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......) 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...
Simultaneous inversion of petrophysical parameters based on geostatistical a priori information
Institute of Scientific and Technical Information of China (English)
Yin Xing-Yao; Sun Rui-Ying; Wang Bao-Li; Zhang Guang-Zhi
2014-01-01
The high-resolution nonlinear simultaneous inversion of petrophysical parameters is based on Bayesian statistics and combines petrophysics with geostatistical a priori information. We used the fast Fourier transform-moving average (FFT-MA) and gradual deformation method (GDM) to obtain a reasonable variogram by using structural analysis and geostatistical a priori information of petrophysical parameters. Subsequently, we constructed the likelihood function according to the statistical petrophysical model. Finally, we used the Metropolis algorithm to sample the posteriori probability density and complete the inversion of the petrophysical parameters. We used the proposed method to process data from an oil fi eld in China and found good match between inversion and real data with high-resolution. In addition, the direct inversion of petrophysical parameters avoids the error accumulation and decreases the uncertainty, and increases the computational effi ciency.
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...
Reducing complexity of inverse problems using geostatistical priors
DEFF Research Database (Denmark)
Hansen, Thomas Mejer; Mosegaard, Klaus; Cordua, Knud Skou
a posterior sample, can be reduced significantly using informed priors based on geostatistical models. We discuss two approaches to include such geostatistically based prior information. One is based on a parametric description of the prior likelihood that applies to 2-point based statistical models...
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...... into account during the inversion. The suggested inversion strategy is tested on synthetic tomographic crosshole ground-penetrating radar full-waveform data using multiple-point-based a priori information. This is, to our knowledge, the first example of obtaining a posteriori realizations of a full......-waveform inverse problem. Benefits of the proposed methodology compared with deterministic inversion approaches include: (1) The a posteriori model variability reflects the states of information provided by the data uncertainties and a priori information, which provides a means of obtaining resolution analysis. (2...
Illman, Walter A.; Berg, Steven J.; Zhao, Zhanfeng
2015-05-01
The robust performance of hydraulic tomography (HT) based on geostatistics has been demonstrated through numerous synthetic, laboratory, and field studies. While geostatistical inverse methods offer many advantages, one key disadvantage is its highly parameterized nature, which renders it computationally intensive for large-scale problems. Another issue is that geostatistics-based HT may produce overly smooth images of subsurface heterogeneity when there are few monitoring interval data. Therefore, some may question the utility of the geostatistical inversion approach in certain situations and seek alternative approaches. To investigate these issues, we simultaneously calibrated different groundwater models with varying subsurface conceptualizations and parameter resolutions using a laboratory sandbox aquifer. The compared models included: (1) isotropic and anisotropic effective parameter models; (2) a heterogeneous model that faithfully represents the geological features; and (3) a heterogeneous model based on geostatistical inverse modeling. The performance of these models was assessed by quantitatively examining the results from model calibration and validation. Calibration data consisted of steady state drawdown data from eight pumping tests and validation data consisted of data from 16 separate pumping tests not used in the calibration effort. Results revealed that the geostatistical inversion approach performed the best among the approaches compared, although the geological model that faithfully represented stratigraphy came a close second. In addition, when the number of pumping tests available for inverse modeling was small, the geological modeling approach yielded more robust validation results. This suggests that better knowledge of stratigraphy obtained via geophysics or other means may contribute to improved results for HT.
Efficient Geostatistical Inversion under Transient Flow Conditions in Heterogeneous Porous Media
Klein, Ole; Cirpka, Olaf A.; Bastian, Peter; Ippisch, Olaf
2014-05-01
The assessment of hydraulic aquifer parameters is important for the evaluation of anthropogenic impacts on groundwater resources. The distribution of these parameters determines flow paths and solute travel times and is therefore critical for the successful design and deployment of remediation schemes at contaminated sites. Direct measurement of these properties is not possible, making indirect observations through dependent quantities and parameter estimation a necessity. The geostatistical approach characterizes these hydraulic parameters without predetermined zonation. The parameter fields are treated as stochastic processes, optionally incorporating a priori information in the probability distribution. Maximizing the likelihood of the parameters with regard to the given observations yields a parameter estimate with high spatial resolution. This approach naturally leads to nonlinear least squares optimization problems, namely objective functions of the form L(Y ) = 1(Y ')TQ -Y1YY ' + 1[F(Y) - z]T Q-z1z [F(Y )- z], 2 2 where Y are the parameters, Y ' their deviations from the a priori estimate, QY Y their covariance matrix, z the measurements, Qzz their covariance matrix and F the forward model mapping parameters to observations. In theory, this objective function may be minimized using standard gradient-based techniques like Gauss-Newton. Due to the typically high number of parameters, however, this is not practical. Let nY be the number of parameters and nz the number of observations. Then QY Y and its inverse are both dense nY ×nY matrices, and the sensitivity matrix Hz := δz/δY is a nz ×nY matrix that has to be assembled using forward or adjoint model runs. Specialized schemes have been developed to reduce the dimensionality of the problem and avoid the high cost of handling products with QY Y -1. This enables efficient inversion in the case of a moderate number of observations as encountered in stationary inversion, where the cost of assembling Hz is in
Nonlinear Least Squares for Inverse Problems
Chavent, Guy
2009-01-01
Presents an introduction into the least squares resolution of nonlinear inverse problems. This title intends to develop a geometrical theory to analyze nonlinear least square (NLS) problems with respect to their quadratic wellposedness, that is, both wellposedness and optimizability
High resolution 3D nonlinear integrated inversion
Institute of Scientific and Technical Information of China (English)
Li Yong; Wang Xuben; Li Zhirong; Li Qiong; Li Zhengwen
2009-01-01
The high resolution 3D nonlinear integrated inversion method is based on nonlinear theory. Under layer control, the log data from several wells (or all wells) in the study area and seismic trace data adjacent to the wells are input to a network with multiple inputs and outputs and are integratedly trained to obtain an adaptive weight function of the entire study area. Integrated nonlinear mapping relationships are built and updated by the lateral and vertical geologic variations of the reservoirs. Therefore, the inversion process and its inversion results can be constrained and controlled and a stable seismic inversion section with high resolution with velocity inversion, impedance inversion, and density inversion sections, can be gained. Good geologic effects have been obtained in model computation tests and real data processing, which verified that this method has high precision, good practicality, and can be used for quantitative reservoir analysis.
O'Malley, D.; Le, E. B.; Vesselinov, V. V.
2015-12-01
We present a fast, scalable, and highly-implementable stochastic inverse method for characterization of aquifer heterogeneity. The method utilizes recent advances in randomized matrix algebra and exploits the structure of the Quasi-Linear Geostatistical Approach (QLGA), without requiring a structured grid like Fast-Fourier Transform (FFT) methods. The QLGA framework is a more stable version of Gauss-Newton iterates for a large number of unknown model parameters, but provides unbiased estimates. The methods are matrix-free and do not require derivatives or adjoints, and are thus ideal for complex models and black-box implementation. We also incorporate randomized least-square solvers and data-reduction methods, which speed up computation and simulate missing data points. The new inverse methodology is coded in Julia and implemented in the MADS computational framework (http://mads.lanl.gov). Julia is an advanced high-level scientific programing language that allows for efficient memory management and utilization of high-performance computational resources. Inversion results based on series of synthetic problems with steady-state and transient calibration data are presented.
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.
Non-Linear Logging Parameters Inversion
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
The non-linear logging parameters inversion is based on the field theory, information optimization and predication theory. It uses seismic charaoters,geological model and logging data as a restriction to inverse 2D, 3D logging parameters data volume. Using this method,
Nonlinear system compound inverse control method
Institute of Scientific and Technical Information of China (English)
Yan ZHANG; Zengqiang CHEN; Peng YANG; Zhuzhi YUAN
2005-01-01
A compound neural network is utilized to identify the dynamic nonlinear system.This network is composed of two parts: one is a linear neural network,and the other is a recurrent neural network.Based on the inverse theory a compound inverse control method is proposed.The controller has also two parts:a linear controller and a nonlinear neural network controller.The stability condition of the closed-loop neural network-based compound inverse control system is demonstrated based on the Lyapunov theory.Simulation studies have shown that this scheme is simple and has good control accuracy and robustness.
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
The role of nonlinearity in inverse problems
Snieder, Roel
1998-06-01
In many practical inverse problems, one aims to retrieve a model that has infinitely many degrees of freedom from a finite amount of data. It follows from a simple variable count that this cannot be done in a unique way. Therefore, inversion entails more than estimating a model: any inversion is not complete without a description of the class of models that is consistent with the data; this is called the appraisal problem. Nonlinearity makes the appraisal problem particularly difficult. The first reason for this is that nonlinear error propagation is a difficult problem. The second reason is that for some nonlinear problems the model parameters affect the way in which the model is being interrogated by the data. Two examples are given of this, and it is shown how the nonlinearity may make the problem more ill-posed. Finally, three attempts are shown to carry out the model appraisal for nonlinear inverse problems that are based on an analytical approach, a numerical approach and a common sense approach.
Nonlinear approximation with dictionaries,.. II: Inverse estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
In this paper we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for separated decomposable dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal mutually...
Nonlinear approximation with dictionaries. II. Inverse Estimates
DEFF Research Database (Denmark)
Gribonval, Rémi; Nielsen, Morten
2006-01-01
In this paper, which is the sequel to [16], we study inverse estimates of the Bernstein type for nonlinear approximation with structured redundant dictionaries in a Banach space. The main results are for blockwise incoherent dictionaries in Hilbert spaces, which generalize the notion of joint block-diagonal...
Full Waveform Inversion Using Nonlinearly Smoothed Wavefields
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.
地质统计学反演在海安凹陷中的应用%Application of geostatistical inversion technique in Haian depression
Institute of Scientific and Technical Information of China (English)
张勇; 钟薇
2015-01-01
地质统计学反演基于地质统计学方法，对储层的空间分布特征进行模拟，预测储层分布规律。相对于常规约束稀疏脉冲反演，地质统计学反演不再受限于地震资料频带宽度，能有效提高反演结果纵向分辨率，识别厚度较小的储层。以海安凹陷曲塘深凹为例，利用地震、测井资料和地质认识，在稀疏脉冲波阻抗反演基础上开展地质统计学反演，进行砂体展布预测。研究结果与钻井资料吻合度较高，符合地质认识，为认识该区砂体分布提供了依据，为寻找有利区奠定了基础。%Geostatistical inversion based on geostatistical method simulate the spatial distribution characteristics of reservoir and predict the reservoir distribution. Compared with conventional constrained sparse spike inversion, the geostatistical inversion no longer limited to the bandwidth of seismic data can effectively improve the vertical resolution of the inversion results and identify thickness smaller reservoir. Taking Qutang deep pit of Haian depression as an example, and by using seismic, logging data and geo⁃logical understanding, geostatistical inversion based on constrained sparse spike inversion was conduct to predict the sandbody res⁃ervoir distribution. The results highly consistent with the drilling data and geological understanding, provide basis for recognizing the sandbody distribution of this area and lay the foundation of finding advantage areas.
