations

    International Nuclear Information System (INIS)

    Anosov, L.A.; Butkovskii, O.Y.; Kravtsov, Y.A.; Surovyatkina, E.D.

    1996-01-01

    Methods for reconstruction chaotic dynamical system structure directly from experimental time series are described. Effectiveness of general methods is illustrated with the results of numerical simulation. It is of common interest that from the single time series it is possible to reconstruct a set of interconnected variables. Predictive power of dynamical models, provided by the nonlinear dynamics inverse problem solution, is limited firstly by the noise level in the system under study and is characterized by the horizon of predictability. New physical results are presented, concerning nonstationary and bifurcation nonlinear systems: (1) algorithms for revealing of nonstationarity in random-like chaotic time-series are suggested based on discriminant analysis with nonlinear discriminant function; (2) an opportunity is established to predict the final state in bifurcation system with quickly varying control parameters; (3) hysteresis is founded out in bifurcation system with quickly varying parameters; (4) delayed correlation left-angle noise-prediction error right-angle in chaotic systems is revealed. copyright 1996 American Institute of Physics

  8. An inverse problem for a semilinear parabolic equation arising from cardiac electrophysiology

    Science.gov (United States)

    Beretta, Elena; Cavaterra, Cecilia; Cerutti, M. Cristina; Manzoni, Andrea; Ratti, Luca

    2017-10-01

    In this paper we develop theoretical analysis and numerical reconstruction techniques for the solution of an inverse boundary value problem dealing with the nonlinear, time-dependent monodomain equation, which models the evolution of the electric potential in the myocardial tissue. The goal is the detection of an inhomogeneity \

  9. Inverse Problems in a Bayesian Setting

    KAUST Repository

    Matthies, Hermann G.

    2016-02-13

    In a Bayesian setting, inverse problems and uncertainty quantification (UQ)—the propagation of uncertainty through a computational (forward) model—are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. We give a detailed account of this approach via conditional approximation, various approximations, and the construction of filters. Together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update in form of a filter is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and nonlinear Bayesian update in form of a filter on some examples.

  10. Inverse Problems in a Bayesian Setting

    KAUST Repository

    Matthies, Hermann G.; Zander, Elmar; Rosić, Bojana V.; Litvinenko, Alexander; Pajonk, Oliver

    2016-01-01

    In a Bayesian setting, inverse problems and uncertainty quantification (UQ)—the propagation of uncertainty through a computational (forward) model—are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. We give a detailed account of this approach via conditional approximation, various approximations, and the construction of filters. Together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update in form of a filter is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and nonlinear Bayesian update in form of a filter on some examples.

  11. Fast inverse nonlinear Fourier transformation using exponential one-step methods : Darboux transformation

    NARCIS (Netherlands)

    Vaibhav, V.K.

    2017-01-01

    This paper considers the non-Hermitian Zakharov-Shabat (ZS) scattering problem which forms the basis for defining the SU(2) nonlinear Fourier transformation (NFT). The theoretical underpinnings of this generalization of the conventional Fourier transformation are quite well established in the

  12. Geostatistical Analysis Methods for Estimation of Environmental Data Homogeneity

    Directory of Open Access Journals (Sweden)

    Aleksandr Danilov

    2018-01-01

    Full Text Available The methodology for assessing the spatial homogeneity of ecosystems with the possibility of subsequent zoning of territories in terms of the degree of disturbance of the environment is considered in the study. The degree of pollution of the water body was reconstructed on the basis of hydrochemical monitoring data and information on the level of the technogenic load in one year. As a result, the greatest environmental stress zones were isolated and correct zoning using geostatistical analysis techniques was proved. Mathematical algorithm computing system was implemented in an object-oriented programming C #. A software application has been obtained that allows quickly assessing the scale and spatial localization of pollution during the initial analysis of the environmental situation.

  13. Geostatistical analysis of the flood risk perception queries in the village of Navaluenga (Central Spain)

    Science.gov (United States)

    Guardiola-Albert, Carolina; Díez-Herrero, Andrés; Amérigo, María; García, Juan Antonio; María Bodoque, José; Fernández-Naranjo, Nuria

    2017-04-01

    Flash floods provoke a high average mortality as they are usually unexpected events which evolve rapidly and affect relatively small areas. The short time available for minimizing risks requires preparedness and response actions to be put into practice. Therefore, it is necessary the development of emergency response plans to evacuate and rescue people in the context of a flash-flood hazard. In this framework, risk management has to integrate the social dimension of flash-flooding and its spatial distribution by understanding the characteristics of local communities in order to enhance community resilience during a flash-flood. In this regard, the flash-flood social risk perception of the village of Navaluenga (Central Spain) has been recently assessed, as well as the level of awareness of civil protection and emergency management strategies (Bodoque et al., 2016). This has been done interviewing 254 adults, representing roughly 12% of the population census. The present study wants to go further in the analysis of the resulting questionnaires, incorporating in the analysis the location of home spatial coordinates in order to characterize the spatial distribution and possible geographical interpretation of flood risk perception. We apply geostatistical methods to analyze spatial relations of social risk perception and level of awareness with distance to the rivers (Alberche and Chorrerón) or to the flood-prone areas (50-year, 100-year and 500-year flood plains). We want to discover spatial patterns, if any, using correlation functions (variograms). Geostatistical analyses results can help to either confirm the logical pattern (i.e., less awareness further to the rivers or high return period of flooding) or reveal departures from expected. It can also be possible to identify hot spots, cold spots, and spatial outliers. The interpretation of these spatial patterns can give valuable information to define strategies to improve the awareness regarding preparedness and

  14. Conditioning the full waveform inversion gradient to welcome anisotropy

    KAUST Repository

    Alkhalifah, Tariq Ali

    2014-01-01

    Multi-parameter full waveform inversion (FWI) suffers from the complex nonlinearity in the objective function, compounded by the eventual tradeoff between the model parameters. A hierarchical approach based on frequency and arrival time data decimation to maneuver the complex nonlinearity associated with this problem usually falls short in anisotropic media. In place of data decimation, I use a model gradient filter approach to access the parts of the gradient more suitable to combat the potential nonlinearity and parameter trade off. The filter is based on representing the gradient in the time-lag normalized domain in which the small scattering angles of the gradient update is initially muted out. A model update hierarchical filtering strategy includes applying varying degree of filtering to the different parameter updates. A feature not easily accessible to simple data decimation. Using both FWI and reection based FWI (RFWI), two strategies to combat the tradeoff between anisotropic parameters are outlined.

  15. Conditioning the full waveform inversion gradient to welcome anisotropy

    KAUST Repository

    Alkhalifah, Tariq Ali

    2014-08-05

    Multi-parameter full waveform inversion (FWI) suffers from the complex nonlinearity in the objective function, compounded by the eventual tradeoff between the model parameters. A hierarchical approach based on frequency and arrival time data decimation to maneuver the complex nonlinearity associated with this problem usually falls short in anisotropic media. In place of data decimation, I use a model gradient filter approach to access the parts of the gradient more suitable to combat the potential nonlinearity and parameter trade off. The filter is based on representing the gradient in the time-lag normalized domain in which the small scattering angles of the gradient update is initially muted out. A model update hierarchical filtering strategy includes applying varying degree of filtering to the different parameter updates. A feature not easily accessible to simple data decimation. Using both FWI and reection based FWI (RFWI), two strategies to combat the tradeoff between anisotropic parameters are outlined.

  16. Bayesian inversion of refraction seismic traveltime data

    Science.gov (United States)

    Ryberg, T.; Haberland, Ch

    2018-03-01

    We apply a Bayesian Markov chain Monte Carlo (McMC) formalism to the inversion of refraction seismic, traveltime data sets to derive 2-D velocity models below linear arrays (i.e. profiles) of sources and seismic receivers. Typical refraction data sets, especially when using the far-offset observations, are known as having experimental geometries which are very poor, highly ill-posed and far from being ideal. As a consequence, the structural resolution quickly degrades with depth. Conventional inversion techniques, based on regularization, potentially suffer from the choice of appropriate inversion parameters (i.e. number and distribution of cells, starting velocity models, damping and smoothing constraints, data noise level, etc.) and only local model space exploration. McMC techniques are used for exhaustive sampling of the model space without the need of prior knowledge (or assumptions) of inversion parameters, resulting in a large number of models fitting the observations. Statistical analysis of these models allows to derive an average (reference) solution and its standard deviation, thus providing uncertainty estimates of the inversion result. The highly non-linear character of the inversion problem, mainly caused by the experiment geometry, does not allow to derive a reference solution and error map by a simply averaging procedure. We present a modified averaging technique, which excludes parts of the prior distribution in the posterior values due to poor ray coverage, thus providing reliable estimates of inversion model properties even in those parts of the models. The model is discretized by a set of Voronoi polygons (with constant slowness cells) or a triangulated mesh (with interpolation within the triangles). Forward traveltime calculations are performed by a fast, finite-difference-based eikonal solver. The method is applied to a data set from a refraction seismic survey from Northern Namibia and compared to conventional tomography. An inversion test

  17. Modelling Loudspeaker Non-Linearities

    DEFF Research Database (Denmark)

    Agerkvist, Finn T.

    2007-01-01

    This paper investigates different techniques for modelling the non-linear parameters of the electrodynamic loudspeaker. The methods are tested not only for their accuracy within the range of original data, but also for the ability to work reasonable outside that range, and it is demonstrated...... that polynomial expansions are rather poor at this, whereas an inverse polynomial expansion or localized fitting functions such as the gaussian are better suited for modelling the Bl-factor and compliance. For the inductance the sigmoid function is shown to give very good results. Finally the time varying...

  18. Waveform inversion for acoustic VTI media in frequency domain

    KAUST Repository

    Wu, Zedong

    2016-09-06

    Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI) by inverting for the background model using a single scattered wavefield from an inverted perturbation. However, current RWI methods are mostly based on isotropic media assumption. We extend the idea of the combining inversion for the background model and perturbations to address transversely isotropic with a vertical axis of symmetry (VTI) media taking into consideration of the optimal parameter sensitivity information. As a result, we apply Born modeling corresponding to perturbations in only for the variable e to derive the relative reflected waveform inversion formulation. To reduce the number of parameters, we assume the background part of η = ε and work with a single variable to describe the anisotropic part of the wave propagation. Thus, the optimization variables are the horizontal velocity v, η = ε and the e perturbation. Application to the anisotropic version of Marmousi model with a single frequency of 2.5 Hz shows that this method can converge to the accurate result starting from a linearly increasing isotropic initial velocity. Application to a real dataset demonstrates the versatility of the approach.

  19. Stability and uncertainty of finite-fault slip inversions: Application to the 2004 Parkfield, California, earthquake

    Science.gov (United States)

    Hartzell, S.; Liu, P.; Mendoza, C.; Ji, C.; Larson, K.M.

    2007-01-01

    The 2004 Parkfield, California, earthquake is used to investigate stability and uncertainty aspects of the finite-fault slip inversion problem with different a priori model assumptions. We utilize records from 54 strong ground motion stations and 13 continuous, 1-Hz sampled, geodetic instruments. Two inversion procedures are compared: a linear least-squares subfault-based methodology and a nonlinear global search algorithm. These two methods encompass a wide range of the different approaches that have been used to solve the finite-fault slip inversion problem. For the Parkfield earthquake and the inversion of velocity or displacement waveforms, near-surface related site response (top 100 m, frequencies above 1 Hz) is shown to not significantly affect the solution. Results are also insensitive to selection of slip rate functions with similar duration and to subfault size if proper stabilizing constraints are used. The linear and nonlinear formulations yield consistent results when the same limitations in model parameters are in place and the same inversion norm is used. However, the solution is sensitive to the choice of inversion norm, the bounds on model parameters, such as rake and rupture velocity, and the size of the model fault plane. The geodetic data set for Parkfield gives a slip distribution different from that of the strong-motion data, which may be due to the spatial limitation of the geodetic stations and the bandlimited nature of the strong-motion data. Cross validation and the bootstrap method are used to set limits on the upper bound for rupture velocity and to derive mean slip models and standard deviations in model parameters. This analysis shows that slip on the northwestern half of the Parkfield rupture plane from the inversion of strong-motion data is model dependent and has a greater uncertainty than slip near the hypocenter.

  20. Linear versus non-linear structural information limit in high-resolution transmission electron microscopy

    International Nuclear Information System (INIS)

    Van Aert, S.; Chen, J.H.; Van Dyck, D.

    2010-01-01

    A widely used performance criterion in high-resolution transmission electron microscopy (HRTEM) is the information limit. It corresponds to the inverse of the maximum spatial object frequency that is linearly transmitted with sufficient intensity from the exit plane of the object to the image plane and is limited due to partial temporal coherence. In practice, the information limit is often measured from a diffractogram or from Young's fringes assuming a weak phase object scattering beyond the inverse of the information limit. However, for an aberration corrected electron microscope, with an information limit in the sub-angstrom range, weak phase objects are no longer applicable since they do not scatter sufficiently in this range. Therefore, one relies on more strongly scattering objects such as crystals of heavy atoms observed along a low index zone axis. In that case, dynamical scattering becomes important such that the non-linear and linear interaction may be equally important. The non-linear interaction may then set the experimental cut-off frequency observed in a diffractogram. The goal of this paper is to quantify both the linear and the non-linear information transfer in terms of closed form analytical expressions. Whereas the cut-off frequency set by the linear transfer can be directly related with the attainable resolution, information from the non-linear transfer can only be extracted using quantitative, model-based methods. In contrast to the historic definition of the information limit depending on microscope parameters only, the expressions derived in this paper explicitly incorporate their dependence on the structure parameters as well. In order to emphasize this dependence and to distinguish from the usual information limit, the expressions derived for the inverse cut-off frequencies will be referred to as the linear and non-linear structural information limit. The present findings confirm the well-known result that partial temporal coherence has

  1. Inverse problem in hydrogeology

    Science.gov (United States)

    Carrera, Jesús; Alcolea, Andrés; Medina, Agustín; Hidalgo, Juan; Slooten, Luit J.

    2005-03-01

    The state of the groundwater inverse problem is synthesized. Emphasis is placed on aquifer characterization, where modelers have to deal with conceptual model uncertainty (notably spatial and temporal variability), scale dependence, many types of unknown parameters (transmissivity, recharge, boundary conditions, etc.), nonlinearity, and often low sensitivity of state variables (typically heads and concentrations) to aquifer properties. Because of these difficulties, calibration cannot be separated from the modeling process, as it is sometimes done in other fields. Instead, it should be viewed as one step in the process of understanding aquifer behavior. In fact, it is shown that actual parameter estimation methods do not differ from each other in the essence, though they may differ in the computational details. It is argued that there is ample room for improvement in groundwater inversion: development of user-friendly codes, accommodation of variability through geostatistics, incorporation of geological information and different types of data (temperature, occurrence and concentration of isotopes, age, etc.), proper accounting of uncertainty, etc. Despite this, even with existing codes, automatic calibration facilitates enormously the task of modeling. Therefore, it is contended that its use should become standard practice. L'état du problème inverse des eaux souterraines est synthétisé. L'accent est placé sur la caractérisation de l'aquifère, où les modélisateurs doivent jouer avec l'incertitude des modèles conceptuels (notamment la variabilité spatiale et temporelle), les facteurs d'échelle, plusieurs inconnues sur différents paramètres (transmissivité, recharge, conditions aux limites, etc.), la non linéarité, et souvent la sensibilité de plusieurs variables d'état (charges hydrauliques, concentrations) des propriétés de l'aquifère. A cause de ces difficultés, le calibrage ne peut êtreséparé du processus de modélisation, comme c'est le

  2. A connectionist-geostatistical approach for classification of deformation types in ice surfaces

    Science.gov (United States)

    Goetz-Weiss, L. R.; Herzfeld, U. C.; Hale, R. G.; Hunke, E. C.; Bobeck, J.

    2014-12-01

    Deformation is a class of highly non-linear geophysical processes from which one can infer other geophysical variables in a dynamical system. For example, in an ice-dynamic model, deformation is related to velocity, basal sliding, surface elevation changes, and the stress field at the surface as well as internal to a glacier. While many of these variables cannot be observed, deformation state can be an observable variable, because deformation in glaciers (once a viscosity threshold is exceeded) manifests itself in crevasses.Given the amount of information that can be inferred from observing surface deformation, an automated method for classifying surface imagery becomes increasingly desirable. In this paper a Neural Network is used to recognize classes of crevasse types over the Bering Bagley Glacier System (BBGS) during a surge (2011-2013-?). A surge is a spatially and temporally highly variable and rapid acceleration of the glacier. Therefore, many different crevasse types occur in a short time frame and in close proximity, and these crevasse fields hold information on the geophysical processes of the surge.The connectionist-geostatistical approach uses directional experimental (discrete) variograms to parameterize images into a form that the Neural Network can recognize. Recognizing that each surge wave results in different crevasse types and that environmental conditions affect the appearance in imagery, we have developed a semi-automated pre-training software to adapt the Neural Net to chaining conditions.The method is applied to airborne and satellite imagery to classify surge crevasses from the BBGS surge. This method works well for classifying spatially repetitive images such as the crevasses over Bering Glacier. We expand the network for less repetitive images in order to analyze imagery collected over the Arctic sea ice, to assess the percentage of deformed ice for model calibration.

  3. Geodynamic inversion to constrain the non-linear rheology of the lithosphere

    Science.gov (United States)

    Baumann, T. S.; Kaus, Boris J. P.

    2015-08-01

    One of the main methods to determine the strength of the lithosphere is by estimating it's effective elastic thickness. This method assumes that the lithosphere is a thin elastic plate that floats on the mantle and uses both topography and gravity anomalies to estimate the plate thickness. Whereas this seems to work well for oceanic plates, it has given controversial results in continental collision zones. For most of these locations, additional geophysical data sets such as receiver functions and seismic tomography exist that constrain the geometry of the lithosphere and often show that it is rather complex. Yet, lithospheric geometry by itself is insufficient to understand the dynamics of the lithosphere as this also requires knowledge of the rheology of the lithosphere. Laboratory experiments suggest that rocks deform in a viscous manner if temperatures are high and stresses low, or in a plastic/brittle manner if the yield stress is exceeded. Yet, the experimental results show significant variability between various rock types and there are large uncertainties in extrapolating laboratory values to nature, which leaves room for speculation. An independent method is thus required to better understand the rheology and dynamics of the lithosphere in collision zones. The goal of this paper is to discuss such an approach. Our method relies on performing numerical thermomechanical forward models of the present-day lithosphere with an initial geometry that is constructed from geophysical data sets. We employ experimentally determined creep-laws for the various parts of the lithosphere, but assume that the parameters of these creep-laws as well as the temperature structure of the lithosphere are uncertain. This is used as a priori information to formulate a Bayesian inverse problem that employs topography, gravity, horizontal and vertical surface velocities to invert for the unknown material parameters and temperature structure. In order to test the general methodology

  4. Nonlinear evolution equations having a physical meaning

    International Nuclear Information System (INIS)

    Nakach, R.