Methodology and applications in non-linear model-based geostatistics
DEFF Research Database (Denmark)
Christensen, Ole Fredslund
Today geostatistics is used in a number of research areas, among others agricultural and environmental sciences.This thesis concerns data and applications where the classical Gaussian spatial model is not appropriate. A transformation could be used in an attempt to obtain data that are approximat......Today geostatistics is used in a number of research areas, among others agricultural and environmental sciences.This thesis concerns data and applications where the classical Gaussian spatial model is not appropriate. A transformation could be used in an attempt to obtain data...
岩石物理参数高分辨率地质统计学反演%High-resolution geostatistical petrophysical-parameter inversion
Institute of Scientific and Technical Information of China (English)
姜文龙; 杨锴
2012-01-01
Geostatistical inversion can well characterize thin-layers for its high-resolution. We discussed the relationship between geostatistical inversion and high-resolution, as well as the problem of geostatistical inversion in petrophysical parameter inversion. Moreover, the algorithm for reducing the uncertainty of inversion was studied. Research results show that along with the alternation of variogram, the resolution of geostatistical inversion result will change, but the conventional Krigging algorithm destroy the continuity of original geologic formations when improving resolution through reducing variogram. Based on the above results, we introduced some restraints such as geologic interpretation strata and dip into geostatistical inversion. The method was applied on the inversion of carbonate mineral components at ODP1144 station sea area in South Sea.%地质统计学反演由于其高分辨率的特点,可以很好地用来描述薄层等信息.就地质统计学反演与高分辨率的关系和地质统计学反演在岩石物理参数反演中存在的问题进行了讨论,并从算法上研究了减小反演不确定性的方法.研究结果表明,随着变差函数变程的改变,地质统计学模拟结果的分辨率也会发生改变,但常规的克里金算法在通过减小变程来提高分辨率的同时,破坏了原有地质层位的连续性.在此基础上提出加入地质解释层位和地层倾角等约束信息的地质统计学反演方法,将该方法应用于南海ODP1144站位海区矿物组分的反演,很好地揭示了该区碳酸盐矿物的沉积特征.
Learning Inverse Rig Mappings by Nonlinear Regression.
Holden, Daniel; Saito, Jun; Komura, Taku
2016-11-11
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.
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.
Analysis of nonlinear channel friction inverse problem
Institute of Scientific and Technical Information of China (English)
CHENG Weiping; LIU Guohua
2007-01-01
Based on the Backus-Gilbert inverse theory, the singular value decomposition (SVD) for general inverse matrices and the optimization algorithm are used to solve the channel friction inverse problem. The resolution and covari- ance friction inverse model in matrix form is developed to examine the reliability of solutions. Theoretical analyses demonstrate that the convergence rate of the general Newton optimization algorithm is in the second-order. The Wiggins method is also incorporated into the algorithm. Using the method, noise can be suppressed effectively, and the results are close to accurate solutions with proper control parameters. Also, the numerical stability can be improved.
Inverse Coefficient Problems for Nonlinear Elliptic Variational Inequalities
Institute of Scientific and Technical Information of China (English)
Run-sheng Yang; Yun-hua Ou
2011-01-01
This paper is devoted to a class of inverse coefficient problems for nonlinear elliptic variational inequalities. The unknown coefficient of elliptic variational inequalities depends on the gradient of the solution and belongs to a set of admissible coefficients. It is shown that the nonlinear elliptic variational inequalities is unique solvable for the given class of coefficients. The existence of quasisolutions of the inverse problems is obtained.
Solving inverse problems through a smooth formulation of multiple-point geostatistics
DEFF Research Database (Denmark)
Melnikova, Yulia
have proposed a smooth formulation of training-image based priors, which was inspired by the Frequency Matching method developed by our group earlier. The proposed smooth generalization, that integrates data and multiple-point statistics in a probabilistic framework, allows us to find solution by use......In oil and gas sector accurate reservoir description play a crucial role in problems associated with recovery of hydrocarbons, risk estimation and predicting reservoir performance. Knowledge on reservoir properties can be inferred from measurements typically made at the surface by solving...... 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...
Discrete-time inverse optimal control for nonlinear systems
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
Minimax theory for a class of nonlinear statistical inverse problems
Ray, Kolyan; Schmidt-Hieber, Johannes
2016-06-01
We study a class of statistical inverse problems with nonlinear pointwise operators motivated by concrete statistical applications. A two-step procedure is proposed, where the first step smoothes the data and inverts the nonlinearity. This reduces the initial nonlinear problem to a linear inverse problem with deterministic noise, which is then solved in a second step. The noise reduction step is based on wavelet thresholding and is shown to be minimax optimal (up to logarithmic factors) in a pointwise function-dependent sense. Our analysis is based on a modified notion of Hölder smoothness scales that are natural in this setting.
Nonlinear inversion flight control for a supermaneuverable aircraft
Snell, S. Antony; Garrard, William L., Jr.; Enns, Dale F.
1990-01-01
This paper describes the use of nonlinear dynamic inversion for the design of a flight control system for a supermaneuverable aircraft. First, the dynamics to be controlled were separated into fast and slow variables. The fast variables were the angular rates and the slow variables were the attitude angles. Then a nonlinear inversion controller was designed for the fast variables. This stabilized the longitudinal short-period and improved the lateral-directional responses over a wide range of angle of attack by making use of a combination for aerodynamic surfaces and thrust vectoring control. Outer loops were then closed to allow the pilot to control the slow dynamics, the angle of attack, side-slip angle and the velocity bank angle. Nonlinear inversion was also used to design of the outer loop control laws. The dynamic inversion control laws were compared with more conventional, gain-scheduled control laws and were shown to yield much better performance.
Nonlinear Damping Identification in Nonlinear Dynamic System Based on Stochastic Inverse Approach
2012-01-01
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...
Nonlinear inversion schemes for fluorescence optical tomography.
Freiberger, Manuel; Egger, Herbert; Scharfetter, Hermann
2010-11-01
Fluorescence optical tomography is a non-invasive imaging modality that employs the absorption and re-emission of light by fluorescent dyes. The aim is to reconstruct the fluorophore distribution in a body from measurements of light intensities at the boundary. Due to the diffusive nature of light propagation in tissue, fluorescence tomography is a nonlinear and severely ill-posed problem, and some sort of regularization is required for a stable solution. In this paper we investigate reconstruction methods based on Tikhonov regularization with nonlinear penalty terms, namely total-variation regularization and a levelset-type method using a nonlinear parameterization of the unknown function. Moreover, we use the full threedimensional nonlinear forward model, which arises from the governing system of partial differential equations. We discuss the numerical realization of the regularization schemes by Newtontype iterations, present some details of the discretization by finite element methods, and outline the efficient implementation of sensitivity systems via adjoint methods. As we will demonstrate in numerical tests, the proposed nonlinear methods provide better reconstructions than standard methods based on linearized forward models and linear penalty terms. We will additionally illustrate, that the careful discretization of the methods derived on the continuous level allows to obtain reliable, mesh independent reconstruction algorithms.
Inverse Problems for Nonlinear Delay Systems
2011-03-15
Ba82]. For nonlinear delay systems such as those discussed here, approximation in the context of a linear semigroup framework as presented [BBu1, BBu2...linear part generates a linear semigroup as in [BBu1, BBu2, BKap]. One then uses the linear semigroup in a vari- ation of parameters implicit...BBu2, BKap] (for the linear semigroup ) plus a Gronwall inequality. An alternative (and more general) approach given in [Ba82] eschews use of the Trotter
Inverse Coefficient Problems for Nonlinear Parabolic Differential Equations
Institute of Scientific and Technical Information of China (English)
Yun Hua OU; Alemdar HASANOV; Zhen Hai LIU
2008-01-01
This paper is devoted to a class of inverse problems for a nonlinear parabolic differential equation.The unknown coefficient of the equation depends on the gradient of the solution and belongs to a set of admissible coefficients.It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence.Based on this result the existence of a quasisolution of the inverse problem is obtained in the appropriate class of admissible coefficients.
A nonlinear approach of elastic reflection waveform inversion
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.
Sparse nonlinear inverse imaging for shot count reduction in inverse lithography.
Wu, Xiaofei; Liu, Shiyuan; Lv, Wen; Lam, Edmund Y
2015-10-19
Inverse lithography technique (ILT) is significant to reduce the feature size of ArF optical lithography due to its strong ability to overcome the optical proximity effect. A critical issue for inverse lithography is the complex curvilinear patterns produced, which are very costly to write due to the large number of shots needed with the current variable shape beam (VSB) writers. In this paper, we devise an inverse lithography method to reduce the shot count by incorporating a model-based fracturing (MBF) in the optimization. The MBF is formulated as a sparse nonlinear inverse imaging problem based on representing the mask as a linear combination of shots followed by a threshold function. The problem is approached with a Gauss-Newton algorithm, which is adapted to promote sparsity of the solution, corresponding to the reduction of the shot count. Simulations of inverse lithography are performed on several test cases, and results demonstrate reduced shot count of the resulting mask.
A Recursive Born Approach to Nonlinear Inverse Scattering
Kamilov, Ulugbek S; Mansour, Hassan; Boufounos, Petros T
2016-01-01
The Iterative Born Approximation (IBA) is a well-known method for describing waves scattered by semi-transparent objects. In this paper, we present a novel nonlinear inverse scattering method that combines IBA with an edge-preserving total variation (TV) regularizer. The proposed method is obtained by relating iterations of IBA to layers of a feedforward neural network and developing a corresponding error backpropagation algorithm for efficiently estimating the permittivity of the object. Simulations illustrate that, by accounting for multiple scattering, the method successfully recovers the permittivity distribution where the traditional linear inverse scattering fails.
Iterative total variation schemes for nonlinear inverse problems
Bachmayr, Markus; Burger, Martin
2009-10-01
In this paper we discuss the construction, analysis and implementation of iterative schemes for the solution of inverse problems based on total variation regularization. Via different approximations of the nonlinearity we derive three different schemes resembling three well-known methods for nonlinear inverse problems in Hilbert spaces, namely iterated Tikhonov, Levenberg-Marquardt and Landweber. These methods can be set up such that all arising subproblems are convex optimization problems, analogous to those appearing in image denoising or deblurring. We provide a detailed convergence analysis and appropriate stopping rules in the presence of data noise. Moreover, we discuss the implementation of the schemes and the application to distributed parameter estimation in elliptic partial differential equations.
Success Stories in Control: Nonlinear Dynamic Inversion Control
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.
Elastic reflection based waveform inversion with a nonlinear approach
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.
Zhang, Kun; Yan, Jiayong; Lü, Qingtian; Zhao, Jinhua; Hu, Hao
2017-04-01
A new inversion method using marine magnetotellurics is proposed based on previous studies using the nonlinear conjugate gradient method. A numerical example is used to verify the inversion algorithm and program. The inversion model and response resemble the synthetic model. Some technologies have been added to the inversion algorithm: parallel structure, terrain inversion and static shift correction.
Application of geostatistical inversion to thin reservoir prediction%地质统计学反演技术在薄储层预测中的应用
Institute of Scientific and Technical Information of China (English)
王香文; 刘红; 滕彬彬; 王连雨
2012-01-01
Taking Ml thin reservoir in H-N oilfield,Southern Ecuador,as an example,this paper documents the challenges and problems of thin reservoir prediction and presents relevant techniques and methods to tackle these problems. Based on analysis of geophysical characteristics of reservoirs and surrounding rocks,a geostatistical inversion technique is applied in this case to identify the thin(l -25ft) reservoirs with rapid lateral changes and strong concealment. Sand distribution is refined through correlation between different data volume including seismic interpretation, CSSI( Constrained Sparse Spike Inversion) and geostatistical inversion,and is further checked by non-well, random-wells and newly drilled wells. The accuracy of thin reservoir prediction is greatly enhanced to a vertical resolution up to 5ft. This technique is successfully applied in H-N oilfield and the new drilling data show that all the prediceted thin sand layers are encountered and the drilling coincidence rate is 82%.%以厄瓜多尔南部H-N油田M1层薄储层为例,阐述了研究区M1层储层预测难点和存在问题,提出针对性的储层预测方法技术.经过储层和围岩地球物理特征分析,论证了储层预测条件,确定了运用以地质统计学反演为核心的储层预测技术对该区进行储层预测研究,来解决该区储层薄(1 ～25 ft)、横向变化大、隐蔽性强的薄储层的识别；通过以地震、稀疏脉冲反演、地质统计学反演不同数据体间砂体进行对比分析,精细解释出该区砂体分布；经过无井、盲井和新钻井校验,实现了薄层的高精度预测,提高了预测精度(垂向分辨率达到5ft).该预测结果经过在H-N油田的实际应用和新钻井钻探证实,砂层钻遇率为100％,钻探符合率达82％,实现了该区新井产能的突破.
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.
Inverse problem for multi-body interaction of nonlinear waves
Marruzzo, Alessia; Antenucci, Fabrizio; Pagnani, Andrea; Leuzzi, Luca
2016-01-01
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we test two methods based on pseudolikelihood, respectively with regularization and with decimation, to determine the coupling constants from sets of measured configurations. We test statistical inference predictions for increasing number of sampled configurations and for an externally tunable {\\em temperature}-like parameter mimicing real data noise and helping minimization procedures. Analyzed models with phasors and rotors are generalizations of problems of real-valued spherical problems (e.g., density fluctuations), discrete spins (Ising and vectorial Potts) or finite number of states (standard Potts): inference methods presented here can, then, be straightforward applied to a large class of inverse problems.
Galerkin approximation for inverse problems for nonautonomous nonlinear distributed systems
Banks, H. T.; Reich, Simeon; Rosen, I. G.
1988-01-01
An abstract framework and convergence theory is developed for Galerkin approximation for inverse problems involving the identification of nonautonomous nonlinear distributed parameter systems. A set of relatively easily verified conditions is provided which are sufficient to guarantee the existence of optimal solutions and their approximation by a sequence of solutions to a sequence of approximating finite dimensional identification problems. The approach is based on the theory of monotone operators in Banach spaces and is applicable to a reasonably broad class of nonlinear distributed systems. Operator theoretic and variational techniques are used to establish a fundamental convergence result. An example involving evolution systems with dynamics described by nonstationary quasilinear elliptic operators along with some applications are presented and discussed.
Output Feedback for Stochastic Nonlinear Systems with Unmeasurable Inverse Dynamics
Institute of Scientific and Technical Information of China (English)
Xin Yu; Na Duan
2009-01-01
This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability (iISS) in deterministic systems and stochastic input-to-state stability (SISS) in stochastic systems, a concept of stochastic integral input-to-state stability (SiISS) using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.
Bayesian inversion analysis of nonlinear dynamics in surface heterogeneous reactions.
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.
Crestel, Benjamin; Alexanderian, Alen; Stadler, Georg; Ghattas, Omar
2017-07-01
The computational cost of solving an inverse problem governed by PDEs, using multiple experiments, increases linearly with the number of experiments. A recently proposed method to decrease this cost uses only a small number of random linear combinations of all experiments for solving the inverse problem. This approach applies to inverse problems where the PDE solution depends linearly on the right-hand side function that models the experiment. As this method is stochastic in essence, the quality of the obtained reconstructions can vary, in particular when only a small number of combinations are used. We develop a Bayesian formulation for the definition and computation of encoding weights that lead to a parameter reconstruction with the least uncertainty. We call these weights A-optimal encoding weights. Our framework applies to inverse problems where the governing PDE is nonlinear with respect to the inversion parameter field. We formulate the problem in infinite dimensions and follow the optimize-then-discretize approach, devoting special attention to the discretization and the choice of numerical methods in order to achieve a computational cost that is independent of the parameter discretization. We elaborate our method for a Helmholtz inverse problem, and derive the adjoint-based expressions for the gradient of the objective function of the optimization problem for finding the A-optimal encoding weights. The proposed method is potentially attractive for real-time monitoring applications, where one can invest the effort to compute optimal weights offline, to later solve an inverse problem repeatedly, over time, at a fraction of the initial cost.
A nonlinear inversion for the velocity background and perturbation models
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.
Inverse design of nonlinearity in energy harvesters for optimum damping
Ghandchi Tehrani, Maryam; Elliott, S. J.
2016-09-01
This paper presents the inverse design method for the nonlinearity in an energy harvester in order to achieve an optimum damping. A single degree-of-freedom electromechanical oscillator is considered as an energy harvester, which is subjected to a harmonic base excitation. The harvester has a limited throw due to the physical constraint of the device, which means that the amplitude of the relative displacement between the mass of the harvester and the base cannot exceed a threshold when the device is driven at resonance and beyond a particular amplitude. This physical constraint requires the damping of the harvester to be adjusted for different excitation amplitudes, such that the relative displacement is controlled and maintained below the limit. For example, the damping can be increased to reduce the amplitude of the relative displacement. For high excitation amplitudes, the optimum damping is, therefore, dependent on the amplitude of the base excitation, and can be synthesised by a nonlinear function. In this paper, a nonlinear function in the form of a bilinear is considered to represent the damping model of the device. A numerical optimisation using Matlab is carried out to fit a curve to the amplitude-dependent damping in order to determine the optimum bilinear model. The nonlinear damping is then used in the time-domain simulations and the relative displacement and the average harvested power are obtained. It is demonstrated that the proposed nonlinear damping can maintain the relative displacement of the harvester at its maximum level for a wide range of excitation, therefore providing the optimum condition for power harvesting.
A geostatistical analysis of geostatistics
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
Inverse problem for multi-body interaction of nonlinear waves.
Marruzzo, Alessia; Tyagi, Payal; Antenucci, Fabrizio; Pagnani, Andrea; Leuzzi, Luca
2017-06-14
The inverse problem is studied in multi-body systems with nonlinear dynamics representing, e.g., phase-locked wave systems, standard multimode and random lasers. Using a general model for four-body interacting complex-valued variables we test two methods based on pseudolikelihood, respectively with regularization and with decimation, to determine the coupling constants from sets of measured configurations. We test statistical inference predictions for increasing number of sampled configurations and for an externally tunable temperature-like parameter mimicing real data noise and helping minimization procedures. Analyzed models with phasors and rotors are generalizations of problems of real-valued spherical problems (e.g., density fluctuations), discrete spins (Ising and vectorial Potts) or finite number of states (standard Potts): inference methods presented here can, then, be straightforward applied to a large class of inverse problems. The high versatility of the exposed techniques also concerns the number of expected interactions: results are presented for different graph topologies, ranging from sparse to dense graphs.
Explanation of the inverse Doppler effect observed in nonlinear transmission lines.
Kozyrev, Alexander B; van der Weide, Daniel W
2005-05-27
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.
Nonlinear inversion for arbitrarily-oriented anisotropic models II: Inversion techniques
Bremner, P. M.; Panning, M. P.
2011-12-01
We present output models from inversion of a synthetic surface wave dataset. We implement new 3-D finite-frequency kernels, based on the Born approximation, to invert for upper mantle structure beneath western North America. The kernels are formulated based on a hexagonal symmetry with an arbitrary orientation. Numerical tests were performed to achieve a robust inversion scheme. Four synthetic input models were created, to include: isotropic, constant strength anisotropic, variable strength anisotropic, and both anisotropic and isotropic together. The reference model was a simplified version of PREM (dubbed PREM LIGHT) in which the crust and 220 km discontinuity have been removed. Output models from inversions of calculated synthetic data are compared against these input models to test for accurate reproduction of input model features, and the resolution of those features. The object of this phase of the study was to determine appropriate nonlinear inversion schemes that adequately recover the input models. The synthetic dataset consists of collected seismic waveforms of 126 earthquake mechanisms, of magnitude 6-7 from Dec 2006 to Feb 2009, from the IRIS database. Events were selected to correlate with USArray deployments, and to have as complete an azimuthal coverage as possible. The events occurred within a circular region of radius 150o centered about 44o lat, -110o lon (an arbitrary location within USArray coverage). Synthetic data were calculated utilizing a spectral element code (SEM) coupled to a normal mode solution. The mesh consists of a 3-D heterogeneous outer shell, representing the upper mantle above 450 km depth, coupled to a spherically symmetric inner sphere. From the synthetic dataset, multi-taper fundamental mode surface wave phase delay measurements are taken. The orthogonal 2.5π -prolate spheroidal wave function eigentapers (Slepian tapers) reduce noise biasing, and can provide error estimates in phase delay measurements. This study is a
Rayleigh scattering and nonlinear inversion of elastic waves
Energy Technology Data Exchange (ETDEWEB)
Gritto, R.
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 {minus}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 k{sub p}R = 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.
MINIMAL INVERSION AND ITS ALGORITHMS OF DISCRETE-TIME NONLINEAR SYSTEMS
Institute of Scientific and Technical Information of China (English)
ZHENG Yufan
2005-01-01
The left-inverse system with minimal order and its algorithms of discrete-time nonlinear systems are studied in a linear algebraic framework. The general structure of left-inverse system is described and computed in symbolic algorithm. Two algorithms are given for constructing left-inverse systems with minimal order.
Nonlinear inverse modeling of sensor based on back-propagation fuzzy logical system
Institute of Scientific and Technical Information of China (English)
Li Jun; Liu Junhua
2007-01-01
Objective To correct the nonlinear error of sensor output, a new approach to sensor inverse modeling based on Back-Propagation Fuzzy Logical System (BP FS) is presented. Methods The BP FS is a computationally efficient nonlinear universal approximator, which is capable of implementing complex nonlinear mapping from its input pattern space to the output with fast convergence speed. Results The neuro-fuzzy hybrid system, i.e. BP FS, is then applied to construct nonlinear inverse model of pressure sensor. The experimental results show that the proposed inverse modeling method automatically compensates the associated nonlinear error in pressure estimation, and thus the performance of pressure sensor is significantly improved. Conclusion The proposed method can be widely used in nonlinearity correction of various kinds of sensors to compensate the effects of nonlinearity and temperature on sensor output.
An inverse problem of determining a nonlinear term in an ordinary differential equation
Kamimura, Yutaka
1998-01-01
An inverse problem for a nonlinear ordinary differential equation is discussed. We prove an existence theorem of a nonlinear term with which a boundary value problem admits a solution. This is an improvement of earlier work by A. Lorenzi. We also prove a uniqueness theorem of the nonlinear term.