    1976-06-01

    The non stationary self-similar solutions of the nonlinear evolution equations which can be solved by the inverse scattering method are studied. It turns out, as shown by means of several examples, that when the L linear operator associated with these equations, is of second order and only then, the self-similar solutions can be expressed in terms of the various Painleve's transcendents [fr

  5. Model Based Beamforming and Bayesian Inversion Signal Processing Methods for Seismic Localization of Underground Source

    DEFF Research Database (Denmark)

    Oh, Geok Lian

    properties such as the elastic wave speeds and soil densities. One processing method is casting the estimation problem into an inverse problem to solve for the unknown material parameters. The forward model for the seismic signals used in the literatures include ray tracing methods that consider only...... density values of the discretized ground medium, which leads to time-consuming computations and instability behaviour of the inversion process. In addition, the geophysics inverse problem is generally ill-posed due to non-exact forward model that introduces errors. The Bayesian inversion method through...... the first arrivals of the reflected compressional P-waves from the subsurface structures, or 3D elastic wave models that model all the seismic wave components. The ray tracing forward model formulation is linear, whereas the full 3D elastic wave model leads to a nonlinear inversion problem. In this Ph...

  6. Conditioning the full-waveform inversion gradient to welcome anisotropy

    KAUST Repository

    Alkhalifah, Tariq Ali

    2015-04-23

    Multiparameter full-waveform inversion (FWI) suffers from complex nonlinearity in the objective function, compounded by the eventual trade-off between the model parameters. A hierarchical approach based on frequency and arrival time data decimation to maneuver the complex nonlinearity associated with this problem usually falls short in anisotropic media. In place of data decimation, I use a model gradient filter approach to access the parts of the gradient more suitable to combat the potential nonlinearity and parameter trade-off. The filter is based on representing the gradient in the time-lag normalized domain, in which small scattering-angles of the gradient update are initially muted out. The model update hierarchical filtering strategy include applying varying degrees of filtering to the different anisotropic parameter updates, a feature not easily accessible to simple data decimation. Using FWI and reflection-based FWI, when the modeled data are obtained with the single-scattering theory, allows access to additional low model wavenumber components. Combining such access to wavenumbers with scattering-angle filters applied to the individual parameter gradients allows for multiple strategies to avoid complex FWI nonlinearity as well as the parameter trade-off.

  7. Second harmonic inversion for ultrasound contrast harmonic imaging

    Energy Technology Data Exchange (ETDEWEB)

    Pasovic, Mirza; Danilouchkine, Mike; Faez, Telli; Van Neer, Paul L M J; Van der Steen, Antonius F W; De Jong, Nico [THORAXCENTER, Department of Biomedical Engineering Ee2302, Erasmus MC, Rotterdam (Netherlands); Cachard, Christian; Basset, Olivier, E-mail: mirza.pasovic@creatis.insa-lyon.fr [CREATIS-LRMN, Universite de Lyon, INSA-Lyon, Universite Lyon 1, Inserm U630, CNRS UMR 5220 (France)

    2011-06-07

    Ultrasound contrast agents (UCAs) are small micro-bubbles that behave nonlinearly when exposed to an ultrasound wave. This nonlinear behavior can be observed through the generated higher harmonics in a back-scattered echo. In past years several techniques have been proposed to detect or image harmonics produced by UCAs. In these proposed works, the harmonics generated in the medium during the propagation of the ultrasound wave played an important role, since these harmonics compete with the harmonics generated by the micro-bubbles. We present a method for the reduction of the second harmonic generated during nonlinear-propagation-dubbed second harmonic inversion (SHI). A general expression for the suppression signals is also derived. The SHI technique uses two pulses, p' and p'', of the same frequency f{sub 0} and the same amplitude P{sub 0} to cancel out the second harmonic generated by nonlinearities of the medium. Simulations show that the second harmonic is reduced by 40 dB on a large axial range. Experimental SHI B-mode images, from a tissue-mimicking phantom and UCAs, show an improvement in the agent-to-tissue ratio (ATR) of 20 dB compared to standard second harmonic imaging and 13 dB of improvement in harmonic power Doppler.

  8. Second harmonic inversion for ultrasound contrast harmonic imaging

    International Nuclear Information System (INIS)

    Pasovic, Mirza; Danilouchkine, Mike; Faez, Telli; Van Neer, Paul L M J; Van der Steen, Antonius F W; De Jong, Nico; Cachard, Christian; Basset, Olivier

    2011-01-01

    Ultrasound contrast agents (UCAs) are small micro-bubbles that behave nonlinearly when exposed to an ultrasound wave. This nonlinear behavior can be observed through the generated higher harmonics in a back-scattered echo. In past years several techniques have been proposed to detect or image harmonics produced by UCAs. In these proposed works, the harmonics generated in the medium during the propagation of the ultrasound wave played an important role, since these harmonics compete with the harmonics generated by the micro-bubbles. We present a method for the reduction of the second harmonic generated during nonlinear-propagation-dubbed second harmonic inversion (SHI). A general expression for the suppression signals is also derived. The SHI technique uses two pulses, p' and p'', of the same frequency f 0 and the same amplitude P 0 to cancel out the second harmonic generated by nonlinearities of the medium. Simulations show that the second harmonic is reduced by 40 dB on a large axial range. Experimental SHI B-mode images, from a tissue-mimicking phantom and UCAs, show an improvement in the agent-to-tissue ratio (ATR) of 20 dB compared to standard second harmonic imaging and 13 dB of improvement in harmonic power Doppler.

  9. A fully general and adaptive inverse analysis method for cementitious materials

    DEFF Research Database (Denmark)

    Jepsen, Michael S.; Damkilde, Lars; Lövgren, Ingemar

    2016-01-01

    The paper presents an adaptive method for inverse determination of the tensile σ - w relationship, direct tensile strength and Young’s modulus of cementitious materials. The method facilitates an inverse analysis with a multi-linear σ - w function. Usually, simple bi- or tri-linear functions...... are applied when modeling the fracture mechanisms in cementitious materials, but the vast development of pseudo-strain hardening, fiber reinforced cementitious materials require inverse methods, capable of treating multi-linear σ - w functions. The proposed method is fully general in the sense that it relies...... of notched specimens and simulated data from a nonlinear hinge model. The paper shows that the results obtained by means of the proposed method is independent on the initial shape of the σ - w function and the initial guess of the tensile strength. The method provides very accurate fits, and the increased...

  10. Solving inversion problems with neural networks

    Science.gov (United States)

    Kamgar-Parsi, Behzad; Gualtieri, J. A.

    1990-01-01

    A class of inverse problems in remote sensing can be characterized by Q = F(x), where F is a nonlinear and noninvertible (or hard to invert) operator, and the objective is to infer the unknowns, x, from the observed quantities, Q. Since the number of observations is usually greater than the number of unknowns, these problems are formulated as optimization problems, which can be solved by a variety of techniques. The feasibility of neural networks for solving such problems is presently investigated. As an example, the problem of finding the atmospheric ozone profile from measured ultraviolet radiances is studied.

  11. Improved Assimilation of Streamflow and Satellite Soil Moisture with the Evolutionary Particle Filter and Geostatistical Modeling

    Science.gov (United States)

    Yan, Hongxiang; Moradkhani, Hamid; Abbaszadeh, Peyman

    2017-04-01

    Assimilation of satellite soil moisture and streamflow data into hydrologic models using has received increasing attention over the past few years. Currently, these observations are increasingly used to improve the model streamflow and soil moisture predictions. However, the performance of this land data assimilation (DA) system still suffers from two limitations: 1) satellite data scarcity and quality; and 2) particle weight degeneration. In order to overcome these two limitations, we propose two possible solutions in this study. First, the general Gaussian geostatistical approach is proposed to overcome the limitation in the space/time resolution of satellite soil moisture products thus improving their accuracy at uncovered/biased grid cells. Secondly, an evolutionary PF approach based on Genetic Algorithm (GA) and Markov Chain Monte Carlo (MCMC), the so-called EPF-MCMC, is developed to further reduce weight degeneration and improve the robustness of the land DA system. This study provides a detailed analysis of the joint and separate assimilation of streamflow and satellite soil moisture into a distributed Sacramento Soil Moisture Accounting (SAC-SMA) model, with the use of recently developed EPF-MCMC and the general Gaussian geostatistical approach. Performance is assessed over several basins in the USA selected from Model Parameter Estimation Experiment (MOPEX) and located in different climate regions. The results indicate that: 1) the general Gaussian approach can predict the soil moisture at uncovered grid cells within the expected satellite data quality threshold; 2) assimilation of satellite soil moisture inferred from the general Gaussian model can significantly improve the soil moisture predictions; and 3) in terms of both deterministic and probabilistic measures, the EPF-MCMC can achieve better streamflow predictions. These results recommend that the geostatistical model is a helpful tool to aid the remote sensing technique and the EPF-MCMC is a

  12. Inverse Raman scattering in silicon: A free-carrier enhanced effect

    International Nuclear Information System (INIS)

    Solli, D. R.; Koonath, P.; Jalali, B.

    2009-01-01

    Stimulated Raman scattering has been harnessed to produce the first silicon lasers and amplifiers. The Raman effect can also produce intensity-dependent nonlinear loss through a corollary process, inverse Raman scattering (IRS). This process has never been observed in a semiconductor. We demonstrate IRS in silicon--a process that is substantially modified by optically generated free carriers--achieving attenuation levels >15 dB with a pump intensity of 4 GW/cm 2 . Surprisingly, free-carrier absorption, the detrimental effect that generally suppresses nonlinear effects in silicon, actually facilitates IRS by delaying the onset of contamination from coherent anti-Stokes Raman scattering. Silicon-based IRS could be a valuable tool for chip-scale signal processing.

  13. Symmetry realization via a dynamical inverse Higgs mechanism

    Science.gov (United States)

    Rothstein, Ira Z.; Shrivastava, Prashant

    2018-05-01

    The Ward identities associated with spontaneously broken symmetries can be saturated by Goldstone bosons. However, when space-time symmetries are broken, the number of Goldstone bosons necessary to non-linearly realize the symmetry can be less than the number of broken generators. The loss of Goldstones may be due to a redundancy or the generation of a gap. In either case the associated Goldstone may be removed from the spectrum. This phenomena is called an Inverse Higgs Mechanism (IHM) and its appearance has a well defined mathematical condition. However, there are cases when a Goldstone boson associated with a broken generator does not appear in the low energy theory despite the lack of the existence of an associated IHM. In this paper we will show that in such cases the relevant broken symmetry can be realized, without the aid of an associated Goldstone, if there exists a proper set of operator constraints, which we call a Dynamical Inverse Higgs Mechanism (DIHM). We consider the spontaneous breaking of boosts, rotations and conformal transformations in the context of Fermi liquids, finding three possible paths to symmetry realization: pure Goldstones, no Goldstones and DIHM, or some mixture thereof. We show that in the two dimensional degenerate electron system the DIHM route is the only consistent way to realize spontaneously broken boosts and dilatations, while in three dimensions these symmetries could just as well be realized via the inclusion of non-derivatively coupled Goldstone bosons. We present the action, including the leading order non-linearities, for the rotational Goldstone (angulon), and discuss the constraint associated with the possible DIHM that would need to be imposed to remove it from the spectrum. Finally we discuss the conditions under which Goldstone bosons are non-derivatively coupled, a necessary condition for the existence of a Dynamical Inverse Higgs Constraint (DIHC), generalizing the results for Vishwanath and Wantanabe.

  14. Polynomial model inversion control: numerical tests and applications

    OpenAIRE

    Novara, Carlo

    2015-01-01

    A novel control design approach for general nonlinear systems is described in this paper. The approach is based on the identification of a polynomial model of the system to control and on the on-line inversion of this model. Extensive simulations are carried out to test the numerical efficiency of the approach. Numerical examples of applicative interest are presented, concerned with control of the Duffing oscillator, control of a robot manipulator and insulin regulation in a type 1 diabetic p...

  15. Morozov-type discrepancy principle for nonlinear ill-posed problems ...

    Indian Academy of Sciences (India)

    [3] Engl H W, Kunisch K and Neubauer A, Convergence rates for Tikhonov regularization of nonliner problems, Inverse Problems 5 (1989) 523–540. [4] Hanke M, Neubauer A and Scherzer O, A convergence analysis of Landweber iteration for nonlinear ill-posed problems, Numer. Math. 72 (1995) 21–37. [5] Hofmann B and ...

  16. Application of Bayesian geostatistics for evaluation of mass discharge uncertainty at contaminated sites

    DEFF Research Database (Denmark)

    Troldborg, Mads; Nowak, Wolfgang; Lange, Ida Vedel

    2012-01-01

    , and (3) uncertain source zone and transport parameters. The method generates conditional realizations of the spatial flow and concentration distribution. An analytical macrodispersive transport solution is employed to simulate the mean concentration distribution, and a geostatistical model of the Box-Cox...... transformed concentration data is used to simulate observed deviations from this mean solution. By combining the flow and concentration realizations, a mass discharge probability distribution is obtained. The method has the advantage of avoiding the heavy computational burden of three-dimensional numerical...

  17. Uncertainty Quantification in Earthquake Source Characterization with Probabilistic Centroid Moment Tensor Inversion

    Science.gov (United States)

    Dettmer, J.; Benavente, R. F.; Cummins, P. R.

    2017-12-01

    This work considers probabilistic, non-linear centroid moment tensor inversion of data from earthquakes at teleseismic distances. The moment tensor is treated as deviatoric and centroid location is parametrized with fully unknown latitude, longitude, depth and time delay. The inverse problem is treated as fully non-linear in a Bayesian framework and the posterior density is estimated with interacting Markov chain Monte Carlo methods which are implemented in parallel and allow for chain interaction. The source mechanism and location, including uncertainties, are fully described by the posterior probability density and complex trade-offs between various metrics are studied. These include the percent of double couple component as well as fault orientation and the probabilistic results are compared to results from earthquake catalogs. Additional focus is on the analysis of complex events which are commonly not well described by a single point source. These events are studied by jointly inverting for multiple centroid moment tensor solutions. The optimal number of sources is estimated by the Bayesian information criterion to ensure parsimonious solutions. [Supported by NSERC.

  18. From nonlinear Schrödinger hierarchy to some (2+1)-dimensional nonlinear pseudodifferential equations

    Science.gov (United States)

    Yang, Xiao; Du, Dianlou

    2010-08-01

    The Poisson structure on CN×RN is introduced to give the Hamiltonian system associated with a spectral problem which yields the nonlinear Schrödinger (NLS) hierarchy. The Hamiltonian system is proven to be Liouville integrable. Some (2+1)-dimensional equations including NLS equation, Kadomtesev-Petviashvili I (KPI) equation, coupled KPI equation, and modified Kadomtesev-Petviashvili (mKP) equation, are decomposed into Hamilton flows via the NLS hierarchy. The algebraic curve, Abel-Jacobi coordinates, and Riemann-Jacobi inversion are used to obtain the algebrogeometric solutions of these equations.

  19. Bright and dark soliton solutions for some nonlinear fractional differential equations

    International Nuclear Information System (INIS)

    Guner, Ozkan; Bekir, Ahmet

    2016-01-01

    In this work, we propose a new approach, namely ansatz method, for solving fractional differential equations based on a fractional complex transform and apply it to the nonlinear partial space–time fractional modified Benjamin–Bona–Mahoney (mBBM) equation, the time fractional mKdV equation and the nonlinear fractional Zoomeron equation which gives rise to some new exact solutions. The physical parameters in the soliton solutions: amplitude, inverse width, free parameters and velocity are obtained as functions of the dependent model coefficients. This method is suitable and more powerful for solving other kinds of nonlinear fractional PDEs arising in mathematical physics. Since the fractional derivatives are described in the modified Riemann–Liouville sense. (paper)

  20. Application of homotopy analysis method and inverse solution of a rectangular wet fin

    International Nuclear Information System (INIS)

    Panda, Srikumar; Bhowmik, Arka; Das, Ranjan; Repaka, Ramjee; Martha, Subash C.

    2014-01-01

    Highlights: • Solution of a wet fin with is obtained by homotopy analysis method (HAM). • Present HAM results have been well-validated with literature results. • Inverse analysis is done using genetic algorithm. • Measurement error of ±10–12% (approx.) is found to yield satisfactory reconstructions. - Abstract: This paper presents the analytical solution of a rectangular fin under the simultaneous heat and mass transfer across the fin surface and the fin tip, and estimates the unknown thermal and geometrical configurations of the fin using inverse heat transfer analysis. The local temperature field is obtained by using homotopy analysis method for insulated and convective fin tip boundary conditions. Using genetic algorithm, the thermal and geometrical parameters, viz., thermal conductivity of the material, surface heat transfer coefficient and dimensions of the fin have been simultaneously estimated for the prescribed temperature field. Earlier inverse studies on wet fin have been restricted to the analysis of nonlinear governing equation with either insulated tip condition or finite tip temperature only. The present study developed a closed-form solution with the consideration of nonlinearity effects in both governing equation and boundary condition. The study on inverse optimization leads to many feasible combination of fin materials, thermal conditions and fin dimensions. Thus allows the flexibility for designing a fin under wet conditions, based on multiple combinations of fin materials, fin dimensions and thermal configurations to achieve the required heat transfer duty. It is further determined that the allowable measurement error should be limited to ±10–12% in order to achieve satisfactory reconstruction

  1. Three-dimensional inversion of multisource array electromagnetic data

    Science.gov (United States)

    Tartaras, Efthimios

    Three-dimensional (3-D) inversion is increasingly important for the correct interpretation of geophysical data sets in complex environments. To this effect, several approximate solutions have been developed that allow the construction of relatively fast inversion schemes. One such method that is fast and provides satisfactory accuracy is the quasi-linear (QL) approximation. It has, however, the drawback that it is source-dependent and, therefore, impractical in situations where multiple transmitters in different positions are employed. I have, therefore, developed a localized form of the QL approximation that is source-independent. This so-called localized quasi-linear (LQL) approximation can have a scalar, a diagonal, or a full tensor form. Numerical examples of its comparison with the full integral equation solution, the Born approximation, and the original QL approximation are given. The objective behind developing this approximation is to use it in a fast 3-D inversion scheme appropriate for multisource array data such as those collected in airborne surveys, cross-well logging, and other similar geophysical applications. I have developed such an inversion scheme using the scalar and diagonal LQL approximation. It reduces the original nonlinear inverse electromagnetic (EM) problem to three linear inverse problems. The first of these problems is solved using a weighted regularized linear conjugate gradient method, whereas the last two are solved in the least squares sense. The algorithm I developed provides the option of obtaining either smooth or focused inversion images. I have applied the 3-D LQL inversion to synthetic 3-D EM data that simulate a helicopter-borne survey over different earth models. The results demonstrate the stability and efficiency of the method and show that the LQL approximation can be a practical solution to the problem of 3-D inversion of multisource array frequency-domain EM data. I have also applied the method to helicopter-borne EM

  2. Analysis of Inverse Kinamtics of an Anthropomorphic Robotic hand

    Directory of Open Access Journals (Sweden)

    Pramod Kumar Parida

    2013-03-01

    Full Text Available In this paper, a new method for solving the inverse kinematics of the fingers of an anthropomorphic hand is proposed. Solution of inverse kinematic equations is a complex problem, the complexity comes from the nonlinearity of joint space and Cartesian space mapping and having multiple solutions.This is a typical problem in robotics that needs to be solved to control the fingers of an anthropomorphic robotic hand to perform tasks it is designated to do. With more complex structures operating in a 3-dimensional space deducing a mathematical soluation for the inverse kinematics may prove challenging. In this paper, using the ability of ANFIS (Adaptive Neuro-Fuzzy Inference System to learn from training data, it is possible to create ANFIS network, an implementation of a representative fuzzy inference system using ANFIS structure, with limited mathematical representation of the system. The main advantages of this method with respect to the other methods are implementation is easy, very fast and shorter computation time and better response with acceptable error.