A practical primer on geostatistics
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
A Practical Primer on Geostatistics
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 has
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.
Diggle, Peter J
2007-01-01
Model-based geostatistics refers to the application of general statistical principles of modeling and inference to geostatistical problems. This volume provides a treatment of model-based geostatistics and emphasizes on statistical methods and applications. It also features analyses of datasets from a range of scientific contexts.
Nonlinear inverse synthesis for high spectral efficiency transmission in optical fibers
Le, Son Thai; Turitsyn, Sergei K
2014-01-01
In linear communication channels, spectral components (modes) defined by the Fourier transform of the signal propagate without interactions with each other. In certain nonlinear channels, such as the one modelled by the classical nonlinear Schr\\"odinger equation, there are nonlinear modes (nonlinear signal spectrum) that also propagate without interacting with each other and without corresponding nonlinear cross talk; effectively, in a linear manner. Here, we describe in a constructive way how to introduce such nonlinear modes for a given input signal. We investigate the performance of the nonlinear inverse synthesis (NIS) method, in which the information is encoded directly onto the continuous part of the nonlinear signal spectrum. This transmission technique, combined with the appropriate distributed Raman amplification, can provide an effective eigenvalue division multiplexing with high spectral efficiency, thanks to highly suppressed channel cross talk. The proposed NIS approach can be integrated with any...
Inverse Learning Control of Nonlinear Systems Using Support Vector Machines
Institute of Scientific and Technical Information of China (English)
HU Zhong-hui; LI Yuan-gui; CAI Yun-ze; XU Xiao-ming
2005-01-01
An inverse learning control scheme using the support vector machine (SVM) for regression was proposed. The inverse learning approach is originally researched in the neural networks. Compared with neural networks, SVMs overcome the problems of local minimum and curse of dimensionality. Additionally, the good generalization performance of SVMs increases the robustness of control system. The method of designing SVM inverselearning controller was presented. The proposed method is demonstrated on tracking problems and the performance is satisfactory.
Heeding the waveform inversion nonlinearity by unwrapping the model and data
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.
Fast Inverse Nonlinear Fourier Transforms for Fiber Bragg Grating Design and Related Problems
Wahls, Sander
2016-01-01
The problem of constructing a fiber Bragg grating profile numerically such that the reflection coefficient of the grating matches a given specification is considered. The well-known analytic solution to this problem is given by a suitable inverse nonlinear Fourier transform (also known as inverse scattering transform) of the specificed reflection coefficient. Many different algorithms have been proposed to compute this inverse nonlinear Fourier transform numerically. The most efficient ones require $\\mathcal{O}(D^{2})$ floating point operations (flops) to generate $D$ samples of the grating profile. In this paper, two new fast inverse nonlinear Fourier transform algorithms that require only $\\mathcal{O}(D\\log^{2}D)$ flops are proposed. The merits of our algorithms are demonstrated in numerical examples, in which they are compared to a conventional layer peeling method, the Toeplitz inner bordering method and integral layer peeling. One of our two algorithms also extends to the design problem for fiber-assiste...
A nonlinear model reference adaptive inverse control algorithm with pre-compensator
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
In this paper, the reduced-order modeling (ROM)technology and its corresponding linear theory are expanded from the linear dynamic system to the nonlinear one, and H∞ control theory is employed in the frequency domain to design some nonlinear system' s pre-compensator in some special way. The adaptive model inverse control (AMIC)theory coping with nonlinear system is improved as well. Such is the model reference adaptive inverse control with pre-compensator (PCMRAIC). The aim of that algorithm is to construct a strategy of control as a whole. As a practical example of the application, the numerical simulation has been given on matlab software packages. The numerical result is given. The proposed strategy realizes the linearization control of nonlinear dynamic system. And it carries out a good performance to deal with the nonlinear system.
Non-linear magnetorheological behaviour of an inverse ferrofluid
de Gans, B.J.; Hoekstra, Hans; Mellema, J.
1999-01-01
The non-linear magnetorheological behaviour is studied of a model system consisting of monodisperse silica particles suspended in a ferrofluid. The stress/strain curve as well as the flow curve was measured as a function of volume fraction silica particles and field strength, using a home-made
Hein, Matthias
2010-01-01
Many problems in machine learning and statistics can be formulated as (generalized) eigenproblems. In terms of the associated optimization problem, computing linear eigenvectors amounts to finding critical points of a quadratic function subject to quadratic constraints. In this paper we show that a certain class of constrained optimization problems with nonquadratic objective and constraints can be understood as nonlinear eigenproblems. We derive a generalization of the inverse power method which is guaranteed to converge to a nonlinear eigenvector. We apply the inverse power method to 1-spectral clustering and sparse PCA which can naturally be formulated as nonlinear eigenproblems. In both applications we achieve state-of-the-art results in terms of solution quality and runtime. Moving beyond the standard eigenproblem should be useful also in many other applications and our inverse power method can be easily adapted to new problems.
An ICPSO-RBFNN nonlinear inversion for electrical resistivity imaging
Institute of Scientific and Technical Information of China (English)
江沸菠; 戴前伟; 董莉
2016-01-01
To improve the global search ability and imaging quality of electrical resistivity imaging(ERI) inversion, a two-stage learning ICPSO algorithm of radial basis function neural network (RBFNN) based on information criterion (IC) and particle swarm optimization (PSO) is presented. In the proposed method, IC is applied to obtain the hidden layer structure by calculating the optimal IC value automatically and PSO algorithm is used to optimize the centers and widths of the radial basis functions in the hidden layer. Meanwhile, impacts of different information criteria to the inversion results are compared, and an implementation of the proposed ICPSO algorithm is given. The optimized neural network has one hidden layer with 261 nodes selected by AKAIKE’s information criterion (AIC) and it is trained on 32 data sets and tested on another 8 synthetic data sets. Two complex synthetic examples are used to verify the feasibility and effectiveness of the proposed method with two learning stages. The results show that the proposed method has better performance and higher imaging quality than three-layer and four-layer back propagation neural networks (BPNNs) and traditional least square(LS) inversion.
Imaging of discontinuities in nonlinear 3-D seismic inversion
Energy Technology Data Exchange (ETDEWEB)
Carrion, P.M.; Cerveny, V. (PPPG/UFBA, Salvador (Brazil))
1990-09-01
The authors present a nonlinear approach for reconstruction of discontinuities in geological environment (earth's crust, say). The advantage of the proposed method is that it is not limited to a Born approximation (small angles of propagation and weak scatterers). One can expect significantly better images since larger apertures including wide angle reflection arrivals can be incorporated into the imaging operator. In this paper, they treat only compressional body waves: shear and surface waves are considered as noise.
Decoupling of Double Extraction Turbo-Unit by Nonlinear Multivariable Inverse System Method
Institute of Scientific and Technical Information of China (English)
黎浩荣; 李立勤; 李东海; 宋兆星; 王伟
2001-01-01
A multivariable inverse nonlinear control scheme is developed to decouple the strongly nonlinear double extraction steam turbo-unit, improving the transient stability of the power and heating system. Computer simulation tests show that not only does the control scheme achieve satisfactory decoupling of the high and low pressure turbines and the electric power, remarkably improving the transient stability, but also the design is very intuitive and concise.
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...
Energy Technology Data Exchange (ETDEWEB)
Alvarez-Estrada, R.F.
1979-08-01
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.
THE APPLICATION OF GENETIC ALGORITHM IN NON-LINEAR INVERSION OF ROCK MECHANICS PARAMETERS
Institute of Scientific and Technical Information of China (English)
赵晓东
1998-01-01
The non-linear inversion of rock mechanics parameters based on genetic algorithm ispresented. The principle and step of genetic algorithm is also given. A brief discussion of thismethod and an application example is presented at the end of this paper. From the satisfied re-sult, quick, convenient and practical new approach is developed to solve this kind of problems.
McMC-based nonlinear EIVAZ inversion driven by rock physics
Pan, Xinpeng; Zhang, Guangzhi; Chen, Huaizhen; Yin, Xingyao
2017-03-01
A single set of vertically aligned fractures embedded in a purely isotropic background medium may be considered as a long-wavelength effective transversely isotropic medium with a horizontal symmetry axis (HTI). The estimation of fracture weaknesses is essential for characterizing the anisotropy in HTI media. Using the fractured anisotropic rock-physics models and the wide-azimuth seismic data, elastic impedance inversion variation with incident angle and azimuth, or simply ‘EIVAZ’ for short, can be carried out for the estimation of the normal and tangential fracture weaknesses with the nonlinear Markov chain Monte Carlo (McMC) strategy. Firstly, an inversion method of nonlinear anisotropic elastic impedance (AEI) with the McMC algorithm was proposed, which is used for the inversion of nonlinear AEI information with different angles of incidence and azimuth. Then we extracted the normal and tangential fracture weaknesses directly using the ratio differences of inverted nonlinear AEI data. So we can eliminate the influence of the isotropic background elastic impedance on the anisotropic perturbation elastic impedance and obtain the normal and tangential fracture weaknesses more stably. A test on a 2D over-thrust model shows that the fracture weaknesses are still estimated reasonably with moderate noise. A test on a real data set demonstrates that the estimated results are in good agreement with the results of the well log interpretation, and our McMC-based nonlinear AEI approach appears to be a stable method for predicting fracture weaknesses.
A Quadratic precision generalized nonlinear global optimization migration velocity inversion method
Institute of Scientific and Technical Information of China (English)
Zhao Taiyin; Hu Guangmin; He Zhenhua; Huang Deji
2009-01-01
An important research topic for prospecting seismology is to provide a fast accurate velocity model from pre-stack depth migration. Aiming at such a problem, we propose a quadratic precision generalized nonlinear global optimization migration velocity inversion. First we discard the assumption that there is a linear relationship between residual depth and residual velocity and propose a velocity model correction equation with quadratic precision which enables the velocity model from each iteration to approach the real model as quickly as possible. Second, we use a generalized nonlinear inversion to get the global optimal velocity perturbation model to all traces. This method can expedite the convergence speed and also can decrease the probability of falling into a local minimum during inversion. The synthetic data and Marmousi data examples show that our method has a higher precision and needs only a few iterations and consequently enhances the practicability and accuracy of migration velocity analysis (MVA) in complex areas.
Solution of the nonlinear inverse scattering problem by T -matrix completion. II. Simulations
Levinson, Howard W.; Markel, Vadim A.
2016-10-01
This is Part II of the paper series on data-compatible T -matrix completion (DCTMC), which is a method for solving nonlinear inverse problems. Part I of the series [H. W. Levinson and V. A. Markel, Phys. Rev. E 94, 043317 (2016), 10.1103/PhysRevE.94.043317] contains theory and here we present simulations for inverse scattering of scalar waves. The underlying mathematical model is the scalar wave equation and the object function that is reconstructed is the medium susceptibility. The simulations are relevant to ultrasound tomographic imaging and seismic tomography. It is shown that DCTMC is a viable method for solving strongly nonlinear inverse problems with large data sets. It provides not only the overall shape of the object, but the quantitative contrast, which can correspond, for instance, to the variable speed of sound in the imaged medium.
Bayesian Geostatistical Design
DEFF Research Database (Denmark)
Diggle, Peter; Lophaven, Søren Nymand
2006-01-01
This paper describes the use of model-based geostatistics for choosing the set of sampling locations, collectively called the design, to be used in a geostatistical analysis. Two types of design situation are considered. These are retrospective design, which concerns the addition of sampling...
Geodynamic inversion to constrain the nonlinear rheology of the lithosphere
Baumann, Tobias; Kaus, Boris
2015-04-01
A common method to determine the strength of the lithosphere is through estimating its effective elastic thickness from the coherence between gravity and topography. This method assumes a priori that the lithosphere is a thin elastic plate floating on a viscous mantle. Whereas this seems to work well with oceanic plates, it has given controversial results in continental collision zones. Usually, continental collisions zones are well-studied areas for which additional geophysical datasets 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. 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 approach is thus required to better understand the rheology and dynamics of the lithosphere in collision zones. Our method combines numerical thermo-mechanical forward models of the present-day lithosphere with a massively parallel Bayesian inversion approach. The geometry of the forward models is part of the a priori knowledge and is constructed from seismological data. We jointly invert topography, gravity, horizontal and vertical surface velocities to constrain the unknown rheological material parameters of the forward models in a probabilistic sense. The model rheology is described with experimentally determined viscous creep laws and other parameters describing the plastic behaviour. As viscosity is temperature dependent, the temperature structure of the forward models is parameterised as well. We apply the method to cross-sections of the India-Asia collision system. In this case, we deal with 17 to 20 model parameters, which requires solving up to 2 × 106 forward
Nonlinear inversion of electrical resistivity imaging using pruning Bayesian neural networks
Jiang, Fei-Bo; Dai, Qian-Wei; Dong, Li
2016-06-01
Conventional artificial neural networks used to solve electrical resistivity imaging (ERI) inversion problem suffer from overfitting and local minima. To solve these problems, we propose to use a pruning Bayesian neural network (PBNN) nonlinear inversion method and a sample design method based on the K-medoids clustering algorithm. In the sample design method, the training samples of the neural network are designed according to the prior information provided by the K-medoids clustering results; thus, the training process of the neural network is well guided. The proposed PBNN, based on Bayesian regularization, is used to select the hidden layer structure by assessing the effect of each hidden neuron to the inversion results. Then, the hyperparameter α k , which is based on the generalized mean, is chosen to guide the pruning process according to the prior distribution of the training samples under the small-sample condition. The proposed algorithm is more efficient than other common adaptive regularization methods in geophysics. The inversion of synthetic data and field data suggests that the proposed method suppresses the noise in the neural network training stage and enhances the generalization. The inversion results with the proposed method are better than those of the BPNN, RBFNN, and RRBFNN inversion methods as well as the conventional least squares inversion.
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...... Difference elastic wave-field numerical method. In this paper, the accuracy and performance of the linear beamformer and nonlinear inverse methods to localize a underground seismic source are checked and compared using computer generated synthetic experimental data. © 2013 Acoustical Society of America....
On the use of nonlinear regularization in inverse method for the tachocline profile determination
Corbard, T; Provost, J P; Blanc-Féraud, L
1998-01-01
Inversions of rotational splittings have shown that the surface layers and the so-called solar tachocline at the base of the convection zone are regions in which high radial gradients of the rotation rate occur. The usual regularization methods tend to smooth out every high gradients in the solution and may not be appropriate for the study of a zone like the tachocline. In this paper we use nonlinear regularization methods that are developed for edge-preserving regularization in computed imaging (e.g. Blanc-Féraud et al. 1995) and we apply them in the helioseismic context of rotational inversions.
Chen, Xiang-Jun; Lam, Wa Kun
2004-06-01
An inverse scattering transform for the derivative nonlinear Schrödinger equation with nonvanishing boundary conditions is derived by introducing an affine parameter to avoid constructing Riemann sheets. A one-soliton solution simpler than that in the literature is obtained, which is a breather and degenerates to a bright or dark soliton as the discrete eigenvalue becomes purely imaginary. The solution is mapped to that of the modified nonlinear Schrödinger equation by a gaugelike transformation, predicting some sub-picosecond solitons in optical fibers.
Shimelevich, M. I.; Obornev, E. A.; Obornev, I. E.; Rodionov, E. A.
2017-07-01
The iterative approximation neural network method for solving conditionally well-posed nonlinear inverse problems of geophysics is presented. The method is based on the neural network approximation of the inverse operator. The inverse problem is solved in the class of grid (block) models of the medium on a regularized parameterization grid. The construction principle of this grid relies on using the calculated values of the continuity modulus of the inverse operator and its modifications determining the degree of ambiguity of the solutions. The method provides approximate solutions of inverse problems with the maximal degree of detail given the specified degree of ambiguity with the total number of the sought parameters n × 103 of the medium. The a priori and a posteriori estimates of the degree of ambiguity of the approximated solutions are calculated. The work of the method is illustrated by the example of the three-dimensional (3D) inversion of the synthesized 2D areal geoelectrical (audio magnetotelluric sounding, AMTS) data corresponding to the schematic model of a kimberlite pipe.
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.
Institute of Scientific and Technical Information of China (English)
杨锴; 艾迪飞; 耿建华
2012-01-01
Based on a geostatistical simulation method conditioned to well-log and crosshole seismic rays, a novel geostatistical reservoir inversion (modeling) technique constrained by well-log, crosshole and surface seismic data is presented. Compared with existing geostatistical inversion methods only the well-log and surface seismic data being honored, all related prior information include well-log, crosshole seismic data and surface seimismic data are honored in presented method. Thus the accuracy of geostatistical inversion/modeling is greatly improved and the uncertainty of inversion/modeling is reduced. The test on synthetic data proved the above points.%利用能够整合测井信息与井间地震信息的地质统计学随机模拟方法,结合传统的地质统计学反演思路,得到了一种能够同时整合测井、井间地震与地面地震三种先验信息的地质统计学反演与储层建模方法.由于井间射线信息、测井信息与地面地震数据在随机反演与建模过程当中都得到了尊重,因此与传统地质统计学反演仅利用了测井与地面地震数据相比,本文的地质统计学反演与建模方法更充分地利用了先验信息,有效提高了反演的精度,降低了随机建模中的多解性.基于理论数据的测试证实了上述观点.
Meyer, G.; Cicolani, L.
1981-01-01
A practical method for the design of automatic flight control systems for aircraft with complex characteristics and operational requirements, such as the powered lift STOL and V/STOL configurations, is presented. The method is effective for a large class of dynamic systems requiring multi-axis control which have highly coupled nonlinearities, redundant controls, and complex multidimensional operational envelopes. It exploits the concept of inverse dynamic systems, and an algorithm for the construction of inverse is given. A hierarchic structure for the total control logic with inverses is presented. The method is illustrated with an application to the Augmentor Wing Jet STOL Research Aircraft equipped with a digital flight control system. Results of flight evaluation of the control concept on this aircraft are presented.
Modified Nonlinear Inverse Synthesis for Optical Links with Distributed Raman Amplification
Le, Son T; Rosa, Pawel; Ania-Castanon, Juan D; Turitsyn, Sergei K
2015-01-01
Nonlinear Fourier transform (NFT) and eigenvalue communication with the use of nonlinear signal spectrum (both discrete and continuous), have been recently discussed as a promising transmission method to combat fiber nonlinearity impairments. However, because the NFT-based transmission method employs the integrability property of the lossless nonlinear Schr\\"odinger equation (NLSE), the original approach can only be applied directly to optical links with ideal distributed Raman amplification. In this paper, we investigate in details the impact of a non-ideal Raman gain profile on the performance of the nonlinear inverse synthesis (NIS) scheme, in which the transmitted information is encoded directly onto the continuous part of the nonlinear signal spectrum. We propose the lossless path-averaged (LPA) model for fiber links with non-ideal Raman gain profile by taking into account the average effect of the Raman gain. We show that the NIS scheme employing the LPA model can offer a performance gain of 3 dB regard...
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.
Franck, I M
2014-01-01
This paper presents an efficient Bayesian framework for solving nonlinear, high-dimensional model calibration problems. It is based on Variational Bayesian formulation that aims at approximating the exact posterior by means of solving an optimization problem in an appropriately selected family of distributions. The goal is two-fold. Firstly, to find lower-dimensional representations of the unknown parameter vector that capture as much as possible of the associated posterior density, and secondly to enable the computation of the approximate posterior density with as few forward calls as possible. We discuss how these objectives can be achieved by using a fully Bayesian argumentation and employing the marginal likelihood or evidence as the ultimate model validation metric for any proposed dimensionality reduction. We demonstrate the performance of the proposed methodology to problems in nonlinear elastography where the identification of the mechanical properties of biological materials can inform non-invasive, ...
Fast Inverse Nonlinear Fourier Transform For Generating Multi-Solitons In Optical Fiber
Wahls, Sander
2015-01-01
The achievable data rates of current fiber-optic wavelength-division-multiplexing (WDM) systems are limited by nonlinear interactions between different subchannels. Recently, it was thus proposed to replace the conventional Fourier transform in WDM systems with an appropriately defined nonlinear Fourier transform (NFT). The computational complexity of NFTs is a topic of current research. In this paper, a fast inverse NFT algorithm for the important special case of multi-solitonic signals is presented. The algorithm requires only $\\mathcal{O}(D\\log^{2}D)$ floating point operations to compute $D$ samples of a multi-soliton. To the best of our knowledge, this is the first algorithm for this problem with $\\log^{2}$-linear complexity. The paper also includes a many samples analysis of the generated nonlinear Fourier spectra.
Directory of Open Access Journals (Sweden)
Yu-Chi Wang
2015-01-01
Full Text Available This paper presents a unified approach to nonlinear dynamic inversion control algorithm with the parameters for desired dynamics determined by using an eigenvalue assignment method, which may be applied in a very straightforward and convenient way. By using this method, it is not necessary to transform the nonlinear equations into linear equations by feedback linearization before beginning control designs. The applications of this method are not limited to affine nonlinear control systems or limited to minimum phase problems if the eigenvalues of error dynamics are carefully assigned so that the desired dynamics is stable. The control design by using this method is shown to be robust to modeling uncertainties. To validate the theory, the design of a UAV control system is presented as an example. Numerical simulations show the performance of the design to be quite remarkable.