  3. The development of computational algorithms for manipulator inverse kinematics

    International Nuclear Information System (INIS)

    Sasaki, Shinobu

    1989-10-01

    A solution technique of the inverse kinematics for multi-joint robot manipulators has been considered to be one of the most cumbersome treatment due to non-linearity properties inclusive of trigonometric functions. The most traditional approach is to use the Jacobian matrix on linearization assumptions. This iterative technique, however, is attended with numerical problems having significant influences on the solution characteristics such as initial guess dependence and singularities. Taking these facts into consideration, new approaches have been proposed from different standpoints, which are based on polynomial transformation of kinematic model, the minimization technique in mathematical programming, vector-geometrical concept, and the separation of joint variables associated with the optimization problem. In terms of computer simulations, each approach was identified to be a useful algorithm which leads to theoretically accurate solutions to complicated inverse problems. In this way, the short-term goal of our studies on manipulator inverse problem in the R and D project of remote handling technology was accomplished with success, and consequently the present report sums up the results of basic studies on this matter. (author)

  4. Efficient Stochastic Inversion Using Adjoint Models and Kernel-PCA

    Energy Technology Data Exchange (ETDEWEB)

    Thimmisetty, Charanraj A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Zhao, Wenju [Florida State Univ., Tallahassee, FL (United States). Dept. of Scientific Computing; Chen, Xiao [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Tong, Charles H. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; White, Joshua A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Atmospheric, Earth and Energy Division

    2017-10-18

    Performing stochastic inversion on a computationally expensive forward simulation model with a high-dimensional uncertain parameter space (e.g. a spatial random field) is computationally prohibitive even when gradient information can be computed efficiently. Moreover, the ‘nonlinear’ mapping from parameters to observables generally gives rise to non-Gaussian posteriors even with Gaussian priors, thus hampering the use of efficient inversion algorithms designed for models with Gaussian assumptions. In this paper, we propose a novel Bayesian stochastic inversion methodology, which is characterized by a tight coupling between the gradient-based Langevin Markov Chain Monte Carlo (LMCMC) method and a kernel principal component analysis (KPCA). This approach addresses the ‘curse-of-dimensionality’ via KPCA to identify a low-dimensional feature space within the high-dimensional and nonlinearly correlated parameter space. In addition, non-Gaussian posterior distributions are estimated via an efficient LMCMC method on the projected low-dimensional feature space. We will demonstrate this computational framework by integrating and adapting our recent data-driven statistics-on-manifolds constructions and reduction-through-projection techniques to a linear elasticity model.

  5. Reservoir Characterization using geostatistical and numerical modeling in GIS with noble gas geochemistry

    Science.gov (United States)

    Vasquez, D. A.; Swift, J. N.; Tan, S.; Darrah, T. H.

    2013-12-01

    The integration of precise geochemical analyses with quantitative engineering modeling into an interactive GIS system allows for a sophisticated and efficient method of reservoir engineering and characterization. Geographic Information Systems (GIS) is utilized as an advanced technique for oil field reservoir analysis by combining field engineering and geological/geochemical spatial datasets with the available systematic modeling and mapping methods to integrate the information into a spatially correlated first-hand approach in defining surface and subsurface characteristics. Three key methods of analysis include: 1) Geostatistical modeling to create a static and volumetric 3-dimensional representation of the geological body, 2) Numerical modeling to develop a dynamic and interactive 2-dimensional model of fluid flow across the reservoir and 3) Noble gas geochemistry to further define the physical conditions, components and history of the geologic system. Results thus far include using engineering algorithms for interpolating electrical well log properties across the field (spontaneous potential, resistivity) yielding a highly accurate and high-resolution 3D model of rock properties. Results so far also include using numerical finite difference methods (crank-nicholson) to solve for equations describing the distribution of pressure across field yielding a 2D simulation model of fluid flow across reservoir. Ongoing noble gas geochemistry results will also include determination of the source, thermal maturity and the extent/style of fluid migration (connectivity, continuity and directionality). Future work will include developing an inverse engineering algorithm to model for permeability, porosity and water saturation.This combination of new and efficient technological and analytical capabilities is geared to provide a better understanding of the field geology and hydrocarbon dynamics system with applications to determine the presence of hydrocarbon pay zones (or

  6. Elastic frequency-domain finite-difference contrast source inversion method

    International Nuclear Information System (INIS)

    He, Qinglong; Chen, Yong; Han, Bo; Li, Yang

    2016-01-01

    In this work, we extend the finite-difference contrast source inversion (FD-CSI) method to the frequency-domain elastic wave equations, where the parameters describing the subsurface structure are simultaneously reconstructed. The FD-CSI method is an iterative nonlinear inversion method, which exhibits several strengths. First, the finite-difference operator only relies on the background media and the given angular frequency, both of which are unchanged during inversion. Therefore, the matrix decomposition is performed only once at the beginning of the iteration if a direct solver is employed. This makes the inversion process relatively efficient in terms of the computational cost. In addition, the FD-CSI method automatically normalizes different parameters, which could avoid the numerical problems arising from the difference of the parameter magnitude. We exploit a parallel implementation of the FD-CSI method based on the domain decomposition method, ensuring a satisfactory scalability for large-scale problems. A simple numerical example with a homogeneous background medium is used to investigate the convergence of the elastic FD-CSI method. Moreover, the Marmousi II model proposed as a benchmark for testing seismic imaging methods is presented to demonstrate the performance of the elastic FD-CSI method in an inhomogeneous background medium. (paper)

  7. On reciprocal Baecklund transformations of inverse scattering schemes

    International Nuclear Information System (INIS)

    Rogers, C.; Wong, P.

    1984-01-01

    The notion of reciprocally related inverse scattering schemes is introduced and is shown to be a key component in the link between the AKNS and WKI schemes. Reciprocal auto-Baecklund transformations are represented both for a generalised Harry-Dym equation and an equation descriptive of nonlinear oscillation of elastic beams. Further, the N-loop soliton solution of the KIW equation is generated in a convenient parametric form via reciprocal Baecklund transformations. Finally, an important reduction to canonical spectral form is shown to be a reciprocal transformation. (Auth.)

  8. Geostatistical modeling of a fluviodeltaic reservoir in the Huyapari Field, Hamaca area, in the Faja Petrolifera del Orinoco, Venezuela

    Energy Technology Data Exchange (ETDEWEB)

    De Ascencao, Erika M.; Munckton, Toni; Digregorio, Ricardo [Petropiar (Venezuela)

    2011-07-01

    The Huyapari field, situated within the Faja Petrolifera del Orinoco (FPO) of Venezuela presents unique problems in terms of modeling. This field is spread over a wide area and is therefore subject to variable oil quality and complex fluvial facies architecture. Ameriven and PDVSA have been working on characterizing the ld's reservoirs in this field since 2000 and the aim of this paper is to present these efforts. Among others, a 3-D seismic survey completed in 1998 and a stratigraphic framework built from 149 vertical wells were used for reservoir characterization. Geostatistical techniques such as sequential Gaussian simulation with locally varying mean and cloud transform were also used. Results showed that these geostatistical methods accurately represented the architecture and properties of the reservoir and its fluid distribution. This paper showed that the application of numerous different techniques in the Hamasca area permitted reservoir complexity to be captured.

  9. Nonlinear Dynamics in Gene Regulation Promote Robustness and Evolvability of Gene Expression Levels.

    Science.gov (United States)

    Steinacher, Arno; Bates, Declan G; Akman, Ozgur E; Soyer, Orkun S

    2016-01-01

    Cellular phenotypes underpinned by regulatory networks need to respond to evolutionary pressures to allow adaptation, but at the same time be robust to perturbations. This creates a conflict in which mutations affecting regulatory networks must both generate variance but also be tolerated at the phenotype level. Here, we perform mathematical analyses and simulations of regulatory networks to better understand the potential trade-off between robustness and evolvability. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics, through the creation of regions presenting sudden changes in phenotype with small changes in genotype. For genotypes embedding low levels of nonlinearity, robustness and evolvability correlate negatively and almost perfectly. By contrast, genotypes embedding nonlinear dynamics allow expression levels to be robust to small perturbations, while generating high diversity (evolvability) under larger perturbations. Thus, nonlinearity breaks the robustness-evolvability trade-off in gene expression levels by allowing disparate responses to different mutations. Using analytical derivations of robustness and system sensitivity, we show that these findings extend to a large class of gene regulatory network architectures and also hold for experimentally observed parameter regimes. Further, the effect of nonlinearity on the robustness-evolvability trade-off is ensured as long as key parameters of the system display specific relations irrespective of their absolute values. We find that within this parameter regime genotypes display low and noisy expression levels. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics. Our results provide a possible solution to the robustness-evolvability trade-off, suggest an explanation for

  10. Nonlinear Dynamics in Gene Regulation Promote Robustness and Evolvability of Gene Expression Levels.

    Directory of Open Access Journals (Sweden)

    Arno Steinacher

    Full Text Available Cellular phenotypes underpinned by regulatory networks need to respond to evolutionary pressures to allow adaptation, but at the same time be robust to perturbations. This creates a conflict in which mutations affecting regulatory networks must both generate variance but also be tolerated at the phenotype level. Here, we perform mathematical analyses and simulations of regulatory networks to better understand the potential trade-off between robustness and evolvability. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics, through the creation of regions presenting sudden changes in phenotype with small changes in genotype. For genotypes embedding low levels of nonlinearity, robustness and evolvability correlate negatively and almost perfectly. By contrast, genotypes embedding nonlinear dynamics allow expression levels to be robust to small perturbations, while generating high diversity (evolvability under larger perturbations. Thus, nonlinearity breaks the robustness-evolvability trade-off in gene expression levels by allowing disparate responses to different mutations. Using analytical derivations of robustness and system sensitivity, we show that these findings extend to a large class of gene regulatory network architectures and also hold for experimentally observed parameter regimes. Further, the effect of nonlinearity on the robustness-evolvability trade-off is ensured as long as key parameters of the system display specific relations irrespective of their absolute values. We find that within this parameter regime genotypes display low and noisy expression levels. Examining the phenotypic effects of mutations, we find an inverse correlation between robustness and evolvability that breaks only with nonlinearity in the network dynamics. Our results provide a possible solution to the robustness-evolvability trade-off, suggest

  11. Latin hypercube sampling and geostatistical modeling of spatial uncertainty in a spatially explicit forest landscape model simulation

    Science.gov (United States)

    Chonggang Xu; Hong S. He; Yuanman Hu; Yu Chang; Xiuzhen Li; Rencang Bu

    2005-01-01

    Geostatistical stochastic simulation is always combined with Monte Carlo method to quantify the uncertainty in spatial model simulations. However, due to the relatively long running time of spatially explicit forest models as a result of their complexity, it is always infeasible to generate hundreds or thousands of Monte Carlo simulations. Thus, it is of great...

  12. Determining site-specific background level with geostatistics for remediation of heavy metals in neighborhood soils

    OpenAIRE

    Tammy M. Milillo; Gaurav Sinha; Joseph A. Gardella Jr.

    2017-01-01

    The choice of a relevant, uncontaminated site for the determination of site-specific background concentrations for pollutants is critical for planning remediation of a contaminated site. The guidelines used to arrive at concentration levels vary from state to state, complicating this process. The residential neighborhood of Hickory Woods in Buffalo, NY is an area where heavy metal concentrations and spatial distributions were measured to plan remediation. A novel geostatistics based decision ...

  13. Indoor radon variations in central Iran and its geostatistical map

    Science.gov (United States)

    Hadad, Kamal; Mokhtari, Javad

    2015-02-01

    We present the results of 2 year indoor radon survey in 10 cities of Yazd province in Central Iran (covering an area of 80,000 km2). We used passive diffusive samplers with LATEX polycarbonate films as Solid State Nuclear Track Detector (SSNTD). This study carried out in central Iran where there are major minerals and uranium mines. Our results indicate that despite few extraordinary high concentrations, average annual concentrations of indoor radon are within ICRP guidelines. When geostatistical spatial distribution of radon mapped onto geographical features of the province it was observed that risk of high radon concentration increases near the Saqand, Bafq, Harat and Abarkooh cities, this depended on the elevation and vicinity of the ores and mines.

  14. Geostatistical modeling of groundwater properties and assessment of their uncertainties

    International Nuclear Information System (INIS)

    Honda, Makoto; Yamamoto, Shinya; Sakurai, Hideyuki; Suzuki, Makoto; Sanada, Hiroyuki; Matsui, Hiroya; Sugita, Yutaka

    2010-01-01

    The distribution of groundwater properties is important for understanding of the deep underground hydrogeological environments. This paper proposes a geostatistical system for modeling the groundwater properties which have a correlation with the ground resistivity data obtained from widespread and exhaustive survey. That is, the methodology for the integration of resistivity data measured by various methods and the methodology for modeling the groundwater properties using the integrated resistivity data has been developed. The proposed system has also been validated using the data obtained in the Horonobe Underground Research Laboratory project. Additionally, the quantification of uncertainties in the estimated model has been tried by numerical simulations based on the data. As a result, the uncertainties of the proposal model have been estimated lower than other traditional model's. (author)

  15. The use of sequential indicator simulation to characterize geostatistical uncertainty

    International Nuclear Information System (INIS)

    Hansen, K.M.

    1992-10-01

    Sequential indicator simulation (SIS) is a geostatistical technique designed to aid in the characterization of uncertainty about the structure or behavior of natural systems. This report discusses a simulation experiment designed to study the quality of uncertainty bounds generated using SIS. The results indicate that, while SIS may produce reasonable uncertainty bounds in many situations, factors like the number and location of available sample data, the quality of variogram models produced by the user, and the characteristics of the geologic region to be modeled, can all have substantial effects on the accuracy and precision of estimated confidence limits. It is recommended that users of SIS conduct validation studies for the technique on their particular regions of interest before accepting the output uncertainty bounds

  16. Lax-pair operators for squared eigenfunctions in the inverse scattering transformations

    International Nuclear Information System (INIS)

    Iino, Kazuhiro; Ichikawa, Yoshihiko.

    1982-05-01

    Modification of the algorithm of Chen, Lee and Liu enables us to construct alternative Lax-pair operators for the Korteweg-de Vries equation and the modified Korteweg-de Vries equation. These Lax-pair operators stand as the Lax-pair operators for the squared eigenfunction and the sum of squared eigenfunctions of the Ablowitz-Kaup-Newell-Segur inverse scattering transformation for these celebrated nonlinear evolution equations. (author)

  17. Solution accelerators for large scale 3D electromagnetic inverse problems

    International Nuclear Information System (INIS)

    Newman, Gregory A.; Boggs, Paul T.

    2004-01-01

    We provide a framework for preconditioning nonlinear 3D electromagnetic inverse scattering problems using nonlinear conjugate gradient (NLCG) and limited memory (LM) quasi-Newton methods. Key to our approach is the use of an approximate adjoint method that allows for an economical approximation of the Hessian that is updated at each inversion iteration. Using this approximate Hessian as a preconditoner, we show that the preconditioned NLCG iteration converges significantly faster than the non-preconditioned iteration, as well as converging to a data misfit level below that observed for the non-preconditioned method. Similar conclusions are also observed for the LM iteration; preconditioned with the approximate Hessian, the LM iteration converges faster than the non-preconditioned version. At this time, however, we see little difference between the convergence performance of the preconditioned LM scheme and the preconditioned NLCG scheme. A possible reason for this outcome is the behavior of the line search within the LM iteration. It was anticipated that, near convergence, a step size of one would be approached, but what was observed, instead, were step lengths that were nowhere near one. We provide some insights into the reasons for this behavior and suggest further research that may improve the performance of the LM methods

  18. Weyl functions, the inverse problem and special solutions for the system auxiliary to the nonlinear optics equation

    International Nuclear Information System (INIS)

    Sakhnovich, Alexander

    2008-01-01

    A Borg–Marchenko-type uniqueness theorem (in terms of the Weyl function) is obtained here for the system auxiliary to the N-wave equation. A procedure to solve the inverse problem is used for this purpose. The asymptotic condition on the Weyl function, under which the inverse problem is uniquely solvable, is completed by a new and simple sufficient condition on the potential, which implies this asymptotic condition. The evolution of the Weyl function is discussed and the solution of an initial-boundary-value problem for the N-wave equation follows. Explicit solutions of an inverse problem are obtained. The system with a shifted argument is treated

  19. Spontaneous emission of semiconductor quantum dots in inverse opal SiO2 photonic crystals at different temperatures.

    Science.gov (United States)

    Yang, Peng; Yang, Yingshu; Wang, Yinghui; Gao, Jiechao; Sui, Ning; Chi, Xiaochun; Zou, Lu; Zhang, Han-Zhuang

    2016-02-01

    The photoluminescence (PL) characteristics of CdSe quantum dots (QDs) infiltrated into inverse opal SiO2 photonic crystals (PCs) are systemically studied. The special porous structure of inverse opal PCs enhanced the thermal exchange rate between the CdSe QDs and their surrounding environment. Finally, inverse opal SiO2 PCs suppressed the nonlinear PL enhancement of CdSe QDs in PCs excited by a continuum laser and effectively modulated the PL characteristics of CdSe QDs in PCs at high temperatures in comparison with that of CdSe QDs out of PCs. The final results are of benefit in further understanding the role of inverse opal PCs on the PL characteristics of QDs. Copyright © 2015 John Wiley & Sons, Ltd.

  20. Adaptive online inverse control of a shape memory alloy wire actuator using a dynamic neural network

    Science.gov (United States)

    Mai, Huanhuan; Song, Gangbing; Liao, Xiaofeng

    2013-01-01

    Shape memory alloy (SMA) actuators exhibit severe hysteresis, a nonlinear behavior, which complicates control strategies and limits their applications. This paper presents a new approach to controlling an SMA actuator through an adaptive inverse model based controller that consists of a dynamic neural network (DNN) identifier, a copy dynamic neural network (CDNN) feedforward term and a proportional (P) feedback action. Unlike fixed hysteresis models used in most inverse controllers, the proposed one uses a DNN to identify online the relationship between the applied voltage to the actuator and the displacement (the inverse model). Even without a priori knowledge of the SMA hysteresis and without pre-training, the proposed controller can precisely control the SMA wire actuator in various tracking tasks by identifying online the inverse model of the SMA actuator. Experiments were conducted, and experimental results demonstrated real-time modeling capabilities of DNN and the performance of the adaptive inverse controller.

  1. Comparing the performance of geostatistical models with additional information from covariates for sewage plume characterization.

    Science.gov (United States)

    Del Monego, Maurici; Ribeiro, Paulo Justiniano; Ramos, Patrícia

    2015-04-01

    In this work, kriging with covariates is used to model and map the spatial distribution of salinity measurements gathered by an autonomous underwater vehicle in a sea outfall monitoring campaign aiming to distinguish the effluent plume from the receiving waters and characterize its spatial variability in the vicinity of the discharge. Four different geostatistical linear models for salinity were assumed, where the distance to diffuser, the west-east positioning, and the south-north positioning were used as covariates. Sample variograms were fitted by the Matèrn models using weighted least squares and maximum likelihood estimation methods as a way to detect eventual discrepancies. Typically, the maximum likelihood method estimated very low ranges which have limited the kriging process. So, at least for these data sets, weighted least squares showed to be the most appropriate estimation method for variogram fitting. The kriged maps show clearly the spatial variation of salinity, and it is possible to identify the effluent plume in the area studied. The results obtained show some guidelines for sewage monitoring if a geostatistical analysis of the data is in mind. It is important to treat properly the existence of anomalous values and to adopt a sampling strategy that includes transects parallel and perpendicular to the effluent dispersion.

  2. SIPPI: A Matlab toolbox for sampling the solution to inverse problems with complex prior information

    DEFF Research Database (Denmark)

    Hansen, Thomas Mejer; Cordua, Knud Skou; Looms, Majken Caroline

    2013-01-01

    We present an application of the SIPPI Matlab toolbox, to obtain a sample from the a posteriori probability density function for the classical tomographic inversion problem. We consider a number of different forward models, linear and non-linear, such as ray based forward models that rely...

  3. Ferroelectric domain inversion and its stability in lithium niobate thin film on insulator with different thicknesses

    Energy Technology Data Exchange (ETDEWEB)

    Shao, Guang-hao; Bai, Yu-hang; Cui, Guo-xin; Li, Chen; Qiu, Xiang-biao; Wu, Di; Lu, Yan-qing, E-mail: yqlu@nju.edu.cn [National Laboratory of Solid State Microstructures, College of Engineering and Applied Sciences, and Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing 210093 (China); Geng, De-qiang [Jinan Jingzheng Electronics Co., Ltd., Jinan 250100 (China)

    2016-07-15

    Ferroelectric domain inversion and its effect on the stability of lithium niobate thin films on insulator (LNOI) are experimentally characterized. Two sets of specimens with different thicknesses varying from submicron to microns are selected. For micron thick samples (∼28 μm), domain structures are achieved by pulsed electric field poling with electrodes patterned via photolithography. No domain structure deterioration has been observed for a month as inspected using polarizing optical microscopy and etching. As for submicron (540 nm) films, large-area domain inversion is realized by scanning a biased conductive tip in a piezoelectric force microscope. A graphic processing method is taken to evaluate the domain retention. A domain life time of 25.0 h is obtained and possible mechanisms are discussed. Our study gives a direct reference for domain structure-related applications of LNOI, including guiding wave nonlinear frequency conversion, nonlinear wavefront tailoring, electro-optic modulation, and piezoelectric devices.

  4. Non-linear feedback control of the p53 protein-mdm2 inhibitor system using the derivative-free non-linear Kalman filter.

    Science.gov (United States)

    Rigatos, Gerasimos G

    2016-06-01

    It is proven that the model of the p53-mdm2 protein synthesis loop is a differentially flat one and using a diffeomorphism (change of state variables) that is proposed by differential flatness theory it is shown that the protein synthesis model can be transformed into the canonical (Brunovsky) form. This enables the design of a feedback control law that maintains the concentration of the p53 protein at the desirable levels. To estimate the non-measurable elements of the state vector describing the p53-mdm2 system dynamics, the derivative-free non-linear Kalman filter is used. Moreover, to compensate for modelling uncertainties and external disturbances that affect the p53-mdm2 system, the derivative-free non-linear Kalman filter is re-designed as a disturbance observer. The derivative-free non-linear Kalman filter consists of the Kalman filter recursion applied on the linearised equivalent of the protein synthesis model together with an inverse transformation based on differential flatness theory that enables to retrieve estimates for the state variables of the initial non-linear model. The proposed non-linear feedback control and perturbations compensation method for the p53-mdm2 system can result in more efficient chemotherapy schemes where the infusion of medication will be better administered.

  5. Azimuthal Seismic Amplitude Variation with Offset and Azimuth Inversion in Weakly Anisotropic Media with Orthorhombic Symmetry

    Science.gov (United States)

    Pan, Xinpeng; Zhang, Guangzhi; Yin, Xingyao

    2018-01-01

    Seismic amplitude variation with offset and azimuth (AVOaz) inversion is well known as a popular and pragmatic tool utilized to estimate fracture parameters. A single set of vertical fractures aligned along a preferred horizontal direction embedded in a horizontally layered medium can be considered as an effective long-wavelength orthorhombic medium. Estimation of Thomsen's weak-anisotropy (WA) parameters and fracture weaknesses plays an important role in characterizing the orthorhombic anisotropy in a weakly anisotropic medium. Our goal is to demonstrate an orthorhombic anisotropic AVOaz inversion approach to describe the orthorhombic anisotropy utilizing the observable wide-azimuth seismic reflection data in a fractured reservoir with the assumption of orthorhombic symmetry. Combining Thomsen's WA theory and linear-slip model, we first derive a perturbation in stiffness matrix of a weakly anisotropic medium with orthorhombic symmetry under the assumption of small WA parameters and fracture weaknesses. Using the perturbation matrix and scattering function, we then derive an expression for linearized PP-wave reflection coefficient in terms of P- and S-wave moduli, density, Thomsen's WA parameters, and fracture weaknesses in such an orthorhombic medium, which avoids the complicated nonlinear relationship between the orthorhombic anisotropy and azimuthal seismic reflection data. Incorporating azimuthal seismic data and Bayesian inversion theory, the maximum a posteriori solutions of Thomsen's WA parameters and fracture weaknesses in a weakly anisotropic medium with orthorhombic symmetry are reasonably estimated with the constraints of Cauchy a priori probability distribution and smooth initial models of model parameters to enhance the inversion resolution and the nonlinear iteratively reweighted least squares strategy. The synthetic examples containing a moderate noise demonstrate the feasibility of the derived orthorhombic anisotropic AVOaz inversion method, and the

  6. Radionuclide release rate inversion of nuclear accidents in nuclear facility based on Kalman filter

    International Nuclear Information System (INIS)

    Tang Xiuhuan; Bao Lihong; Li Hua; Wan Junsheng

    2014-01-01

    The rapidly and continually back-calculating source term is important for nuclear emergency response. The Gaussian multi-puff atmospheric dispersion model was used to produce regional environment monitoring data virtually, and then a Kalman filter was designed to inverse radionuclide release rate of nuclear accidents in nuclear facility and the release rate tracking in real time was achieved. The results show that the Kalman filter combined with Gaussian multi-puff atmospheric dispersion model can successfully track the virtually stable, linear or nonlinear release rate after being iterated about 10 times. The standard error of inversion results increases with the true value. Meanwhile extended Kalman filter cannot inverse the height parameter of accident release as interceptive error is too large to converge. Kalman filter constructed from environment monitoring data and Gaussian multi-puff atmospheric dispersion model can be applied to source inversion in nuclear accident which is characterized by static height and position, short and continual release in nuclear facility. Hence it turns out to be an alternative source inversion method in nuclear emergency response. (authors)

  7. Quantifying uncertainties of seismic Bayesian inversion of Northern Great Plains

    Science.gov (United States)

    Gao, C.; Lekic, V.

    2017-12-01

    Elastic waves excited by earthquakes are the fundamental observations of the seismological studies. Seismologists measure information such as travel time, amplitude, and polarization to infer the properties of earthquake source, seismic wave propagation, and subsurface structure. Across numerous applications, seismic imaging has been able to take advantage of complimentary seismic observables to constrain profiles and lateral variations of Earth's elastic properties. Moreover, seismic imaging plays a unique role in multidisciplinary studies of geoscience by providing direct constraints on the unreachable interior of the Earth. Accurate quantification of uncertainties of inferences made from seismic observations is of paramount importance for interpreting seismic images and testing geological hypotheses. However, such quantification remains challenging and subjective due to the non-linearity and non-uniqueness of geophysical inverse problem. In this project, we apply a reverse jump Markov chain Monte Carlo (rjMcMC) algorithm for a transdimensional Bayesian inversion of continental lithosphere structure. Such inversion allows us to quantify the uncertainties of inversion results by inverting for an ensemble solution. It also yields an adaptive parameterization that enables simultaneous inversion of different elastic properties without imposing strong prior information on the relationship between them. We present retrieved profiles of shear velocity (Vs) and radial anisotropy in Northern Great Plains using measurements from USArray stations. We use both seismic surface wave dispersion and receiver function data due to their complementary constraints of lithosphere structure. Furthermore, we analyze the uncertainties of both individual and joint inversion of those two data types to quantify the benefit of doing joint inversion. As an application, we infer the variation of Moho depths and crustal layering across the northern Great Plains.

  8. Geostatistical and adjoint sensitivity techniques applied to a conceptual model of ground-water flow in the Paradox Basin, Utah

    International Nuclear Information System (INIS)

    Metcalfe, D.E.; Campbell, J.E.; RamaRao, B.S.; Harper, W.V.; Battelle Project Management Div., Columbus, OH)

    1985-01-01

    Sensitivity and uncertainty analysis are important components of performance assessment activities for potential high-level radioactive waste repositories. The application of geostatistical and adjoint sensitivity techniques to aid in the calibration of an existing conceptual model of ground-water flow is demonstrated for the Leadville Limestone in Paradox Basin, Utah. The geostatistical method called kriging is used to statistically analyze the measured potentiometric data for the Leadville. This analysis consists of identifying anomalous data and data trends and characterizing the correlation structure between data points. Adjoint sensitivity analysis is then performed to aid in the calibration of a conceptual model of ground-water flow to the Leadville measured potentiometric data. Sensitivity derivatives of the fit between the modeled Leadville potentiometric surface and the measured potentiometric data to model parameters and boundary conditions are calculated by the adjoint method. These sensitivity derivatives are used to determine which model parameter and boundary condition values should be modified to most efficiently improve the fit of modeled to measured potentiometric conditions

  9. A variational Bayesian method to inverse problems with impulsive noise

    KAUST Repository

    Jin, Bangti

    2012-01-01

    We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise to achieve robustness with respect to outliers. A hierarchical model with all hyper-parameters automatically determined from the given data is described. An algorithm of variational type by minimizing the Kullback-Leibler divergence between the true posteriori distribution and a separable approximation is developed. The numerical method is illustrated on several one- and two-dimensional linear and nonlinear inverse problems arising from heat conduction, including estimating boundary temperature, heat flux and heat transfer coefficient. The results show its robustness to outliers and the fast and steady convergence of the algorithm. © 2011 Elsevier Inc.

  10. Fermat's principle and nonlinear traveltime tomography

    International Nuclear Information System (INIS)

    Berryman, J.G.; Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, New York 10012)

    1989-01-01

    Fermat's principle shows that a definite convex set of feasible slowness models, depending only on the traveltime data, exists for the fully nonlinear traveltime inversion problem. In a new iterative reconstruction algorithm, the minimum number of nonfeasible ray paths is used as a figure of merit to determine the optimum size of the model correction at each step. The numerical results show that the new algorithm is robust, stable, and produces very good reconstructions even for high contrast materials where standard methods tend to diverge

  11. Joint inversion of geophysical data for site characterization and restoration monitoring. FY97 annual progress report for EMSP

    International Nuclear Information System (INIS)

    Berge, P.A.; Berryman, J.G.; Bonner, B.P.; Roberts, J.J.; Wildenschild

    1997-01-01

    'The purpose of this project is to develop a computer code for joint in-version of seismic and electrical data, to improve underground imaging for site characterization and remediation monitoring. The computer code developed in this project will invert geophysical data to obtain direct estimates of porosity and saturation underground, rather than inverting for seismic velocity and electrical resistivity or other geophysical properties. This is intended to be a significant improvement in the state-of-the-art of under-ground imaging, since interpretation of data collected at a contaminated site would become much less subjective. The schedule of this project is as follows: In the first year, investigators perform laboratory measurements of elastic and electrical properties of sand-clay mixtures containing various fluids. Investigators also develop methods of relating measurable geophysical properties to porosity and saturation by using rock physics theories, geostatistical, and empirical techniques together with available laboratory measurements. In the second year, investigators finish any necessary laboratory measurements and apply the methods developed in the first year to invert available borehole log data to predict measured properties of cores and sediments from a borehole. Investigators refine the inversion code in the third year and carry out a field experiment to collect seismic and electrical data. Investigators then use the inversion code to invert the field data to produce estimates of porosity and saturation in the field area where the data were collected. This report describes progress made in the first year of this three-year project.'

  12. Mapping nonlinear shallow-water tides: a look at the past and future

    DEFF Research Database (Denmark)

    Andersen, Ole Baltazar; Egbert, G.D.; Erofeeva, S.Y.

    2006-01-01

    advanced by the pioneering researches of Christian Le Provost who employed analytical theory, physical modeling, and numerical modeling in many extensive studies, especially of the tides of the English Channel. Le Provost's complementary work with satellite altimetry motivates our attempts to merge...... these two interests. After a brief review, we describe initial steps toward the assimilation of altimetry into models of nonlinear tides via generalized inverse methods. A series of barotropic inverse solutions is computed for the M-4 tide over the northwest European Shelf. Future applications of altimetry...

  13. UNCERT: geostatistics, uncertainty analysis and visualization software applied to groundwater flow and contaminant transport modeling

    International Nuclear Information System (INIS)

    Wingle, W.L.; Poeter, E.P.; McKenna, S.A.

    1999-01-01

    UNCERT is a 2D and 3D geostatistics, uncertainty analysis and visualization software package applied to ground water flow and contaminant transport modeling. It is a collection of modules that provides tools for linear regression, univariate statistics, semivariogram analysis, inverse-distance gridding, trend-surface analysis, simple and ordinary kriging and discrete conditional indicator simulation. Graphical user interfaces for MODFLOW and MT3D, ground water flow and contaminant transport models, are provided for streamlined data input and result analysis. Visualization tools are included for displaying data input and output. These include, but are not limited to, 2D and 3D scatter plots, histograms, box and whisker plots, 2D contour maps, surface renderings of 2D gridded data and 3D views of gridded data. By design, UNCERT's graphical user interface and visualization tools facilitate model design and analysis. There are few built in restrictions on data set sizes and each module (with two exceptions) can be run in either graphical or batch mode. UNCERT is in the public domain and is available from the World Wide Web with complete on-line and printable (PDF) documentation. UNCERT is written in ANSI-C with a small amount of FORTRAN77, for UNIX workstations running X-Windows and Motif (or Lesstif). This article discusses the features of each module and demonstrates how they can be used individually and in combination. The tools are applicable to a wide range of fields and are currently used by researchers in the ground water, mining, mathematics, chemistry and geophysics, to name a few disciplines. (Copyright (c) 1999 Elsevier Science B.V., Amsterdam. All rights reserved.)

  14. Uniqueness and numerical methods in inverse obstacle scattering

    International Nuclear Information System (INIS)

    Kress, Rainer

    2007-01-01

    The inverse problem we consider in this tutorial is to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic plane waves. In the first part we will concentrate on the issue of uniqueness, i.e., we will investigate under what conditions an obstacle and its boundary condition can be identified from a knowledge of its far field pattern for incident plane waves. We will review some classical and some recent results and draw attention to open problems. In the second part we will survey on numerical methods for solving inverse obstacle scattering problems. Roughly speaking, these methods can be classified into three groups. Iterative methods interpret the inverse obstacle scattering problem as a nonlinear ill-posed operator equation and apply iterative schemes such as regularized Newton methods, Landweber iterations or conjugate gradient methods for its solution. Decomposition methods, in principle, separate the inverse scattering problem into an ill-posed linear problem to reconstruct the scattered wave from its far field and the subsequent determination of the boundary of the scatterer from the boundary condition. Finally, the third group consists of the more recently developed sampling methods. These are based on the numerical evaluation of criteria in terms of indicator functions that decide whether a point lies inside or outside the scatterer. The tutorial will give a survey by describing one or two representatives of each group including a discussion on the various advantages and disadvantages

  15. Symbolic-computation study of the perturbed nonlinear Schrodinger model in inhomogeneous optical fibers

    International Nuclear Information System (INIS)

    Tian Bo; Gao Yitian

    2005-01-01

    A realistic, inhomogeneous fiber in the optical communication systems can be described by the perturbed nonlinear Schrodinger model (also named as the normalized nonlinear Schrodinger model with periodically varying coefficients, dispersion managed nonlinear Schrodinger model or nonlinear Schrodinger model with variable coefficients). Hereby, we extend to this model a direct method, perform symbolic computation and obtain two families of the exact, analytic bright-solitonic solutions, with or without the chirp respectively. The parameters addressed include the shape of the bright soliton, soliton amplitude, inverse width of the soliton, chirp, frequency, center of the soliton and center of the phase of the soliton. Of optical and physical interests, we discuss some previously-published special cases of our solutions. Those solutions could help the future studies on the optical communication systems. ms

  16. Adaptive online inverse control of a shape memory alloy wire actuator using a dynamic neural network

    International Nuclear Information System (INIS)

    Mai, Huanhuan; Liao, Xiaofeng; Song, Gangbing

    2013-01-01

    Shape memory alloy (SMA) actuators exhibit severe hysteresis, a nonlinear behavior, which complicates control strategies and limits their applications. This paper presents a new approach to controlling an SMA actuator through an adaptive inverse model based controller that consists of a dynamic neural network (DNN) identifier, a copy dynamic neural network (CDNN) feedforward term and a proportional (P) feedback action. Unlike fixed hysteresis models used in most inverse controllers, the proposed one uses a DNN to identify online the relationship between the applied voltage to the actuator and the displacement (the inverse model). Even without a priori knowledge of the SMA hysteresis and without pre-training, the proposed controller can precisely control the SMA wire actuator in various tracking tasks by identifying online the inverse model of the SMA actuator. Experiments were conducted, and experimental results demonstrated real-time modeling capabilities of DNN and the performance of the adaptive inverse controller. (paper)

  17. Assessment of nitrate pollution in the Grand Morin aquifers (France): Combined use of geostatistics and physically based modeling

    Energy Technology Data Exchange (ETDEWEB)

    Flipo, Nicolas [Centre de Geosciences, UMR Sisyphe, ENSMP, 35 rue Saint-Honore, F-77305 Fontainebleau (France)]. E-mail: nicolas.flipo@ensmp.fr; Jeannee, Nicolas [Geovariances, 49 bis, avenue Franklin Roosevelt, F-77212 Avon (France); Poulin, Michel [Centre de Geosciences, UMR Sisyphe, ENSMP, 35 rue Saint-Honore, F-77305 Fontainebleau (France); Even, Stephanie [Centre de Geosciences, UMR Sisyphe, ENSMP, 35 rue Saint-Honore, F-77305 Fontainebleau (France); Ledoux, Emmanuel [Centre de Geosciences, UMR Sisyphe, ENSMP, 35 rue Saint-Honore, F-77305 Fontainebleau (France)

    2007-03-15

    The objective of this work is to combine several approaches to better understand nitrate fate in the Grand Morin aquifers (2700 km{sup 2}), part of the Seine basin. CAWAQS results from the coupling of the hydrogeological model NEWSAM with the hydrodynamic and biogeochemical model of river PROSE. CAWAQS is coupled with the agronomic model STICS in order to simulate nitrate migration in basins. First, kriging provides a satisfactory representation of aquifer nitrate contamination from local observations, to set initial conditions for the physically based model. Then associated confidence intervals, derived from data using geostatistics, are used to validate CAWAQS results. Results and evaluation obtained from the combination of these approaches are given (period 1977-1988). Then CAWAQS is used to simulate nitrate fate for a 20-year period (1977-1996). The mean nitrate concentrations increase in aquifers is 0.09 mgN L{sup -1} yr{sup -1}, resulting from an average infiltration flux of 3500 kgN.km{sup -2} yr{sup -1}. - Combined use of geostatistics and physically based modeling allows assessment of nitrate concentrations in aquifer systems.