Inversion of geothermal heat flux in a thermomechanically coupled nonlinear Stokes ice sheet model
Zhu, Hongyu; Petra, Noemi; Stadler, Georg; Isaac, Tobin; Hughes, Thomas J. R.; Ghattas, Omar
2016-07-01
We address the inverse problem of inferring the basal geothermal heat flux from surface velocity observations using a steady-state thermomechanically coupled nonlinear Stokes ice flow model. This is a challenging inverse problem since the map from basal heat flux to surface velocity observables is indirect: the heat flux is a boundary condition for the thermal advection-diffusion equation, which couples to the nonlinear Stokes ice flow equations; together they determine the surface ice flow velocity. This multiphysics inverse problem is formulated as a nonlinear least-squares optimization problem with a cost functional that includes the data misfit between surface velocity observations and model predictions. A Tikhonov regularization term is added to render the problem well posed. We derive adjoint-based gradient and Hessian expressions for the resulting partial differential equation (PDE)-constrained optimization problem and propose an inexact Newton method for its solution. As a consequence of the Petrov-Galerkin discretization of the energy equation, we show that discretization and differentiation do not commute; that is, the order in which we discretize the cost functional and differentiate it affects the correctness of the gradient. Using two- and three-dimensional model problems, we study the prospects for and limitations of the inference of the geothermal heat flux field from surface velocity observations. The results show that the reconstruction improves as the noise level in the observations decreases and that short-wavelength variations in the geothermal heat flux are difficult to recover. We analyze the ill-posedness of the inverse problem as a function of the number of observations by examining the spectrum of the Hessian of the cost functional. Motivated by the popularity of operator-split or staggered solvers for forward multiphysics problems - i.e., those that drop two-way coupling terms to yield a one-way coupled forward Jacobian - we study the
Directory of Open Access Journals (Sweden)
Adéla Volfová
2012-10-01
Full Text Available Geostatistics is a scientific field which provides methods for processing spatial data. In our project, geostatistics is used as a tool for describing spatial continuity and making predictions of some natural phenomena. An open source statistical project called R is used for all calculations. Listeners will be provided with a brief introduction to R and its geostatistical packages and basic principles of kriging and cokriging methods. Heavy mathematical background is omitted due to its complexity. In the second part of the presentation, several examples are shown of how to make a prediction in the whole area of interest where observations were made in just a few points. Results of these methods are compared.
Nonlinear inversion-based output tracking control of a boiler-turbine unit
Institute of Scientific and Technical Information of China (English)
Fang FANG; Jizhen LIU; Wen TAN
2005-01-01
The capability to perform fast load-following has been an important issue in the power industry. An output tracking control system of a boiler-turbine unit is developed. The system is composed of stable inversion and feedback controller.The stable inversion is implemented as a feedforward controller to improve the load-following capability, and the feedback controller is utilized to guarantee the stability and robustness of the whole system. Loop-shaping H∞ method is used to design the feedback controller and the final controller is reduced to a multivariable PI form. The output tracking control system takes account of the multivariable, nonlinear and coupling behavior of boiler-turbine system, and the simulation tests show that the control system works well and can be widely applied.
Nonlinear Inversion of Potential-Field Data Using an Improved Genetic Algorithm
Institute of Scientific and Technical Information of China (English)
Feng Gangding; Chen Chao
2004-01-01
The genetic algorithm is useful for solving an inversion of complex nonlinear geophysical equations. The multi-point search of the genetic algorithm makes it easier to find a globally optimal solution and avoid falling into a local extremum. The search efficiency of the genetic algorithm is a key to producing successful solutions in a huge multi-parameter model space. The encoding mechanism of the genetic algorithm affects the searching processes in the evolution. Not all genetic operations perform perfectly in a search under either a binary or decimal encoding system. As such, a standard genetic algorithm (SGA) is sometimes unable to resolve an optimization problem such as a simple geophysical inversion. With the binary encoding system the operation of the crossover may produce more new individuals. The decimal encoding system, on the other hand, makes the mutation generate more new genes. This paper discusses approaches of exploiting the search potentials of genetic operations with different encoding systems and presents a hybrid-encoding mechanism for the genetic algorithm. This is referred to as the hybrid-encoding genetic algorithm (HEGA). The method is based on the routine in which the mutation operation is executed in decimal code and other operations in binary code. HEGA guarantees the birth of better genes by mutation processing with a high probability, so that it is beneficial for resolving the inversions of complicated problems. Synthetic and real-world examples demonstrate the advantages of using HEGA in the inversion of potential-field data.
Directory of Open Access Journals (Sweden)
Morteza Ebrahimi
2012-01-01
Full Text Available The purpose of the present study is to provide a fast and accurate algorithm for identifying the medium temperature and the unknown radiation term from an overspecified condition on the boundary in an inverse problem of linear heat equation with nonlinear boundary condition. The design of the paper is to employ Taylor’s series expansion for linearize nonlinear term and then finite-difference approximation to discretize the problem domain. Owing to the application of the finite difference scheme, a large sparse system of linear algebraic equations is obtained. An approach of Monte Carlo method is employed to solve the linear system and estimate unknown radiation term. The Monte Carlo optimization is adopted to modify the estimated values. Results show that a good estimation on the radiation term can be obtained within a couple of minutes CPU time at pentium IV-2.4 GHz PC.
Murio, Diego A.
1991-01-01
An explicit and unconditionally stable finite difference method for the solution of the transient inverse heat conduction problem in a semi-infinite or finite slab mediums subject to nonlinear radiation boundary conditions is presented. After measuring two interior temperature histories, the mollification method is used to determine the surface transient heat source if the energy radiation law is known. Alternatively, if the active surface is heated by a source at a rate proportional to a given function, the nonlinear surface radiation law is then recovered as a function of the interface temperature when the problem is feasible. Two typical examples corresponding to Newton cooling law and Stefan-Boltzmann radiation law respectively are illustrated. In all cases, the method predicts the surface conditions with an accuracy suitable for many practical purposes.
Buried Object Detection by an Inexact Newton Method Applied to Nonlinear Inverse Scattering
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Matteo Pastorino
2012-01-01
Full Text Available An approach to reconstruct buried objects is proposed. It is based on the integral equations of the electromagnetic inverse scattering problem, written in terms of the Green’s function for half-space geometries. The full nonlinearity of the problem is exploited in order to inspect strong scatterers. After discretization of the continuous model, the resulting equations are solved in a regularization sense by means of a two-step inexact Newton algorithm. The capabilities and limitations of the method are evaluated by means of some numerical simulations.
Directory of Open Access Journals (Sweden)
Slavica M. Perovich
2011-06-01
Full Text Available The subject of the theoretical analysis presented in this paper is an analytical approach to the temperature estimation, as an inverse problem, for different thermistors – linear resistances structures: series and parallel ones, by the STFT - Special Trans Functions Theory (S.M. Perovich. The mathematical formulae genesis of both cases is given. Some numerical and graphical simulations in MATHEMATICA program have been realized. The estimated temperature intervals for strongly determined values of the equivalent resistances of the nonlinear structures are given, as well.
Gamma ray vortices from nonlinear inverse Compton scattering of circularly polarized light
Taira, Yoshitaka; Katoh, Masahiro
2016-01-01
Inverse Compton scattering (ICS) is an elemental radiation process that produces high-energy photons both in nature and in the laboratory. Non-linear ICS is a process in which multiple photons are converted to a single high-energy photon. Here, we theoretically show that the photon produced by non-linear ICS of circularly polarized photons is a vortex, which means that it possesses a helical wave front and carries orbital angular momentum. Our work explains a recent experimental result regarding non-linear Compton scattering that clearly shows an annular intensity distribution as a remarkable feature of a vortex beam. Our work implies that gamma ray vortices should be produced in various situations in astrophysics in which high-energy electrons and intense circularly polarized light fields coexist. They should play a critical role in stellar nucleosynthesis. Non-linear ICS is the most promising radiation process for realizing a gamma ray vortex source based on currently available laser and accelerator technol...
Geostatistical inference using crosshole ground-penetrating radar
DEFF Research Database (Denmark)
Looms, Majken C; Hansen, Thomas Mejer; Cordua, Knud Skou
2010-01-01
, the moisture content will reflect the variation of the physical properties of the subsurface, which determine the flow patterns in the unsaturated zone. Deterministic least-squares inversion of crosshole groundpenetrating-radar GPR traveltimes result in smooth, minimumvariance estimates of the subsurface radar...... wave velocity structure, which may diminish the utility of these images for geostatistical inference. We have used a linearized stochastic inversion technique to infer the geostatistical properties of the subsurface radar wave velocity distribution using crosshole GPR traveltimes directly. Expanding...... 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...
A limited memory BFGS method for a nonlinear inverse problem in digital breast tomosynthesis
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.
Geostatistical inference using crosshole ground-penetrating radar
DEFF Research Database (Denmark)
Looms, Majken C; Hansen, Thomas Mejer; Cordua, Knud Skou
2010-01-01
, the moisture content will reflect the variation of the physical properties of the subsurface, which determine the flow patterns in the unsaturated zone. Deterministic least-squares inversion of crosshole groundpenetrating-radar GPR traveltimes result in smooth, minimumvariance estimates of the subsurface radar...... wave velocity structure, which may diminish the utility of these images for geostatistical inference. We have used a linearized stochastic inversion technique to infer the geostatistical properties of the subsurface radar wave velocity distribution using crosshole GPR traveltimes directly. Expanding...
Uieda, Leonardo; Barbosa, Valéria C. F.
2016-10-01
Estimating the relief of the Moho from gravity data is a computationally intensive non-linear inverse problem. What is more, the modeling must take the Earths curvature into account when the study area is of regional scale or greater. We present a regularized non-linear 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 hyper-parameters: 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 Basins, and the Borborema province. These differences suggest the existence of crustal or mantle density anomalies that were unaccounted for during gravity data processing.
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.
Sparse-grid, reduced-basis Bayesian inversion: Nonaffine-parametric nonlinear equations
Chen, Peng; Schwab, Christoph
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 assimilation
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
A general nonlinear inverse transport algorithm using forward and adjoint flux computations
Energy Technology Data Exchange (ETDEWEB)
Norton, S.J. [Oak Ridge National Lab., TN (United States)
1997-04-01
Iterative approaches to the nonlinear inverse transport problem are described, which give rise to the structure that best predicts a set of transport observations. Such methods are based on minimizing a global error functional measuring the discrepancy between predicted and observed transport data. Required for this minimization is the functional gradient (Frechet derivative) of the global error evaluated with respect to a set of unknown material parameters (specifying boundary locations, scattering cross sections, etc.) which are to be determined. It is shown how this functional gradient is obtained from numerical solutions to the forward and adjoint transport problems computed once per iteration. This approach is not only far more efficient, but also more accurate, than a finite-difference method for computing the gradient of the global error. The general technique can be applied to inverse-transport problems of all descriptions, provided only that solutions to the forward and adjoint problems can be found numerically. As an illustration, two inverse problems are treated: the reconstruction of an anisotropic scattering function in a one-dimensional homogeneous slab and the two-dimensional imaging of a spatially-varying scattering cross section.
Inverse solution technique of steady-state responses for local nonlinear structures
Wang, Xing; Guan, Xin; Zheng, Gangtie
2016-03-01
An inverse solution technique with the ability of obtaining complete steady-state primary harmonic responses of local nonlinear structures in the frequency domain is proposed in the present paper. In this method, the nonlinear dynamic equations of motion is first condensed from many to only one algebraic amplitude-frequency equation of relative motion. Then this equation is transformed into a polynomial form, and with its frequency as the unknown variable, the polynomial equation is solved by tracing all the solutions of frequency with the increase of amplitude. With this solution technique, some complicated dynamic behaviors such as sharp tuning, anomalous jumps, breaks in responses and detached resonance curves could be obtained. The proposed method is demonstrated and validated through a finite element beam under force excitations and a lumped parameter model with a local nonlinear element under base excitations. The phenomenon of detached resonance curves in the frequency response and its coupling effects with multiple linear modes in the latter example are observed.