  18. Assessment of nitrate pollution in the Grand Morin aquifers (France): Combined use of geostatistics and physically based modeling

    International Nuclear Information System (INIS)

    Flipo, Nicolas; Jeannee, Nicolas; Poulin, Michel; Even, Stephanie; Ledoux, Emmanuel

    2007-01-01

    The objective of this work is to combine several approaches to better understand nitrate fate in the Grand Morin aquifers (2700 km 2 ), part of the Seine basin. CAWAQS results from the coupling of the hydrogeological model NEWSAM with the hydrodynamic and biogeochemical model of river PROSE. CAWAQS is coupled with the agronomic model STICS in order to simulate nitrate migration in basins. First, kriging provides a satisfactory representation of aquifer nitrate contamination from local observations, to set initial conditions for the physically based model. Then associated confidence intervals, derived from data using geostatistics, are used to validate CAWAQS results. Results and evaluation obtained from the combination of these approaches are given (period 1977-1988). Then CAWAQS is used to simulate nitrate fate for a 20-year period (1977-1996). The mean nitrate concentrations increase in aquifers is 0.09 mgN L -1 yr -1 , resulting from an average infiltration flux of 3500 kgN.km -2 yr -1 . - Combined use of geostatistics and physically based modeling allows assessment of nitrate concentrations in aquifer systems

  19. Acoustic Impedance Inversion of Seismic Data Using Genetic Algorithm

    Science.gov (United States)

    Eladj, Said; Djarfour, Noureddine; Ferahtia, Djalal; Ouadfeul, Sid-Ali

    2013-04-01

    The inversion of seismic data can be used to constrain estimates of the Earth's acoustic impedance structure. This kind of problem is usually known to be non-linear, high-dimensional, with a complex search space which may be riddled with many local minima, and results in irregular objective functions. We investigate here the performance and the application of a genetic algorithm, in the inversion of seismic data. The proposed algorithm has the advantage of being easily implemented without getting stuck in local minima. The effects of population size, Elitism strategy, uniform cross-over and lower mutation are examined. The optimum solution parameters and performance were decided as a function of the testing error convergence with respect to the generation number. To calculate the fitness function, we used L2 norm of the sample-to-sample difference between the reference and the inverted trace. The cross-over probability is of 0.9-0.95 and mutation has been tested at 0.01 probability. The application of such a genetic algorithm to synthetic data shows that the inverted acoustic impedance section was efficient. Keywords: Seismic, Inversion, acoustic impedance, genetic algorithm, fitness functions, cross-over, mutation.

  20. Bayesian inversion of microtremor array dispersion data in southwestern British Columbia

    Science.gov (United States)

    Molnar, Sheri; Dosso, Stan E.; Cassidy, John F.

    2010-11-01

    This paper applies Bayesian inversion, with evaluation of data errors and model parametrization, to produce the most-probable shear-wave velocity profile together with quantitative uncertainty estimates from microtremor array dispersion data. Generally, the most important property for characterizing earthquake site response is the shear-wave velocity (VS) profile. The microtremor array method determines phase velocity dispersion of Rayleigh surface waves from multi-instrument recordings of urban noise. Inversion of dispersion curves for VS structure is a non-unique and non-linear problem such that meaningful evaluation of confidence intervals is required. Quantitative uncertainty estimation requires not only a non-linear inversion approach that samples models proportional to their probability, but also rigorous estimation of the data error statistics and an appropriate model parametrization. This paper applies a Bayesian formulation that represents the solution of the inverse problem in terms of the posterior probability density (PPD) of the geophysical model parameters. Markov-chain Monte Carlo methods are used with an efficient implementation of Metropolis-Hastings sampling to provide an unbiased sample from the PPD to compute parameter uncertainties and inter-relationships. Nonparametric estimation of a data error covariance matrix from residual analysis is applied with rigorous a posteriori statistical tests to validate the covariance estimate and the assumption of a Gaussian error distribution. The most appropriate model parametrization is determined using the Bayesian information criterion, which provides the simplest model consistent with the resolving power of the data. Parametrizations considered vary in the number of layers, and include layers with uniform, linear and power-law gradients. Parameter uncertainties are found to be underestimated when data error correlations are neglected and when compressional-wave velocity and/or density (nuisance

  1. Non-linear wave equations:Mathematical techniques

    International Nuclear Information System (INIS)

    1978-01-01

    An account of certain well-established mathematical methods, which prove useful to deal with non-linear partial differential equations is presented. Within the strict framework of Functional Analysis, it describes Semigroup Techniques in Banach Spaces as well as variational approaches towards critical points. Detailed proofs are given of the existence of local and global solutions of the Cauchy problem and of the stability of stationary solutions. The formal approach based upon invariance under Lie transformations deserves attention due to its wide range of applicability, even if the explicit solutions thus obtained do not allow for a deep analysis of the equations. A compre ensive introduction to the inverse scattering approach and to the solution concept for certain non-linear equations of physical interest are also presented. A detailed discussion is made about certain convergence and stability problems which arise in importance need not be emphasized. (author) [es

  2. Inverse Diffusion Curves Using Shape Optimization.

    Science.gov (United States)

    Zhao, Shuang; Durand, Fredo; Zheng, Changxi

    2018-07-01

    The inverse diffusion curve problem focuses on automatic creation of diffusion curve images that resemble user provided color fields. This problem is challenging since the 1D curves have a nonlinear and global impact on resulting color fields via a partial differential equation (PDE). We introduce a new approach complementary to previous methods by optimizing curve geometry. In particular, we propose a novel iterative algorithm based on the theory of shape derivatives. The resulting diffusion curves are clean and well-shaped, and the final image closely approximates the input. Our method provides a user-controlled parameter to regularize curve complexity, and generalizes to handle input color fields represented in a variety of formats.

  3. Modeling and inversion of PS-wave moveout asymmetry for tilted TI media: Part 1 - Horizontal TTI layer

    Digital Repository Service at National Institute of Oceanography (India)

    Dewangan, P.; Tsvankin, I.

    when the symmetry axis deviates by 20 degrees-30 degrees from the vertical horizontal direction. All relevant parameters of a TTI layer can be estimated by nonlinear inversion of the NMO velocities and zero-offset traveltimes of PP- and SS-(SVSV) waves...

  4. Chapter J: Issues and challenges in the application of geostatistics and spatial-data analysis to the characterization of sand-and-gravel resources

    Science.gov (United States)

    Hack, Daniel R.

    2005-01-01

    Sand-and-gravel (aggregate) resources are a critical component of the Nation's infrastructure, yet aggregate-mining technologies lag far behind those of metalliferous mining and other sectors. Deposit-evaluation and site-characterization methodologies are antiquated, and few serious studies of the potential applications of spatial-data analysis and geostatistics have been published. However, because of commodity usage and the necessary proximity of a mine to end use, aggregate-resource exploration and evaluation differ fundamentally from comparable activities for metalliferous ores. Acceptable practices, therefore, can reflect this cruder scale. The increasing use of computer technologies is colliding with the need for sand-and-gravel mines to modernize and improve their overall efficiency of exploration, mine planning, scheduling, automation, and other operations. The emergence of megaquarries in the 21st century will also be a contributing factor. Preliminary research into the practical applications of exploratory-data analysis (EDA) have been promising. For example, EDA was used to develop a linear-regression equation to forecast freeze-thaw durability from absorption values for Lower Paleozoic carbonate rocks mined for crushed aggregate from quarries in Oklahoma. Applications of EDA within a spatial context, a method of spatial-data analysis, have also been promising, as with the investigation of undeveloped sand-and-gravel resources in the sedimentary deposits of Pleistocene Lake Bonneville, Utah. Formal geostatistical investigations of sand-and-gravel deposits are quite rare, and the primary focus of those studies that have been completed is on the spatial characterization of deposit thickness and its subsequent effect on ore reserves. A thorough investigation of a gravel deposit in an active aggregate-mining area in central Essex, U.K., emphasized the problems inherent in the geostatistical characterization of particle-size-analysis data. Beyond such factors

  5. Demonstration of a geostatistical approach to physically consistent downscaling of climate modeling simulations

    KAUST Repository

    Jha, Sanjeev Kumar; Mariethoz, Gregoire; Evans, Jason P.; McCabe, Matthew

    2013-01-01

    A downscaling approach based on multiple-point geostatistics (MPS) is presented. The key concept underlying MPS is to sample spatial patterns from within training images, which can then be used in characterizing the relationship between different variables across multiple scales. The approach is used here to downscale climate variables including skin surface temperature (TSK), soil moisture (SMOIS), and latent heat flux (LH). The performance of the approach is assessed by applying it to data derived from a regional climate model of the Murray-Darling basin in southeast Australia, using model outputs at two spatial resolutions of 50 and 10 km. The data used in this study cover the period from 1985 to 2006, with 1985 to 2005 used for generating the training images that define the relationships of the variables across the different spatial scales. Subsequently, the spatial distributions for the variables in the year 2006 are determined at 10 km resolution using the 50 km resolution data as input. The MPS geostatistical downscaling approach reproduces the spatial distribution of TSK, SMOIS, and LH at 10 km resolution with the correct spatial patterns over different seasons, while providing uncertainty estimates through the use of multiple realizations. The technique has the potential to not only bridge issues of spatial resolution in regional and global climate model simulations but also in feature sharpening in remote sensing applications through image fusion, filling gaps in spatial data, evaluating downscaled variables with available remote sensing images, and aggregating/disaggregating hydrological and groundwater variables for catchment studies.

  6. Inverse Magnetoresistance in Polymer Spin Valves.

    Science.gov (United States)

    Ding, Shuaishuai; Tian, Yuan; Li, Yang; Mi, Wenbo; Dong, Huanli; Zhang, Xiaotao; Hu, Wenping; Zhu, Daoben

    2017-05-10

    In this work, both negative and positive magnetoresistance (MR) in solution-processed regioregular poly(3-hexylthiophene) (RR-P3HT) is observed in organic spin valves (OSVs) with vertical La 2/3 Sr 1/3 MnO 3 (LSMO)/P3HT/AlO x /Co configuration. The ferromagnetic (FM) LSMO electrode with near-atomic flatness is fabricated by a DC facing-target magnetron sputtering method. This research is focused on the origin of the MR inversion. Two types of devices are investigated in details: One with Co penetration shows a negative MR of 0.2%, while the other well-defined device with a nonlinear behavior has a positive MR of 15.6%. The MR measurements in LSMO/AlO x /Co and LSMO/Co junctions are carried to exclude the interference of insulating layer and two FM electrodes themselves. By examining the Co thicknesses and their corresponding magnetic hysteresis loops, a spin-dependent hybrid-interface-state model by Co penetration is induced to explain the MR sign inversion. These results proven by density functional theory (DFT) calculations may shed light on the controllable interfacial properties in designing novel OSV devices.

  7. Image-domain full waveform inversion

    KAUST Repository

    Zhang, Sanzong

    2013-08-20

    The main difficulty with the data-domain full waveform inversion (FWI) is that it tends to get stuck in the local minima associated with the waveform misfit function. This is because the waveform misfit function is highly nonlinear with respect to changes in velocity model. To reduce this nonlinearity, we define the image-domain objective function to minimize the difference of the suboffset-domain common image gathers (CIGs) obtained by migrating the observed data and the calculated data. The derivation shows that the gradient of this new objective function is the combination of the gradient of the conventional FWI and the image-domain differential semblance optimization (DSO). Compared to the conventional FWI, the imagedomain FWI is immune to cycle skipping problems by smearing the nonzero suboffset images along wavepath. It also can avoid the edge effects and the gradient artifacts that are inherent in DSO due to the falsely over-penalized focused images. This is achieved by subtracting the focused image associated with the calculated data from the unfocused image associated with the observed data in the image-domain misfit function. The numerical results of the Marmousi model show that image-domain FWI is less sensitive the initial model than the conventional FWI. © 2013 SEG.

  8. Image-domain full waveform inversion

    KAUST Repository

    Zhang, Sanzong; Schuster, Gerard T.

    2013-01-01

    The main difficulty with the data-domain full waveform inversion (FWI) is that it tends to get stuck in the local minima associated with the waveform misfit function. This is because the waveform misfit function is highly nonlinear with respect to changes in velocity model. To reduce this nonlinearity, we define the image-domain objective function to minimize the difference of the suboffset-domain common image gathers (CIGs) obtained by migrating the observed data and the calculated data. The derivation shows that the gradient of this new objective function is the combination of the gradient of the conventional FWI and the image-domain differential semblance optimization (DSO). Compared to the conventional FWI, the imagedomain FWI is immune to cycle skipping problems by smearing the nonzero suboffset images along wavepath. It also can avoid the edge effects and the gradient artifacts that are inherent in DSO due to the falsely over-penalized focused images. This is achieved by subtracting the focused image associated with the calculated data from the unfocused image associated with the observed data in the image-domain misfit function. The numerical results of the Marmousi model show that image-domain FWI is less sensitive the initial model than the conventional FWI. © 2013 SEG.

  9. Estimation of bone Calcium-to-Phosphorous mass ratio using dual-energy nonlinear polynomial functions

    International Nuclear Information System (INIS)

    Sotiropoulou, P; Koukou, V; Martini, N; Nikiforidis, G; Michail, C; Kandarakis, I; Fountos, G; Kounadi, E

    2015-01-01

    In this study an analytical approximation of dual-energy inverse functions is presented for the estimation of the calcium-to-phosphorous (Ca/P) mass ratio, which is a crucial parameter in bone health. Bone quality could be examined by the X-ray dual-energy method (XDEM), in terms of bone tissue material properties. Low- and high-energy, log- intensity measurements were combined by using a nonlinear function, to cancel out the soft tissue structures and generate the dual energy bone Ca/P mass ratio. The dual-energy simulated data were obtained using variable Ca and PO 4 thicknesses on a fixed total tissue thickness. The XDEM simulations were based on a bone phantom. Inverse fitting functions with least-squares estimation were used to obtain the fitting coefficients and to calculate the thickness of each material. The examined inverse mapping functions were linear, quadratic, and cubic. For every thickness, the nonlinear quadratic function provided the optimal fitting accuracy while requiring relative few terms. The dual-energy method, simulated in this work could be used to quantify bone Ca/P mass ratio with photon-counting detectors. (paper)

  10. Full waveform inversion based on scattering angle enrichment with application to real dataset

    KAUST Repository

    Wu, Zedong

    2015-08-19

    Reflected waveform inversion (RWI) provides a method to reduce the nonlinearity of the standard full waveform inversion (FWI). However, the drawback of the existing RWI methods is inability to utilize diving waves and the extra sensitivity to the migrated image. We propose a combined FWI and RWI optimization problem through dividing the velocity into the background and perturbed components. We optimize both the background and perturbed components, as independent parameters. The new objective function is quadratic with respect to the perturbed component, which will reduce the nonlinearity of the optimization problem. Solving this optimization provides a true amplitude image and utilizes the diving waves to update the velocity of the shallow parts. To insure a proper wavenumber continuation, we use an efficient scattering angle filter to direct the inversion at the early stages to direct energy corresponding to large (smooth velocity) scattering angles to the background velocity update and the small (high wavenumber) scattering angles to the perturbed velocity update. This efficient implementation of the filter is fast and requires less memory than the conventional approach based on extended images. Thus, the new FWI procedure updates the background velocity mainly along the wavepath for both diving and reflected waves in the initial stages. At the same time, it updates the perturbation with mainly reflections (filtering out the diving waves). To demonstrate the capability of this method, we apply it to a real 2D marine dataset.

  11. Reentry Vehicle Flight Controls Design Guidelines: Dynamic Inversion

    Science.gov (United States)

    Ito, Daigoro; Georgie, Jennifer; Valasek, John; Ward, Donald T.

    2002-01-01

    This report addresses issues in developing a flight control design for vehicles operating across a broad flight regime and with highly nonlinear physical descriptions of motion. Specifically it addresses the need for reentry vehicles that could operate through reentry from space to controlled touchdown on Earth. The latter part of controlled descent is achieved by parachute or paraglider - or by all automatic or a human-controlled landing similar to that of the Orbiter. Since this report addresses the specific needs of human-carrying (not necessarily piloted) reentry vehicles, it deals with highly nonlinear equations of motion, and then-generated control systems must be robust across a very wide range of physics. Thus, this report deals almost exclusively with some form of dynamic inversion (DI). Two vital aspects of control theory - noninteracting control laws and the transformation of nonlinear systems into equivalent linear systems - are embodied in DI. Though there is no doubt that the mathematical tools and underlying theory are widely available, there are open issues as to the practicality of using DI as the only or primary design approach for reentry articles. This report provides a set of guidelines that can be used to determine the practical usefulness of the technique.

  12. Bridges between multiple-point geostatistics and texture synthesis: Review and guidelines for future research

    Science.gov (United States)

    Mariethoz, Gregoire; Lefebvre, Sylvain

    2014-05-01

    Multiple-Point Simulations (MPS) is a family of geostatistical tools that has received a lot of attention in recent years for the characterization of spatial phenomena in geosciences. It relies on the definition of training images to represent a given type of spatial variability, or texture. We show that the algorithmic tools used are similar in many ways to techniques developed in computer graphics, where there is a need to generate large amounts of realistic textures for applications such as video games and animated movies. Similarly to MPS, these texture synthesis methods use training images, or exemplars, to generate realistic-looking graphical textures. Both domains of multiple-point geostatistics and example-based texture synthesis present similarities in their historic development and share similar concepts. These disciplines have however remained separated, and as a result significant algorithmic innovations in each discipline have not been universally adopted. Texture synthesis algorithms present drastically increased computational efficiency, patterns reproduction and user control. At the same time, MPS developed ways to condition models to spatial data and to produce 3D stochastic realizations, which have not been thoroughly investigated in the field of texture synthesis. In this paper we review the possible links between these disciplines and show the potential and limitations of using concepts and approaches from texture synthesis in MPS. We also provide guidelines on how recent developments could benefit both fields of research, and what challenges remain open.

  13. Inverse problem for in vivo NMR spatial localization

    International Nuclear Information System (INIS)

    Hasenfeld, A.C.

    1985-11-01

    The basic physical problem of NMR spatial localization is considered. To study diseased sites, one must solve the problem of adequately localizing the NMR signal. We formulate this as an inverse problem. As the NMR Bloch equations determine the motion of nuclear spins in applied magnetic fields, a theoretical study is undertaken to answer the question of how to design magnetic field configurations to achieve these localized excited spin populations. Because of physical constraints in the production of the relevant radiofrequency fields, the problem factors into a temporal one and a spatial one. We formulate the temporal problem as a nonlinear transformation, called the Bloch Transform, from the rf input to the magnetization response. In trying to invert this transformation, both linear (for the Fourier Transform) and nonlinear (for the Bloch Transform) modes of radiofrequency excitation are constructed. The spatial problem is essentially a statics problem for the Maxwell equations of electromagnetism, as the wavelengths of the radiation considered are on the order of ten meters, and so propagation effects are negligible. In the general case, analytic solutions are unavailable, and so the methods of computer simulation are used to map the rf field spatial profiles. Numerical experiments are also performed to verify the theoretical analysis, and experimental confirmation of the theory is carried out on the 0.5 Tesla IBM/Oxford Imaging Spectrometer at the LBL NMR Medical Imaging Facility. While no explicit inverse is constructed to ''solve'' this problem, the combined theoretical/numerical analysis is validated experimentally, justifying the approximations made. 56 refs., 31 figs

  14. Inverse problem for in vivo NMR spatial localization

    Energy Technology Data Exchange (ETDEWEB)

    Hasenfeld, A.C.

    1985-11-01

    The basic physical problem of NMR spatial localization is considered. To study diseased sites, one must solve the problem of adequately localizing the NMR signal. We formulate this as an inverse problem. As the NMR Bloch equations determine the motion of nuclear spins in applied magnetic fields, a theoretical study is undertaken to answer the question of how to design magnetic field configurations to achieve these localized excited spin populations. Because of physical constraints in the production of the relevant radiofrequency fields, the problem factors into a temporal one and a spatial one. We formulate the temporal problem as a nonlinear transformation, called the Bloch Transform, from the rf input to the magnetization response. In trying to invert this transformation, both linear (for the Fourier Transform) and nonlinear (for the Bloch Transform) modes of radiofrequency excitation are constructed. The spatial problem is essentially a statics problem for the Maxwell equations of electromagnetism, as the wavelengths of the radiation considered are on the order of ten meters, and so propagation effects are negligible. In the general case, analytic solutions are unavailable, and so the methods of computer simulation are used to map the rf field spatial profiles. Numerical experiments are also performed to verify the theoretical analysis, and experimental confirmation of the theory is carried out on the 0.5 Tesla IBM/Oxford Imaging Spectrometer at the LBL NMR Medical Imaging Facility. While no explicit inverse is constructed to ''solve'' this problem, the combined theoretical/numerical analysis is validated experimentally, justifying the approximations made. 56 refs., 31 figs.

  15. An adaptive ANOVA-based PCKF for high-dimensional nonlinear inverse modeling

    Science.gov (United States)

    Li, Weixuan; Lin, Guang; Zhang, Dongxiao

    2014-02-01

    The probabilistic collocation-based Kalman filter (PCKF) is a recently developed approach for solving inverse problems. It resembles the ensemble Kalman filter (EnKF) in every aspect-except that it represents and propagates model uncertainty by polynomial chaos expansion (PCE) instead of an ensemble of model realizations. Previous studies have shown PCKF is a more efficient alternative to EnKF for many data assimilation problems. However, the accuracy and efficiency of PCKF depends on an appropriate truncation of the PCE series. Having more polynomial chaos basis functions in the expansion helps to capture uncertainty more accurately but increases computational cost. Selection of basis functions is particularly important for high-dimensional stochastic problems because the number of polynomial chaos basis functions required to represent model uncertainty grows dramatically as the number of input parameters (random dimensions) increases. In classic PCKF algorithms, the PCE basis functions are pre-set based on users' experience. Also, for sequential data assimilation problems, the basis functions kept in PCE expression remain unchanged in different Kalman filter loops, which could limit the accuracy and computational efficiency of classic PCKF algorithms. To address this issue, we present a new algorithm that adaptively selects PCE basis functions for different problems and automatically adjusts the number of basis functions in different Kalman filter loops. The algorithm is based on adaptive functional ANOVA (analysis of variance) decomposition, which approximates a high-dimensional function with the summation of a set of low-dimensional functions. Thus, instead of expanding the original model into PCE, we implement the PCE expansion on these low-dimensional functions, which is much less costly. We also propose a new adaptive criterion for ANOVA that is more suited for solving inverse problems. The new algorithm was tested with different examples and demonstrated

  16. Use of geostatistics in high level radioactive waste repository site characterization

    Energy Technology Data Exchange (ETDEWEB)

    Doctor, P G [Pacific Northwest Laboratory, Richland, WA (USA)

    1980-09-01

    In evaluating and characterizing sites that are candidates for use as repositories for high-level radioactive waste, there is an increasing need to estimate the uncertainty in hydrogeologic data and in the quantities calculated from them. This paper discusses the use of geostatistical techniques to estimate hydrogeologic surfaces, such as the top of a basalt formation, and to provide a measure of the uncertainty in that estimate. Maps of the uncertainty estimate, called the kriging error, can be used to evaluate where new data should be taken to affect the greatest reduction in uncertainty in the estimated surface. The methods are illustrated on a set of site-characterization data; the top-of-basalt elevations at the Hanford Site near Richland, Washington.

  17. Geostatistical analysis of potentiometric data in Wolfcamp aquifer of the Palo Duro Basin, Texas

    International Nuclear Information System (INIS)

    Harper, W.V.; Furr, J.M.

    1986-04-01

    This report details a geostatistical analysis of potentiometric data from the Wolfcamp aquifer in the Palo Duro Basin, Texas. Such an analysis is a part of an overall uncertainty analysis for a high-level waste repository in salt. Both an expected potentiometric surface and the associated standard error surface are produced. The Wolfcamp data are found to be well explained by a linear trend with a superimposed spherical semivariogram. A cross-validation of the analysis confirms this. In addition, the cross-validation provides a point-by-point check to test for possible anomalous data

  18. Real-time cardiovascular magnetic resonance at high temporal resolution: radial FLASH with nonlinear inverse reconstruction

    Directory of Open Access Journals (Sweden)

    Merboldt Klaus-Dietmar

    2010-07-01

    Full Text Available Abstract Background Functional assessments of the heart by dynamic cardiovascular magnetic resonance (CMR commonly rely on (i electrocardiographic (ECG gating yielding pseudo real-time cine representations, (ii balanced gradient-echo sequences referred to as steady-state free precession (SSFP, and (iii breath holding or respiratory gating. Problems may therefore be due to the need for a robust ECG signal, the occurrence of arrhythmia and beat to beat variations, technical instabilities (e.g., SSFP "banding" artefacts, and limited patient compliance and comfort. Here we describe a new approach providing true real-time CMR with image acquisition times as short as 20 to 30 ms or rates of 30 to 50 frames per second. Methods The approach relies on a previously developed real-time MR method, which combines a strongly undersampled radial FLASH CMR sequence with image reconstruction by regularized nonlinear inversion. While iterative reconstructions are currently performed offline due to limited computer speed, online monitoring during scanning is accomplished using gridding reconstructions with a sliding window at the same frame rate but with lower image quality. Results Scans of healthy young subjects were performed at 3 T without ECG gating and during free breathing. The resulting images yield T1 contrast (depending on flip angle with an opposed-phase or in-phase condition for water and fat signals (depending on echo time. They completely avoid (i susceptibility-induced artefacts due to the very short echo times, (ii radiofrequency power limitations due to excitations with flip angles of 10° or less, and (iii the risk of peripheral nerve stimulation due to the use of normal gradient switching modes. For a section thickness of 8 mm, real-time images offer a spatial resolution and total acquisition time of 1.5 mm at 30 ms and 2.0 mm at 22 ms, respectively. Conclusions Though awaiting thorough clinical evaluation, this work describes a robust and

  19. Real-time cardiovascular magnetic resonance at high temporal resolution: radial FLASH with nonlinear inverse reconstruction.

    Science.gov (United States)

    Zhang, Shuo; Uecker, Martin; Voit, Dirk; Merboldt, Klaus-Dietmar; Frahm, Jens

    2010-07-08

    Functional assessments of the heart by dynamic cardiovascular magnetic resonance (CMR) commonly rely on (i) electrocardiographic (ECG) gating yielding pseudo real-time cine representations, (ii) balanced gradient-echo sequences referred to as steady-state free precession (SSFP), and (iii) breath holding or respiratory gating. Problems may therefore be due to the need for a robust ECG signal, the occurrence of arrhythmia and beat to beat variations, technical instabilities (e.g., SSFP "banding" artefacts), and limited patient compliance and comfort. Here we describe a new approach providing true real-time CMR with image acquisition times as short as 20 to 30 ms or rates of 30 to 50 frames per second. The approach relies on a previously developed real-time MR method, which combines a strongly undersampled radial FLASH CMR sequence with image reconstruction by regularized nonlinear inversion. While iterative reconstructions are currently performed offline due to limited computer speed, online monitoring during scanning is accomplished using gridding reconstructions with a sliding window at the same frame rate but with lower image quality. Scans of healthy young subjects were performed at 3 T without ECG gating and during free breathing. The resulting images yield T1 contrast (depending on flip angle) with an opposed-phase or in-phase condition for water and fat signals (depending on echo time). They completely avoid (i) susceptibility-induced artefacts due to the very short echo times, (ii) radiofrequency power limitations due to excitations with flip angles of 10 degrees or less, and (iii) the risk of peripheral nerve stimulation due to the use of normal gradient switching modes. For a section thickness of 8 mm, real-time images offer a spatial resolution and total acquisition time of 1.5 mm at 30 ms and 2.0 mm at 22 ms, respectively. Though awaiting thorough clinical evaluation, this work describes a robust and flexible acquisition and reconstruction technique for

  20. Optimization-Based Inverse Identification of the Parameters of a Concrete Cap Material Model

    Science.gov (United States)

    Král, Petr; Hokeš, Filip; Hušek, Martin; Kala, Jiří; Hradil, Petr

    2017-10-01

    Issues concerning the advanced numerical analysis of concrete building structures in sophisticated computing systems currently require the involvement of nonlinear mechanics tools. The efforts to design safer, more durable and mainly more economically efficient concrete structures are supported via the use of advanced nonlinear concrete material models and the geometrically nonlinear approach. The application of nonlinear mechanics tools undoubtedly presents another step towards the approximation of the real behaviour of concrete building structures within the framework of computer numerical simulations. However, the success rate of this application depends on having a perfect understanding of the behaviour of the concrete material models used and having a perfect understanding of the used material model parameters meaning. The effective application of nonlinear concrete material models within computer simulations often becomes very problematic because these material models very often contain parameters (material constants) whose values are difficult to obtain. However, getting of the correct values of material parameters is very important to ensure proper function of a concrete material model used. Today, one possibility, which permits successful solution of the mentioned problem, is the use of optimization algorithms for the purpose of the optimization-based inverse material parameter identification. Parameter identification goes hand in hand with experimental investigation while it trying to find parameter values of the used material model so that the resulting data obtained from the computer simulation will best approximate the experimental data. This paper is focused on the optimization-based inverse identification of the parameters of a concrete cap material model which is known under the name the Continuous Surface Cap Model. Within this paper, material parameters of the model are identified on the basis of interaction between nonlinear computer simulations

  1. Modelling and control of a nonlinear magnetostrictive actuator system

    Science.gov (United States)

    Ramli, M. H. M.; Majeed, A. P. P. Abdul; Anuar, M. A. M.; Mohamed, Z.

    2018-04-01

    This paper explores the implementation of a feedforward control method to a nonlinear control system, in particular, Magnetostrictive Actuators (MA) that has excellent properties of energy conversion between the mechanical and magnetic form through magnetostriction effects which could be used in actuating and sensing application. MA is known to exhibit hysteresis behaviour and it is rate dependent (the level of hysteresis depends closely on the rate of input excitation frequency). This is, nonetheless, an undesirable behaviour and has to be eliminated in realising high precision application. The MA is modelled by a phenomenological modelling approach via Prandtl-Ishlinskii (P-I) operator to characterise the hysteresis nonlinearities. A feedforward control strategy is designed and implemented to linearize and eliminate the hysteresis by model inversion. The results show that the P-I operator has the capability to model the hysteretic nonlinearity of MA with an acceptable accuracy. Furthermore, the proposed control scheme has demonstrated to be effective in providing superior trajectory tracking.

  2. Input Forces Estimation for Nonlinear Systems by Applying a Square-Root Cubature Kalman Filter.

    Science.gov (United States)

    Song, Xuegang; Zhang, Yuexin; Liang, Dakai

    2017-10-10

    This work presents a novel inverse algorithm to estimate time-varying input forces in nonlinear beam systems. With the system parameters determined, the input forces can be estimated in real-time from dynamic responses, which can be used for structural health monitoring. In the process of input forces estimation, the Runge-Kutta fourth-order algorithm was employed to discretize the state equations; a square-root cubature Kalman filter (SRCKF) was employed to suppress white noise; the residual innovation sequences, a priori state estimate, gain matrix, and innovation covariance generated by SRCKF were employed to estimate the magnitude and location of input forces by using a nonlinear estimator. The nonlinear estimator was based on the least squares method. Numerical simulations of a large deflection beam and an experiment of a linear beam constrained by a nonlinear spring were employed. The results demonstrated accuracy of the nonlinear algorithm.

  3. Input Forces Estimation for Nonlinear Systems by Applying a Square-Root Cubature Kalman Filter

    Directory of Open Access Journals (Sweden)

    Xuegang Song

    2017-10-01

    Full Text Available This work presents a novel inverse algorithm to estimate time-varying input forces in nonlinear beam systems. With the system parameters determined, the input forces can be estimated in real-time from dynamic responses, which can be used for structural health monitoring. In the process of input forces estimation, the Runge-Kutta fourth-order algorithm was employed to discretize the state equations; a square-root cubature Kalman filter (SRCKF was employed to suppress white noise; the residual innovation sequences, a priori state estimate, gain matrix, and innovation covariance generated by SRCKF were employed to estimate the magnitude and location of input forces by using a nonlinear estimator. The nonlinear estimator was based on the least squares method. Numerical simulations of a large deflection beam and an experiment of a linear beam constrained by a nonlinear spring were employed. The results demonstrated accuracy of the nonlinear algorithm.

  4. Documentation and analysis of the Schlumberger interactive 1-D inversion program slumb

    Energy Technology Data Exchange (ETDEWEB)

    Sandberg, S.

    1979-09-01

    This computer program is designed to accept field data from a Schlumberger resistivity array and invert it in terms of a one-dimensional layered geoelectrical model. Because the inverse problem is non-linear, an initial guess model is required. This input model can be obtained by traditional curve matching, or by repeated use of a forward algorithm. This program was written in FORTRAN V and developed on a UNIVAC 1108 computer.

  5. On-line Multiple-model Based Adaptive Control Reconfiguration for a Class of Non-linear Control Systems

    DEFF Research Database (Denmark)

    Yang, Z.; Izadi-Zamanabadi, R.; Blanke, Mogens

    2000-01-01

    of LTI models are employed to approximate the faulty, reconfigured and nominal nonlinear systems respectively with respect to the on-line information of the operating system, and a set of compensating modules are proposed and designed so as to make the local LTI model approximating to the reconfigured...... nonlinear system match the corresponding LTI model approximating to the nominal nonlinear system in some optimal sense. The compensating modules are designed by the Pseudo-Inverse Method based on the local LTI models for the nominal and faulty nonlinear systems. Moreover, these modules should update...... corresponding to the updating of local LTI models, which validations are determined by the model approximation errors and the optimal index of local design. The test on a nonlinear ship propulsion system shows the promising potential of this method for system reconfiguration...

  6. Modeling and Implementing Nonlinear Equations in Solid-State Lasers for Studying their Performance

    Directory of Open Access Journals (Sweden)

    Ali Roudehghat Shotorbani

    2018-05-01

    Full Text Available In this paper, the effect of radius variation of beam light on output efficacy of SFD Yttrium aluminium borate laser doped with Neodymium ion, which is simultaneously a non-linear and active laser crystal, is investigated in a double-pass cavity. This is done with a concave lens that concentrates (Reduction of optical radius within nonlinear material as much optical laser as possible, resulting in increasing the laser efficiency, second harmonic and the population inversion difference. In this study, we first developed five discrete differential equations describing the interactions of 807 nm pump beam, 1060nm laser beam and 530nm second harmonic beam. Output efficiencies of laser and second harmonic beams at pumping power of Pp =20W and beam radius of 5μm have been presented. Meanwhile, in this paper, the first experiment for creating second harmonic in solid state lasers was fully described with a figure and its procedure was investigated and then the equations (second harmonic and laser and population inversion were studied. Radius variation of beam light aims at increasing laser output efficacy and improving second harmonic and population inversion. The analytic methods which have been solved the discrete differential equations via Matlab.