Energy Technology Data Exchange (ETDEWEB)
Xie, G.; Li, J.; Majer, E.; Zuo, D.
1998-07-01
This paper describes a new 3D parallel GILD electromagnetic (EM) modeling and nonlinear inversion algorithm. The algorithm consists of: (a) a new magnetic integral equation instead of the electric integral equation to solve the electromagnetic forward modeling and inverse problem; (b) a collocation finite element method for solving the magnetic integral and a Galerkin finite element method for the magnetic differential equations; (c) a nonlinear regularizing optimization method to make the inversion stable and of high resolution; and (d) a new parallel 3D modeling and inversion using a global integral and local differential domain decomposition technique (GILD). The new 3D nonlinear electromagnetic inversion has been tested with synthetic data and field data. The authors obtained very good imaging for the synthetic data and reasonable subsurface EM imaging for the field data. The parallel algorithm has high parallel efficiency over 90% and can be a parallel solver for elliptic, parabolic, and hyperbolic modeling and inversion. The parallel GILD algorithm can be extended to develop a high resolution and large scale seismic and hydrology modeling and inversion in the massively parallel computer.
Geostatistics and Analysis of Spatial Data
DEFF Research Database (Denmark)
Nielsen, Allan Aasbjerg
2007-01-01
This note deals with geostatistical measures for spatial correlation, namely the auto-covariance function and the semi-variogram, as well as deterministic and geostatistical methods for spatial interpolation, namely inverse distance weighting and kriging. Some semi-variogram models are mentioned......, specifically the spherical, the exponential and the Gaussian models. Equations to carry out simple og ordinary kriging are deduced. Other types of kriging are mentioned, and references to international literature, Internet addresses and state-of-the-art software in the field are given. A very simple example...... to illustrate the computations and a more realistic example with height data from an area near Slagelse, Denmark, are given. Finally, a series of attractive characteristics of kriging are mentioned, and a simple sampling strategic consideration is given based on the dependence of the kriging variance...
Bayesian Geostatistical Design
DEFF Research Database (Denmark)
Diggle, Peter; Lophaven, Søren Nymand
2006-01-01
This paper describes the use of model-based geostatistics for choosing the set of sampling locations, collectively called the design, to be used in a geostatistical analysis. Two types of design situation are considered. These are retrospective design, which concerns the addition of sampling...... locations to, or deletion of locations from, an existing design, and prospective design, which consists of choosing positions for a new set of sampling locations. We propose a Bayesian design criterion which focuses on the goal of efficient spatial prediction whilst allowing for the fact that model...... parameter values are unknown. The results show that in this situation a wide range of interpoint distances should be included in the design, and the widely used regular design is often not the best choice....
Weng, Su-Ming; Sheng, Zheng-Ming; Zhang, Jie
2009-11-01
Inverse bremsstrahlung (IB) absorption and evolution of the electron distribution function (EDF) in a wide laser intensity range (10;{12}-10;{17} W/cm;{2}) have been studied systematically by a two velocity-dimension Fokker-Planck code. It is found that Langdon's IB operator overestimates the absorption rate at high laser intensity, consequently with an overdistorted non-Maxwellian EDF. According to the small anisotropy of EDF in the oscillation frame, we introduce an IB operator which is similar to Langdon's but without the low laser intensity limit. This operator is appropriate for self-consistently tackling the nonlinear effects of high laser intensity as well as non-Maxwellian EDF. Particularly, our operator is capable of treating IB absorption properly in the indirect and direct-drive inertial confinement fusion schemes with the National Ignition Facility and Laser MegaJoule laser parameters at focused laser intensity beyond 10;{15} W/cm;{2} .
Nonlinear Inverse Problem for an Ion-Exchange Filter Model: Numerical Recovery of Parameters
Directory of Open Access Journals (Sweden)
Balgaisha Mukanova
2015-01-01
Full Text Available This paper considers the problem of identifying unknown parameters for a mathematical model of an ion-exchange filter via measurement at the outlet of the filter. The proposed mathematical model consists of a material balance equation, an equation describing the kinetics of ion-exchange for the nonequilibrium case, and an equation for the ion-exchange isotherm. The material balance equation includes a nonlinear term that depends on the kinetics of ion-exchange and several parameters. First, a numerical solution of the direct problem, the calculation of the impurities concentration at the outlet of the filter, is provided. Then, the inverse problem, finding the parameters of the ion-exchange process in nonequilibrium conditions, is formulated. A method for determining the approximate values of these parameters from the impurities concentration measured at the outlet of the filter is proposed.
Doyuran, Adnan; Joshi, Chandrashekhar; Lim, Jae; Rosenzweig, James E; Tochitsky, Sergei Ya; Travish, Gil; Williams, Oliver
2005-01-01
An Inverse Compton Scattering (ICS) experiment investigating the polarized harmonic production in the nonlinear regime has begun which will utilize the existing terawatt CO2 laser system and 15 MeV photoinjector in the Neptune Laboratory at UCLA. A major motivation for a source of high brightness polarized x-rays is the production of polarized positrons for use in future linear collider experiments. Analytical calculations have been performed to predict the angular and frequency spectrums for various polarizations and different scattering angles. Currently, the experiment is running and we report the set-up and initial results. The advantages and limitations of using a high laser vector potential, ao, in an ICS-based polarized positron source are expected to be revealed with further measurement of the harmonic spectrum and angular characteristics.
Energy Technology Data Exchange (ETDEWEB)
Belendez, A; Gimeno, E; Mendez, D I; Alvarez, M L [Departamento de Fisica, IngenierIa de Sistemas y TeorIa de la Senal, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain); Fernandez, E [Departamento de Optica, FarmacologIa y AnatomIa, Universidad de Alicante, Apartado 99, E-03080 Alicante (Spain)], E-mail: a.belendez@ua.es
2008-06-15
A modified generalized, rational harmonic balance method is used to construct approximate frequency-amplitude relations for a conservative nonlinear singular oscillator in which the restoring force is inversely proportional to the dependent variable. The procedure is used to solve the nonlinear differential equation approximately. The approximate frequency obtained using this procedure is more accurate than those obtained using other approximate methods and the discrepancy between the approximate frequency and the exact one is lower than 0.40%.
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.
10th International Geostatistics Congress
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.
Nonlinear inversion of potential-field data using a hybrid-encoding genetic algorithm
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
Directory of Open Access Journals (Sweden)
Y. Sakai
2017-06-01
Full Text Available Inverse Compton scattering (ICS is a unique mechanism for producing fast pulses—picosecond and below—of bright photons, ranging from x to γ rays. These nominally narrow spectral bandwidth electromagnetic radiation pulses are efficiently produced in the interaction between intense, well-focused electron and laser beams. The spectral characteristics of such sources are affected by many experimental parameters, with intense laser effects often dominant. A laser field capable of inducing relativistic oscillatory motion may give rise to harmonic generation and, importantly for the present work, nonlinear redshifting, both of which dilute the spectral brightness of the radiation. As the applications enabled by this source often depend sensitively on its spectra, it is critical to resolve the details of the wavelength and angular distribution obtained from ICS collisions. With this motivation, we present an experimental study that greatly improves on previous spectral measurement methods based on x-ray K-edge filters, by implementing a multilayer bent-crystal x-ray spectrometer. In tandem with a collimating slit, this method reveals a projection of the double differential angular-wavelength spectrum of the ICS radiation in a single shot. The measurements enabled by this diagnostic illustrate the combined off-axis and nonlinear-field-induced redshifting in the ICS emission process. The spectra obtained illustrate in detail the strength of the normalized laser vector potential, and provide a nondestructive measure of the temporal and spatial electron-laser beam overlap.
Directory of Open Access Journals (Sweden)
Syed Zaki Hassan Kazmi
Full Text Available The dynamical fluctuations in the rhythms of biological systems provide valuable information about the underlying functioning of these systems. During the past few decades analysis of cardiac function based on the heart rate variability (HRV; variation in R wave to R wave intervals has attracted great attention, resulting in more than 17000-publications (PubMed list. However, it is still controversial about the underling mechanisms of HRV. In this study, we performed both linear (time domain and frequency domain and nonlinear analysis of HRV data acquired from humans and animals to identify the relationship between HRV and heart rate (HR. The HRV data consists of the following groups: (a human normal sinus rhythm (n = 72; (b human congestive heart failure (n = 44; (c rabbit sinoatrial node cells (SANC; n = 67; (d conscious rat (n = 11. In both human and animal data at variant pathological conditions, both linear and nonlinear analysis techniques showed an inverse correlation between HRV and HR, supporting the concept that HRV is dependent on HR, and therefore, HRV cannot be used in an ordinary manner to analyse autonomic nerve activity of a heart.
Sakai, Y.; Gadjev, I.; Hoang, P.; Majernik, N.; Nause, A.; Fukasawa, A.; Williams, O.; Fedurin, M.; Malone, B.; Swinson, C.; Kusche, K.; Polyanskiy, M.; Babzien, M.; Montemagno, M.; Zhong, Z.; Siddons, P.; Pogorelsky, I.; Yakimenko, V.; Kumita, T.; Kamiya, Y.; Rosenzweig, J. B.
2017-06-01
Inverse Compton scattering (ICS) is a unique mechanism for producing fast pulses—picosecond and below—of bright photons, ranging from x to γ rays. These nominally narrow spectral bandwidth electromagnetic radiation pulses are efficiently produced in the interaction between intense, well-focused electron and laser beams. The spectral characteristics of such sources are affected by many experimental parameters, with intense laser effects often dominant. A laser field capable of inducing relativistic oscillatory motion may give rise to harmonic generation and, importantly for the present work, nonlinear redshifting, both of which dilute the spectral brightness of the radiation. As the applications enabled by this source often depend sensitively on its spectra, it is critical to resolve the details of the wavelength and angular distribution obtained from ICS collisions. With this motivation, we present an experimental study that greatly improves on previous spectral measurement methods based on x-ray K -edge filters, by implementing a multilayer bent-crystal x-ray spectrometer. In tandem with a collimating slit, this method reveals a projection of the double differential angular-wavelength spectrum of the ICS radiation in a single shot. The measurements enabled by this diagnostic illustrate the combined off-axis and nonlinear-field-induced redshifting in the ICS emission process. The spectra obtained illustrate in detail the strength of the normalized laser vector potential, and provide a nondestructive measure of the temporal and spatial electron-laser beam overlap.
Adaptive fuzzy control with smooth inverse for nonlinear systems preceded by non-symmetric dead-zone
Wang, Xingjian; Wang, Shaoping
2016-07-01
In this study, the adaptive output feedback control problem of a class of nonlinear systems preceded by non-symmetric dead-zone is considered. To cope with the possible control signal chattering phenomenon which is caused by non-smooth dead-zone inverse, a new smooth inverse is proposed for non-symmetric dead-zone compensation. For the systematic design procedure of the adaptive fuzzy control algorithm, we combine the backstepping technique and small-gain approach. The Takagi-Sugeno fuzzy logic systems are used to approximate unknown system nonlinearities. The closed-loop stability is studied by using small gain theorem and the closed-loop system is proved to be semi-globally uniformly ultimately bounded. Simulation results indicate that, compared to the algorithm with the non-smooth inverse, the proposed control strategy can achieve better tracking performance and the chattering phenomenon can be avoided effectively.