  7. Nonlinear Fourier transform for dual-polarization optical communication system

    OpenAIRE

    Gaiarin, Simone

    2018-01-01

    New services and applications are causing an exponential increase in the internet traffic. In a few years, the current fiber-optic communication system infrastructure will not be able to meet this demand because fiber nonlinearity dramatically limits the information transmission rate. Eigenvalue communication is considered an emerging paradigm in fiber-optic communications that could potentially overcome these limitations. It relies on a mathematical technique called “inverse scattering trans...

  8. A Decoupling Control Method for Shunt Hybrid Active Power Filter Based on Generalized Inverse System

    Directory of Open Access Journals (Sweden)

    Xin Li

    2017-01-01

    Full Text Available In this paper, a novel decoupling control method based on generalized inverse system is presented to solve the problem of SHAPF (Shunt Hybrid Active Power Filter possessing the characteristics of 2-input-2-output nonlinearity and strong coupling. Based on the analysis of operation principle, the mathematical model of SHAPF is firstly built, which is verified to be invertible using interactor algorithm; then the generalized inverse system of SHAPF is obtained to connect in series with the original system so that the composite system is decoupled under the generalized inverse system theory. The PI additional controller is finally designed to control the decoupled 1-order pseudolinear system to make it possible to adjust the performance of the subsystem. The simulation results demonstrated by MATLAB show that the presented generalized inverse system strategy can realise the dynamic decoupling of SHAPF. And the control system has fine dynamic and static performance.

  9. Origin of unipolar half-cycle pulses generation in inversion symmetric media

    International Nuclear Information System (INIS)

    Song, Xiaohong; Hao, Zhizhen; Yan, Ming; Wu, Miaoli; Yang, Weifeng

    2015-01-01

    We investigate the physical mechanism of unipolar half-cycle pulses generation in resonant two-level media with inversion symmetry. The unipolar half-cycle pulse contains substantial nonzero dc or zero-frequency component in its Fourier spectrum of the electric field. Here the origin of zero-frequency component generation in inversion symmetric media driven by symmetric electric field is identified. We show that in the regime of extreme nonlinear optics, i.e. the Rabi frequency is comparable to or even larger than the carrier frequency of the laser pulse, the time evolution of the polarization can display obvious up-down asymmetric structure under certain conditions, which manifests in the zero-frequency component generation, and is responsible for the formation of unipolar half-cycle pulses in the course of pulse propagation. (letter)

  10. Mapping aboveground woody biomass using forest inventory, remote sensing and geostatistical techniques.

    Science.gov (United States)

    Yadav, Bechu K V; Nandy, S

    2015-05-01

    Mapping forest biomass is fundamental for estimating CO₂ emissions, and planning and monitoring of forests and ecosystem productivity. The present study attempted to map aboveground woody biomass (AGWB) integrating forest inventory, remote sensing and geostatistical techniques, viz., direct radiometric relationships (DRR), k-nearest neighbours (k-NN) and cokriging (CoK) and to evaluate their accuracy. A part of the Timli Forest Range of Kalsi Soil and Water Conservation Division, Uttarakhand, India was selected for the present study. Stratified random sampling was used to collect biophysical data from 36 sample plots of 0.1 ha (31.62 m × 31.62 m) size. Species-specific volumetric equations were used for calculating volume and multiplied by specific gravity to get biomass. Three forest-type density classes, viz. 10-40, 40-70 and >70% of Shorea robusta forest and four non-forest classes were delineated using on-screen visual interpretation of IRS P6 LISS-III data of December 2012. The volume in different strata of forest-type density ranged from 189.84 to 484.36 m(3) ha(-1). The total growing stock of the forest was found to be 2,024,652.88 m(3). The AGWB ranged from 143 to 421 Mgha(-1). Spectral bands and vegetation indices were used as independent variables and biomass as dependent variable for DRR, k-NN and CoK. After validation and comparison, k-NN method of Mahalanobis distance (root mean square error (RMSE) = 42.25 Mgha(-1)) was found to be the best method followed by fuzzy distance and Euclidean distance with RMSE of 44.23 and 45.13 Mgha(-1) respectively. DRR was found to be the least accurate method with RMSE of 67.17 Mgha(-1). The study highlighted the potential of integrating of forest inventory, remote sensing and geostatistical techniques for forest biomass mapping.

  11. Image Reconstruction Based on Homotopy Perturbation Inversion Method for Electrical Impedance Tomography

    Directory of Open Access Journals (Sweden)

    Jing Wang

    2013-01-01

    Full Text Available The image reconstruction for electrical impedance tomography (EIT mathematically is a typed nonlinear ill-posed inverse problem. In this paper, a novel iteration regularization scheme based on the homotopy perturbation technique, namely, homotopy perturbation inversion method, is applied to investigate the EIT image reconstruction problem. To verify the feasibility and effectiveness, simulations of image reconstruction have been performed in terms of considering different locations, sizes, and numbers of the inclusions, as well as robustness to data noise. Numerical results indicate that this method can overcome the numerical instability and is robust to data noise in the EIT image reconstruction. Moreover, compared with the classical Landweber iteration method, our approach improves the convergence rate. The results are promising.

  12. On the solutions of the dKP equation: the nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking

    International Nuclear Information System (INIS)

    Manakov, S V; Santini, P M

    2008-01-01

    We have recently solved the inverse scattering problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev-Petviashvili (dKP) equation. We showed, in particular, that the associated inverse problems can be expressed in terms of nonlinear Riemann-Hilbert problems on the real axis. In this paper, we make use of the nonlinear Riemann-Hilbert problem of dKP (i) to construct the longtime behaviour of the solutions of its Cauchy problem; (ii) to characterize a class of implicit solutions; (iii) to elucidate the spectral mechanism causing the gradient catastrophe of localized solutions of dKP, at finite time as well as in the longtime regime, and the corresponding universal behaviours near breaking

  13. On the solutions of the dKP equation: the nonlinear Riemann Hilbert problem, longtime behaviour, implicit solutions and wave breaking

    Energy Technology Data Exchange (ETDEWEB)

    Manakov, S V [Landau Institute for Theoretical Physics, Moscow (Russian Federation); Santini, P M [Dipartimento di Fisica, Universita di Roma ' La Sapienza' , and Istituto Nazionale di Fisica Nucleare, Sezione di Roma 1, Piazz.le Aldo Moro 2, I-00185 Rome (Italy)

    2008-02-08

    We have recently solved the inverse scattering problem for one-parameter families of vector fields, and used this result to construct the formal solution of the Cauchy problem for a class of integrable nonlinear partial differential equations in multidimensions, including the second heavenly equation of Plebanski and the dispersionless Kadomtsev-Petviashvili (dKP) equation. We showed, in particular, that the associated inverse problems can be expressed in terms of nonlinear Riemann-Hilbert problems on the real axis. In this paper, we make use of the nonlinear Riemann-Hilbert problem of dKP (i) to construct the longtime behaviour of the solutions of its Cauchy problem; (ii) to characterize a class of implicit solutions; (iii) to elucidate the spectral mechanism causing the gradient catastrophe of localized solutions of dKP, at finite time as well as in the longtime regime, and the corresponding universal behaviours near breaking.

  14. Lamé Parameter Estimation from Static Displacement Field Measurements in the Framework of Nonlinear Inverse Problems

    DEFF Research Database (Denmark)

    Hubmer, Simon; Sherina, Ekaterina; Neubauer, Andreas

    2018-01-01

    . The main result of this paper is the verification of a nonlinearity condition in an infinite dimensional Hilbert space context. This condition guarantees convergence of iterative regularization methods. Furthermore, numerical examples for recovery of the Lam´e parameters from displacement data simulating......We consider a problem of quantitative static elastography, the estimation of the Lam´e parameters from internal displacement field data. This problem is formulated as a nonlinear operator equation. To solve this equation, we investigate the Landweber iteration both analytically and numerically...... a static elastography experiment are presented....

  15. An efficient algorithm for some highly nonlinear fractional PDEs in mathematical physics.

    Directory of Open Access Journals (Sweden)

    Jamshad Ahmad

    Full Text Available In this paper, a fractional complex transform (FCT is used to convert the given fractional partial differential equations (FPDEs into corresponding partial differential equations (PDEs and subsequently Reduced Differential Transform Method (RDTM is applied on the transformed system of linear and nonlinear time-fractional PDEs. The results so obtained are re-stated by making use of inverse transformation which yields it in terms of original variables. It is observed that the proposed algorithm is highly efficient and appropriate for fractional PDEs and hence can be extended to other complex problems of diversified nonlinear nature.

  16. Bayesian Uncertainty Quantification for Subsurface Inversion Using a Multiscale Hierarchical Model

    KAUST Repository

    Mondal, Anirban

    2014-07-03

    We consider a Bayesian approach to nonlinear inverse problems in which the unknown quantity is a random field (spatial or temporal). The Bayesian approach contains a natural mechanism for regularization in the form of prior information, can incorporate information from heterogeneous sources and provide a quantitative assessment of uncertainty in the inverse solution. The Bayesian setting casts the inverse solution as a posterior probability distribution over the model parameters. The Karhunen-Loeve expansion is used for dimension reduction of the random field. Furthermore, we use a hierarchical Bayes model to inject multiscale data in the modeling framework. In this Bayesian framework, we show that this inverse problem is well-posed by proving that the posterior measure is Lipschitz continuous with respect to the data in total variation norm. Computational challenges in this construction arise from the need for repeated evaluations of the forward model (e.g., in the context of MCMC) and are compounded by high dimensionality of the posterior. We develop two-stage reversible jump MCMC that has the ability to screen the bad proposals in the first inexpensive stage. Numerical results are presented by analyzing simulated as well as real data from hydrocarbon reservoir. This article has supplementary material available online. © 2014 American Statistical Association and the American Society for Quality.

  17. Geostatistical modelling of the spatial life history of post-larval deepwater hake Merluccius paradoxus in the Benguela Current Large Marine Ecosystem

    DEFF Research Database (Denmark)

    Jansen, T; Kristensen, K; Fairweather, T. P.

    2017-01-01

    paradoxus are not reflected in the current assessment and management practices for the Benguela Current Large Marine Ecosystem. In this study, we compiled data from multiple demersal trawl surveys from the entire distribution area and applied state-of the-art geostatistical population modelling (Geo...

  18. FOREWORD: Tackling inverse problems in a Banach space environment: from theory to applications Tackling inverse problems in a Banach space environment: from theory to applications

    Science.gov (United States)

    Schuster, Thomas; Hofmann, Bernd; Kaltenbacher, Barbara

    2012-10-01

    Inverse problems can usually be modelled as operator equations in infinite-dimensional spaces with a forward operator acting between Hilbert or Banach spaces—a formulation which quite often also serves as the basis for defining and analyzing solution methods. The additional amount of structure and geometric interpretability provided by the concept of an inner product has rendered these methods amenable to a convergence analysis, a fact which has led to a rigorous and comprehensive study of regularization methods in Hilbert spaces over the last three decades. However, for numerous problems such as x-ray diffractometry, certain inverse scattering problems and a number of parameter identification problems in PDEs, the reasons for using a Hilbert space setting seem to be based on conventions rather than an appropriate and realistic model choice, so often a Banach space setting would be closer to reality. Furthermore, non-Hilbertian regularization and data fidelity terms incorporating a priori information on solution and noise, such as general Lp-norms, TV-type norms, or the Kullback-Leibler divergence, have recently become very popular. These facts have motivated intensive investigations on regularization methods in Banach spaces, a topic which has emerged as a highly active research field within the area of inverse problems. Meanwhile some of the most well-known regularization approaches, such as Tikhonov-type methods requiring the solution of extremal problems, and iterative ones like the Landweber method, the Gauss-Newton method, as well as the approximate inverse method, have been investigated for linear and nonlinear operator equations in Banach spaces. Convergence with rates has been proven and conditions on the solution smoothness and on the structure of nonlinearity have been formulated. Still, beyond the existing results a large number of challenging open questions have arisen, due to the more involved handling of general Banach spaces and the larger variety

  19. Solution of 3D inverse scattering problems by combined inverse equivalent current and finite element methods

    International Nuclear Information System (INIS)

    Kılıç, Emre; Eibert, Thomas F.

    2015-01-01

    An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained

  20. Solution of 3D inverse scattering problems by combined inverse equivalent current and finite element methods

    Energy Technology Data Exchange (ETDEWEB)

    Kılıç, Emre, E-mail: emre.kilic@tum.de; Eibert, Thomas F.

    2015-05-01

    An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.

  1. Nonlinear mode conversion with chaotic soliton generation at plasma resonance

    International Nuclear Information System (INIS)

    Pietsch, H.; Laedke, E.W.; Spatschek, K.H.

    1993-01-01

    The resonant absorption of electromagnetic waves near the critical density in inhomogeneous plasmas is studied. A driven nonlinear Schroedinger equation for the mode-converted oscillations is derived by multiple-scaling techniques. The model is simulated numerically. The generic transition from a stationary to a time-dependent solution is investigated. Depending on the parameters, a time-chaotic behavior is found. By a nonlinear analysis, based on the inverse scattering transform, solitons of a corresponding integrable equation are identified as the dominant coherent structures of the chaotic dynamics. Finally, a map is presented which predicts chaotic soliton generation and emission at the critical density. Its qualitative behavior, concerning the bifurcation points, is in excellent agreement with the numerical simulations

  2. Electron acceleration during the decay of nonlinear Whistler waves in low-beta electron-ion plasma

    International Nuclear Information System (INIS)

    Umeda, Takayuki; Saito, Shinji; Nariyuki, Yasuhiro

    2014-01-01

    Relativistic electron acceleration through dissipation of a nonlinear, short-wavelength, and monochromatic electromagnetic whistler wave in low-beta plasma is investigated by utilizing a one-dimensional fully relativistic electromagnetic particle-in-cell code. The nonlinear (large-amplitude) parent whistler wave decays through the parametric instability which enhances electrostatic ion acoustic waves and electromagnetic whistler waves. These waves satisfy the condition of three-wave coupling. Through the decay instability, the energy of electron bulk velocity supporting the parent wave is converted to the thermal energy perpendicular to the background magnetic field. Increase of the perpendicular temperature triggers the electron temperature anisotropy instability which generates broadband whistler waves and heats electrons in the parallel direction. The broadband whistler waves are inverse-cascaded during the relaxation of the electron temperature anisotropy. In lower-beta conditions, electrons with a pitch angle of about 90° are successively accelerated by inverse-cascaded whistler waves, and selected electrons are accelerated to over a Lorentz factor of 10. The result implies that the nonlinear dissipation of a finite-amplitude and short-wavelength whistler wave plays an important role in producing relativistic nonthermal electrons over a few MeV especially at lower beta plasmas.

  3. Thickness-dependent nonlinear optical properties of CsPbBr3 perovskite nanosheets.

    Science.gov (United States)

    Zhang, Jun; Jiang, Tian; Zheng, Xin; Shen, Chao; Cheng, Xiang'ai

    2017-09-01

    Halide perovskite has attracted significant attention because of excellent optical properties. Here, we study the optical properties of CsPbBr 3 perovskite nanosheets and observe that the nonlinear optical properties can be tuned by the thickness. The photoluminescence (PL) properties and nonlinear absorption effects induced by saturation absorption (SA) and two-photon absorption (TPA) in CsPbBr 3 nanosheets with different thicknesses (from 104.6 to 195.4 nm) have been studied. The PL intensity increases nearly three times with changing from the thinnest one to the thinnest under the same excitation condition. Moreover, the same phenomenon takes place no matter when SA or TPA effects happen. The PL lifetime (τ) varies inversely with the thickness. When SA happens, τ decreases from 11.54 to 9.43 ns while when TPA happens new decay channels emerge with the increase of the thickness. Besides, both saturation intensity (I sat ) and the modulation depth are proportional to the thickness (I sat rises from 3.12 to 4.79  GW/cm 2 , the modulation depth increases from 18.6% to 32.3%), while the TPA coefficient (β) is inversely proportional with the thickness (decreases from 10.94 to 4.73  cm/GW). In addition, quantum yields and thicknesses are in the direct ratio. This Letter advocates great promise for nonlinear optical property related photonics devices.

  4. Inverse photoemission

    International Nuclear Information System (INIS)

    Namatame, Hirofumi; Taniguchi, Masaki

    1994-01-01

    Photoelectron spectroscopy is regarded as the most powerful means since it can measure almost perfectly the occupied electron state. On the other hand, inverse photoelectron spectroscopy is the technique for measuring unoccupied electron state by using the inverse process of photoelectron spectroscopy, and in principle, the similar experiment to photoelectron spectroscopy becomes feasible. The development of the experimental technology for inverse photoelectron spectroscopy has been carried out energetically by many research groups so far. At present, the heightening of resolution of inverse photoelectron spectroscopy, the development of inverse photoelectron spectroscope in which light energy is variable and so on are carried out. But the inverse photoelectron spectroscope for vacuum ultraviolet region is not on the market. In this report, the principle of inverse photoelectron spectroscopy and the present state of the spectroscope are described, and the direction of the development hereafter is groped. As the experimental equipment, electron guns, light detectors and so on are explained. As the examples of the experiment, the inverse photoelectron spectroscopy of semimagnetic semiconductors and resonance inverse photoelectron spectroscopy are reported. (K.I.)

  5. Fully probabilistic seismic source inversion – Part 1: Efficient parameterisation

    Directory of Open Access Journals (Sweden)

    S. C. Stähler

    2014-11-01

    Full Text Available Seismic source inversion is a non-linear problem in seismology where not just the earthquake parameters themselves but also estimates of their uncertainties are of great practical importance. Probabilistic source inversion (Bayesian inference is very adapted to this challenge, provided that the parameter space can be chosen small enough to make Bayesian sampling computationally feasible. We propose a framework for PRobabilistic Inference of Seismic source Mechanisms (PRISM that parameterises and samples earthquake depth, moment tensor, and source time function efficiently by using information from previous non-Bayesian inversions. The source time function is expressed as a weighted sum of a small number of empirical orthogonal functions, which were derived from a catalogue of >1000 source time functions (STFs by a principal component analysis. We use a likelihood model based on the cross-correlation misfit between observed and predicted waveforms. The resulting ensemble of solutions provides full uncertainty and covariance information for the source parameters, and permits propagating these source uncertainties into travel time estimates used for seismic tomography. The computational effort is such that routine, global estimation of earthquake mechanisms and source time functions from teleseismic broadband waveforms is feasible.

  6. Nonlinear perturbations of systems of partial differential equations with constant coefficients

    Directory of Open Access Journals (Sweden)

    Carmen J. Vanegas

    2000-01-01

    Full Text Available In this article, we show the existence of solutions to boundary-value problems, consisting of nonlinear systems of partial differential equations with constant coefficients. For this purpose, we use the right inverse of an associated operator and a fix point argument. As illustrations, we apply this method to Helmholtz equations and to second order systems of elliptic equations.

  7. An Inverse Neural Controller Based on the Applicability Domain of RBF Network Models

    Directory of Open Access Journals (Sweden)

    Alex Alexandridis

    2018-01-01

    Full Text Available This paper presents a novel methodology of generic nature for controlling nonlinear systems, using inverse radial basis function neural network models, which may combine diverse data originating from various sources. The algorithm starts by applying the particle swarm optimization-based non-symmetric variant of the fuzzy means (PSO-NSFM algorithm so that an approximation of the inverse system dynamics is obtained. PSO-NSFM offers models of high accuracy combined with small network structures. Next, the applicability domain concept is suitably tailored and embedded into the proposed control structure in order to ensure that extrapolation is avoided in the controller predictions. Finally, an error correction term, estimating the error produced by the unmodeled dynamics and/or unmeasured external disturbances, is included to the control scheme to increase robustness. The resulting controller guarantees bounded input-bounded state (BIBS stability for the closed loop system when the open loop system is BIBS stable. The proposed methodology is evaluated on two different control problems, namely, the control of an experimental armature-controlled direct current (DC motor and the stabilization of a highly nonlinear simulated inverted pendulum. For each one of these problems, appropriate case studies are tested, in which a conventional neural controller employing inverse models and a PID controller are also applied. The results reveal the ability of the proposed control scheme to handle and manipulate diverse data through a data fusion approach and illustrate the superiority of the method in terms of faster and less oscillatory responses.

  8. An operational procedure for precipitable and cloud liquid water estimate in non-raining conditions over sea Study on the assessment of the nonlinear physical inversion algorithm

    CERN Document Server

    Nativi, S; Mazzetti, P

    2004-01-01

    In a previous work, an operative procedure to estimate precipitable and liquid water in non-raining conditions over sea was developed and assessed. The procedure is based on a fast non-linear physical inversion scheme and a forward model; it is valid for most of satellite microwave radiometers and it also estimates water effective profiles. This paper presents two improvements of the procedure: first, a refinement to provide modularity of the software components and portability across different computation system architectures; second, the adoption of the CERN MINUIT minimisation package, which addresses the problem of global minimisation but is computationally more demanding. Together with the increased computational performance that allowed to impose stricter requirements on the quality of fit, these refinements improved fitting precision and reliability, and allowed to relax the requirements on the initial guesses for the model parameters. The re-analysis of the same data-set considered in the previous pap...

  9. Source Estimation by Full Wave Form Inversion

    Energy Technology Data Exchange (ETDEWEB)

    Sjögreen, Björn [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing; Petersson, N. Anders [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing

    2013-08-07

    Given time-dependent ground motion recordings at a number of receiver stations, we solve the inverse problem for estimating the parameters of the seismic source. The source is modeled as a point moment tensor source, characterized by its location, moment tensor components, the start time, and frequency parameter (rise time) of its source time function. In total, there are 11 unknown parameters. We use a non-linear conjugate gradient algorithm to minimize the full waveform misfit between observed and computed ground motions at the receiver stations. An important underlying assumption of the minimization problem is that the wave propagation is accurately described by the elastic wave equation in a heterogeneous isotropic material. We use a fourth order accurate finite difference method, developed in [12], to evolve the waves forwards in time. The adjoint wave equation corresponding to the discretized elastic wave equation is used to compute the gradient of the misfit, which is needed by the non-linear conjugated minimization algorithm. A new source point moment source discretization is derived that guarantees that the Hessian of the misfit is a continuous function of the source location. An efficient approach for calculating the Hessian is also presented. We show how the Hessian can be used to scale the problem to improve the convergence of the non-linear conjugated gradient algorithm. Numerical experiments are presented for estimating the source parameters from synthetic data in a layer over half-space problem (LOH.1), illustrating rapid convergence of the proposed approach.

  10. 2D acoustic-elastic coupled waveform inversion in the Laplace domain

    KAUST Repository

    Bae, Hoseuk

    2010-04-01

    Although waveform inversion has been intensively studied in an effort to properly delineate the Earth\\'s structures since the early 1980s, most of the time- and frequency-domain waveform inversion algorithms still have critical limitations in their applications to field data. This may be attributed to the highly non-linear objective function and the unreliable low-frequency components. To overcome the weaknesses of conventional waveform inversion algorithms, the acoustic Laplace-domain waveform inversion has been proposed. The Laplace-domain waveform inversion has been known to provide a long-wavelength velocity model even for field data, which may be because it employs the zero-frequency component of the damped wavefield and a well-behaved logarithmic objective function. However, its applications have been confined to 2D acoustic media.We extend the Laplace-domain waveform inversion algorithm to a 2D acoustic-elastic coupled medium, which is encountered in marine exploration environments. In 2D acoustic-elastic coupled media, the Laplace-domain pressures behave differently from those of 2D acoustic media, although the overall features are similar to each other. The main differences are that the pressure wavefields for acoustic-elastic coupled media show negative values even for simple geological structures unlike in acoustic media, when the Laplace damping constant is small and the water depth is shallow. The negative values may result from more complicated wave propagation in elastic media and at fluid-solid interfaces.Our Laplace-domain waveform inversion algorithm is also based on the finite-element method and logarithmic wavefields. To compute gradient direction, we apply the back-propagation technique. Under the assumption that density is fixed, P- and S-wave velocity models are inverted from the pressure data. We applied our inversion algorithm to the SEG/EAGE salt model and the numerical results showed that the Laplace-domain waveform inversion

  11. Comparing the applicability of some geostatistical methods to predict the spatial distribution of topsoil Calcium Carbonate in part of farmland of Zanjan Province

    Science.gov (United States)

    Sarmadian, Fereydoon; Keshavarzi, Ali

    2010-05-01

    Most of soils in iran, were located in the arid and semi-arid regions and have high pH (more than 7) and high amount of calcium carbonate and this problem cause to their calcification.In calcareous soils, plant growing and production is difficult. Most part of this problem, in relation to high pH and high concentration of calcium ion that cause to fixation and unavailability of elements which were dependent to pH, especially Phosphorous and some micro nutrients such as Fe, Zn, Mn and Cu. Prediction of soil calcium carbonate in non-sampled areas and mapping the calcium carbonate variability in order to sustainable management of soil fertility is very important.So, this research was done with the aim of evaluation and analyzing spatial variability of topsoil calcium carbonate as an aspect of soil fertility and plant nutrition, comparing geostatistical methods such as kriging and co-kriging and mapping topsoil calcium carbonate. For geostatistical analyzing, sampling was done with stratified random method and soil samples from 0 to 15 cm depth were collected with auger within 23 locations.In co-kriging method, salinity data was used as auxiliary variable. For comparing and evaluation of geostatistical methods, cross validation were used by statistical parameters of RMSE. The results showed that co-kriging method has the highest correlation coefficient and less RMSE and has the higher accuracy than kriging method to prediction of calcium carbonate content in non-sampled areas.

  12. Relative Nonlinear Electrodynamics Interaction of Charged Particles with Strong and Super Strong Laser Fields

    CERN Document Server

    Avetissian, Hamlet

    2006-01-01

    This book covers a large class of fundamental investigations into Relativistic Nonlinear Electrodynamics. It explores the interaction between charged particles and strong laser fields, mainly concentrating on contemporary problems of x-ray lasers, new type small set-up high-energy accelerators of charged particles, as well as electron-positron pair production from super powerful laser fields of relativistic intensities. It will also discuss nonlinear phenomena of threshold nature that eliminate the concurrent inverse processes in the problems of Laser Accelerator and Free Electron Laser, thus creating new opportunities for solving these problems.

  13. Characterization of groundwater quality using water evaluation indices, multivariate statistics and geostatistics in central Bangladesh

    Directory of Open Access Journals (Sweden)

    Md. Bodrud-Doza

    2016-04-01

    Full Text Available This study investigates the groundwater quality in the Faridpur district of central Bangladesh based on preselected 60 sample points. Water evaluation indices and a number of statistical approaches such as multivariate statistics and geostatistics are applied to characterize water quality, which is a major factor for controlling the groundwater quality in term of drinking purposes. The study reveal that EC, TDS, Ca2+, total As and Fe values of groundwater samples exceeded Bangladesh and international standards. Ground water quality index (GWQI exhibited that about 47% of the samples were belonging to good quality water for drinking purposes. The heavy metal pollution index (HPI, degree of contamination (Cd, heavy metal evaluation index (HEI reveal that most of the samples belong to low level of pollution. However, Cd provide better alternative than other indices. Principle component analysis (PCA suggests that groundwater quality is mainly related to geogenic (rock–water interaction and anthropogenic source (agrogenic and domestic sewage in the study area. Subsequently, the findings of cluster analysis (CA and correlation matrix (CM are also consistent with the PCA results. The spatial distributions of groundwater quality parameters are determined by geostatistical modeling. The exponential semivariagram model is validated as the best fitted models for most of the indices values. It is expected that outcomes of the study will provide insights for decision makers taking proper measures for groundwater quality management in central Bangladesh.

  14. Study of the permeability up-scaling by direct filtering of geostatistical model; Etude du changement d'echelle des permeabilites par filtrage direct du modele geostatistique

    Energy Technology Data Exchange (ETDEWEB)

    Zargar, G

    2005-10-15

    In this thesis, we present a new approach, which consists in directly up-scaling the geostatistical permeability distribution rather than the individual realizations. Practically, filtering techniques based on. the FFT (Fast Fourier Transform), allows us to generate geostatistical images, which sample the up-scaled distributions. In the log normal case, an equivalence hydraulic criterion is proposed, allowing to re-estimate the geometric mean of the permeabilities. In the anisotropic case, the effective geometric mean becomes a tensor which depends on the level of filtering used and it can be calculated by a method of renormalisation. Then, the method was generalized for the categorial model. Numerical tests of the method were set up for isotropic, anisotropic and categorial models, which shows good agreement with theory. (author)

  15. Estimating the burden of malaria in Senegal: Bayesian zero-inflated binomial geostatistical modeling of the MIS 2008 data.

    Directory of Open Access Journals (Sweden)

    Federica Giardina

    Full Text Available The Research Center for Human Development in Dakar (CRDH with the technical assistance of ICF Macro and the National Malaria Control Programme (NMCP conducted in 2008/2009 the Senegal Malaria Indicator Survey (SMIS, the first nationally representative household survey collecting parasitological data and malaria-related indicators. In this paper, we present spatially explicit parasitaemia risk estimates and number of infected children below 5 years. Geostatistical Zero-Inflated Binomial models (ZIB were developed to take into account the large number of zero-prevalence survey locations (70% in the data. Bayesian variable selection methods were incorporated within a geostatistical framework in order to choose the best set of environmental and climatic covariates associated with the parasitaemia risk. Model validation confirmed that the ZIB model had a better predictive ability than the standard Binomial analogue. Markov chain Monte Carlo (MCMC methods were used for inference. Several insecticide treated nets (ITN coverage indicators were calculated to assess the effectiveness of interventions. After adjusting for climatic and socio-economic factors, the presence of at least one ITN per every two household members and living in urban areas reduced the odds of parasitaemia by 86% and 81% respectively. Posterior estimates of the ORs related to the wealth index show a decreasing trend with the quintiles. Infection odds appear to be increasing with age. The population-adjusted prevalence ranges from 0.12% in Thillé-Boubacar to 13.1% in Dabo. Tambacounda has the highest population-adjusted predicted prevalence (8.08% whereas the region with the highest estimated number of infected children under the age of 5 years is Kolda (13940. The contemporary map and estimates of malaria burden identify the priority areas for future control interventions and provide baseline information for monitoring and evaluation. Zero-Inflated formulations are more appropriate

  16. Survey and Zoning of Soil Physical and Chemical Properties Using Geostatistical Methods in GIS (Case Study: Miankangi Region in Sistan

    Directory of Open Access Journals (Sweden)

    M. Hashemi

    2017-02-01

    Full Text Available Introduction: In order to provide a database, it is essential having access to accurate information on soil spatial variation for soil sustainable management such as proper application of fertilizers. Spatial variations in soil properties are common but it is important for understanding these changes, particularly in agricultural lands for careful planning and land management. Materials and Methods: To this end, in winter 1391, 189 undisturbed soil samples (0-30 cm depth in a regular lattice with a spacing of 500 m were gathered from the surface of Miankangi land, Sistan plain, and their physical and chemical properties were studied. The land area of the region is about 4,500 hectares; the average elevation of studied area is 489.2 meters above sea level with different land uses. Soil texture was measured by the hydrometer methods (11, Also EC and pH (39, calcium carbonate equivalent (37 and the saturation percentage of soils were determined. Kriging, Co-Kriging, Inverse Distance Weighting and Local Polynomial Interpolation techniques were evaluated to produce a soil characteristics map of the study area zoning and to select the best geostatistical methods. Cross-validation techniques and Root Mean Square Error (RMSE were used. Results and Discussion: Normalized test results showed that all of the soil properties except calcium carbonate and soil clay content had normal distribution. In addition, the results of correlation test showed that the soil saturation percentage was positively correlated with silt content (r=0.43 and p

  17. Modal model for the nonlinear multimode Rayleigh endash Taylor instability

    International Nuclear Information System (INIS)

    Ofer, D.; Alon, U.; Shvarts, D.; McCrory, R.L.; Verdon, C.P.

    1996-01-01

    A modal model for the Rayleigh endash Taylor (RT) instability, applicable at all stages of the flow, is introduced. The model includes a description of nonlinear low-order mode coupling, mode growth saturation, and post-saturation mode coupling. It is shown to significantly extend the range of applicability of a previous model proposed by Haan, to cases where nonlinear mode generation is important. Using the new modal model, we study the relative importance of mode coupling at late nonlinear stages and resolve the difference between cases in which mode generation assumes a dominant role, leading to the late time inverse cascade of modes and loss of memory of initial conditions, and cases where mode generation is not important and memory of initial conditions is retained. Effects of finite density ratios (Atwood number A<1) are also included in the model and the difference between various measures of the mixing zone penetration depth for A<1 is discussed. copyright 1996 American Institute of Physics

  18. Bayesian geostatistical modeling of leishmaniasis incidence in Brazil.

    Directory of Open Access Journals (Sweden)

    Dimitrios-Alexios Karagiannis-Voules

    Full Text Available BACKGROUND: Leishmaniasis is endemic in 98 countries with an estimated 350 million people at risk and approximately 2 million cases annually. Brazil is one of the most severely affected countries. METHODOLOGY: We applied Bayesian geostatistical negative binomial models to analyze reported incidence data of cutaneous and visceral leishmaniasis in Brazil covering a 10-year period (2001-2010. Particular emphasis was placed on spatial and temporal patterns. The models were fitted using integrated nested Laplace approximations to perform fast approximate Bayesian inference. Bayesian variable selection was employed to determine the most important climatic, environmental, and socioeconomic predictors of cutaneous and visceral leishmaniasis. PRINCIPAL FINDINGS: For both types of leishmaniasis, precipitation and socioeconomic proxies were identified as important risk factors. The predicted number of cases in 2010 were 30,189 (standard deviation [SD]: 7,676 for cutaneous leishmaniasis and 4,889 (SD: 288 for visceral leishmaniasis. Our risk maps predicted the highest numbers of infected people in the states of Minas Gerais and Pará for visceral and cutaneous leishmaniasis, respectively. CONCLUSIONS/SIGNIFICANCE: Our spatially explicit, high-resolution incidence maps identified priority areas where leishmaniasis control efforts should be targeted with the ultimate goal to reduce disease incidence.

  19. Geologic shapes inversion in field engineering using production data; Inversion de formes geologiques en ingenierie de gisements en utilisant les donnees de production

    Energy Technology Data Exchange (ETDEWEB)

    Edoa, P.F.

    1999-03-09

    The work of this thesis is to study and to solve a shape inversion problem in petroleum reservoir engineering. We developed history matching methods of production data such as well measurements in order to better identify the geometry of geological bodies in a reservoir. Fluid flows are single phase or multiphase. The numerical simulation of these flows is based on a finite volume method on structured meshes. In this context, classical shape optimisation techniques based on mesh perturbations can not be applicable. In fact, each time the surface describing the region to optimize crosses a new grid mesh, the discrete problem gets non differentiable. In order to overcome the difficulty, some authors propose very expensive optimisation methods that only need evaluations of the criterion to be minimized. In this thesis, we propose an approach that consists in working on the continuous problem that is differentiable. In our problem, we generally work a great number of parameters. For this reason, the adjoint state method has been used to calculate the derivative of the cost function with respect to the geometry. Then, it allowed us to calculate rapidly the gradients by discretization of the derivative obtained and to elaborate inversion. processes based on classical algorithms of optimisation. During this thesis, we also pointed out the possibility to modify the topology of the domain using the idea of topological gradient. The development of this topological optimisation method was made possible thanks to the efficiency of the adjoint state method. The adaptation cost of the results was small, especially for the calculation of the sensitivities with respect to the position of small size obstacles. The proposed applications concern the identification of the thickness and the width of channels of the position and the size of faults, of top surface and reservoir limits. An example of application of topological optimisation was performed with geostatistical models

  20. Law of nonlinear flow in saturated clays and radial consolidation

    Institute of Scientific and Technical Information of China (English)

    2007-01-01

    It was derived that micro-scale amount level of average pore radius of clay changed from 0.01 to 0.1 micron by an equivalent concept of flow in porous media. There is good agreement between the derived results and test ones. Results of experiments show that flow in micro-scale pore of saturated clays follows law of nonlinear flow. Theoretical analyses demonstrate that an interaction of solid-liquid interfaces varies inversely with permeability or porous radius. The interaction is an important reason why nonlinear flow in saturated clays occurs. An exact mathematical model was presented for nonlinear flow in micro-scale pore of saturated clays. Dimension and physical meanings of parameters of it are definite. A new law of nonlinear flow in saturated clays was established. It can describe characteristics of flow curve of the whole process of the nonlinear flow from low hydraulic gradient to high one. Darcy law is a special case of the new law. A mathematical model was presented for consolidation of nonlinear flow in radius direction in saturated clays with constant rate based on the new law of nonlinear flow. Equations of average mass conservation and moving boundary, and formula of excess pore pressure distribution and average degree of consolidation for nonlinear flow in saturated clay were derived by using an idea of viscous boundary layer, a method of steady state in stead of transient state and a method of integral of an equation. Laws of excess pore pressure distribution and changes of average degree of consolidation with time were obtained. Results show that velocity of moving boundary decreases because of the nonlinear flow in saturated clay. The results can provide geology engineering and geotechnical engineering of saturated clay with new scientific bases. Calculations of average degree of consolidation of the Darcy flow are a special case of that of the nonlinear flow.