7th International Geostatistics Congress
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...
4th International Geostatistics Congress
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.
Llibre, Jaume; Ramírez, Rafael; Ramírez, Valentín
2017-09-01
We consider polynomial vector fields X with a linear type and with homogenous nonlinearities. It is well-known that X has a center at the origin if and only if X has an analytic first integral of the form H =1/2 (x2 +y2) + ∑ j = 3 ∞Hj, where Hj =Hj (x , y) is a homogenous polynomial of degree j. The classical center-focus problem already studied by H. Poincaré consists in distinguishing when the origin of X is either a center or a focus. In this paper we study the inverse center-focus problem. In particular for a given analytic function H defined in a neighborhood of the origin we want to determine the homogenous polynomials in such a way that H is a first integral of X and consequently the origin of X will be a center. We study the particular case of centers which have a local analytic first integral of the form H =1/2 (x2 +y2) (1 + ∑ j = 1 ∞ϒj) , in a neighborhood of the origin, where ϒj is a convenient homogenous polynomial of degree j, for j ≥ 1. These centers are called weak centers, they contain the class of center studied by Alwash and Lloyd, the uniform isochronous centers and the isochronous holomorphic centers, but they do not coincide with the class of isochronous centers. We give a classification of the weak centers for quadratic and cubic vector fields with homogenous nonlinearities.
CHAOS-REGULARIZATION HYBRID ALGORITHM FOR NONLINEAR TWO-DIMENSIONAL INVERSE HEAT CONDUCTION PROBLEM
Institute of Scientific and Technical Information of China (English)
王登刚; 刘迎曦; 李守巨
2002-01-01
A numerical model of nonlinear two-dimensional steady inverse heat conduction problem was established considering the thermal conductivity changing with temperature.Combining the chaos optimization algorithm with the gradient regularization method, a chaos-regularization hybrid algorithm was proposed to solve the established numerical model.The hybrid algorithm can give attention to both the advantages of chaotic optimization algorithm and those of gradient regularization method. The chaos optimization algorithm was used to help the gradient regalarization method to escape from local optima in the hybrid algorithm. Under the assumption of temperature-dependent thermal conductivity changing with temperature in linear rule, the thermal conductivity and the linear rule were estimated by using the present method with the aid of boundary temperature measurements. Numerical simulation results show that good estimation on the thermal conductivity and the linear function can be obtained with arbitrary initial guess values, and that the present hybrid algorithm is much more efficient than conventional genetic algorithm and chaos optimization algorithm.
Directory of Open Access Journals (Sweden)
S. L. Han
2012-01-01
Full Text Available The nonlinear responses of ship rolling motion characterized by a roll damping moment are of great interest to naval architects and ocean engineers. Modeling and identification of the nonlinear damping moment are essential to incorporate the inherent nonlinearity in design, analysis, and control of a ship. A stochastic nonparametric approach for identification of nonlinear damping in the general mechanical system has been presented in the literature (Han and Kinoshits 2012. The method has been also applied to identification of the nonlinear damping moment of a ship at zero-forward speed (Han and Kinoshits 2013. In the presence of forward speed, however, the characteristic of roll damping moment of a ship is significantly changed due to the lift effect. In this paper, the stochastic inverse method is applied to identification of the nonlinear damping moment of a ship moving at nonzero-forward speed. The workability and validity of the method are verified with laboratory tests under controlled conditions. In experimental trials, two different types of ship rolling motion are considered: time-dependent transient motion and frequency-dependent periodic motion. It is shown that this method enables the inherent nonlinearity in damping moment to be estimated, including its reliability analysis.
Directory of Open Access Journals (Sweden)
Na Duan
2012-01-01
Full Text Available The adaptive stabilization scheme based on tuning function for stochastic nonlinear systems with stochastic integral input-to-state stability (SiISS inverse dynamics is investigated. By combining the stochastic LaSalle theorem and small-gain type conditions on SiISS, an adaptive output feedback controller is constructively designed. It is shown that all the closed-loop signals are bounded almost surely and the stochastic closed-loop system is globally stable in probability.
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.
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.
Elizondo, D.; Cappelaere, B.; Faure, Ch.
2002-04-01
Emerging tools for automatic differentiation (AD) of computer programs should be of great benefit for the implementation of many derivative-based numerical methods such as those used for inverse modeling. The Odyssée software, one such tool for Fortran 77 codes, has been tested on a sample model that solves a 2D non-linear diffusion-type equation. Odyssée offers both the forward and the reverse differentiation modes, that produce the tangent and the cotangent models, respectively. The two modes have been implemented on the sample application. A comparison is made with a manually-produced differentiated code for this model (MD), obtained by solving the adjoint equations associated with the model's discrete state equations. Following a presentation of the methods and tools and of their relative advantages and drawbacks, the performances of the codes produced by the manual and automatic methods are compared, in terms of accuracy and of computing efficiency (CPU and memory needs). The perturbation method (finite-difference approximation of derivatives) is also used as a reference. Based on the test of Taylor, the accuracy of the two AD modes proves to be excellent and as high as machine precision permits, a good indication of Odyssée's capability to produce error-free codes. In comparison, the manually-produced derivatives (MD) sometimes appear to be slightly biased, which is likely due to the fact that a theoretical model (state equations) and a practical model (computer program) do not exactly coincide, while the accuracy of the perturbation method is very uncertain. The MD code largely outperforms all other methods in computing efficiency, a subject of current research for the improvement of AD tools. Yet these tools can already be of considerable help for the computer implementation of many numerical methods, avoiding the tedious task of hand-coding the differentiation of complex algorithms.
Santaren, D.; Peylin, P.; Viovy, N.; Ciais, P.
2003-04-01
Global model of Carbone, water, and energy exchanges between the biosphere and the atmosphere are usually validated and calibrated with intensive measurement made over specific ecosystem like those of the fluxnet networks.However the nonlinear dependance between fluxes and model parameters generally complicate the optimization of the major parameters.In this study, we estimate few key parameters of the ORCHIDEE french model,using diurnal variation measurements of latent heat,sensible heat and net CO2 fluxes for 3 weeks over pine forest (Landes, France).The model is forced with the observed climatic forcing: Temperature, income solar radiations,wind velocity norm, air humidity, pressure and precipitations. We will first present the inverse methodology and the problem linkedto the non linearity. The result of the optimization shows correlations within the initial ensemble of parameters which allow us to choose only five parameters determined independently from the observations. Directly related to the net CO2 flux, the maximum rate of carboxylation,Vcmax,and the stomatal conductance, gs, are significantly changed from their apriori estimate for that period. The aerodynamic resistance, the albedo and a parameter linked to maintenance respiration were also modified within their physical range.Overall the model fit to the data was largely improved. Note however that some discrepancies remain for sensible heat flux which would probably require some model improvements for the stocking of energy in the soil. Such work is currently extended in time to account for parameter variations between the season. The application to other ecosystems and with the supplementary data of the Leaf Area Index will be also discussed.
Convergence of Chahine's nonlinear relaxation inversion method used for limb viewing remote sensing
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.
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
Chew, Huck Beng
2013-01-01
Determining the tractions along a surface or interface from measurement data in the far-fields of nonlinear materials is a challenging inverse problem which has significant engineering and nanoscience applications. Previously, a field projection method was established to identify the crack-tip cohesive zone constitutive relations in an isotropic elastic solid (Hong and Kim, 2003. J. Mech. Phys. Solids 51, 1267). In this paper, the field projection method is further generalized to extracting the tractions along interfaces bounded by nonlinear materials, both with and without pre-existing cracks. The new formulation is based on Maxwell-Betti's reciprocal theorem with a reciprocity gap associated with nonlinear materials. We express the unknown normal and shear tractions along the interface in terms of the Fourier series, and use specially constructed analytical auxiliary fields in the reciprocal theorem to extract the unknown Fourier coefficients from far-field data; the reciprocity gap in the formulation is iteratively determined with a set of numerical algorithms. Our detailed numerical experiments demonstrate that this nonlinear field projection method (NFPM) is well-suited for extracting the interfacial tractions from the far-field data of any nonlinear elastic or elasto-plastic material with known constitutive laws. Applications of the NFPM to experiments and atomistic simulations are discussed.
Stochastic Local Interaction (SLI) model: Bridging machine learning and geostatistics
Hristopulos, Dionissios T.
2015-12-01
Machine learning and geostatistics are powerful mathematical frameworks for modeling spatial data. Both approaches, however, suffer from poor scaling of the required computational resources for large data applications. We present the Stochastic Local Interaction (SLI) model, which employs a local representation to improve computational efficiency. SLI combines geostatistics and machine learning with ideas from statistical physics and computational geometry. It is based on a joint probability density function defined by an energy functional which involves local interactions implemented by means of kernel functions with adaptive local kernel bandwidths. SLI is expressed in terms of an explicit, typically sparse, precision (inverse covariance) matrix. This representation leads to a semi-analytical expression for interpolation (prediction), which is valid in any number of dimensions and avoids the computationally costly covariance matrix inversion.
Ranjan, Rajiv; Mallick, Ashis; Prasad, Dilip K.
2016-07-01
The performance characteristics and temperature field of conducting-convecting-radiating annular fin are investigated. The nonlinear variation of thermal conductivity, power law dependency of heat transfer coefficient, linear variation of surface emissivity, and heat generation with the temperature are considered in the analysis. A semi-analytical approach, homotopy perturbation method is employed to solve the nonlinear differential equation of heat transfer. The analysis is presented in non-dimensional form, and the effect of various non-dimensional thermal parameters such as conduction-convection parameter, conduction-radiation parameter, linear and nonlinear variable thermal conductivity parameter, emissivity parameter, heat generation number and variable heat generation parameter are studied. For the correctness of the present analytical solution, the results are compared with the results available in the literature. In addition to forward problem, an inverse approach namely differential evolution method is employed for estimating the unknown thermal parameters for a given temperature field. The temperature fields are reconstructed using the inverse parameters and found to be in good agreement with the forward solution.
Ranjan, Rajiv; Mallick, Ashis; Prasad, Dilip K.
2017-03-01
The performance characteristics and temperature field of conducting-convecting-radiating annular fin are investigated. The nonlinear variation of thermal conductivity, power law dependency of heat transfer coefficient, linear variation of surface emissivity, and heat generation with the temperature are considered in the analysis. A semi-analytical approach, homotopy perturbation method is employed to solve the nonlinear differential equation of heat transfer. The analysis is presented in non-dimensional form, and the effect of various non-dimensional thermal parameters such as conduction-convection parameter, conduction-radiation parameter, linear and nonlinear variable thermal conductivity parameter, emissivity parameter, heat generation number and variable heat generation parameter are studied. For the correctness of the present analytical solution, the results are compared with the results available in the literature. In addition to forward problem, an inverse approach namely differential evolution method is employed for estimating the unknown thermal parameters for a given temperature field. The temperature fields are reconstructed using the inverse parameters and found to be in good agreement with the forward solution.
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.
Model Selection for Geostatistical Models
Energy Technology Data Exchange (ETDEWEB)
Hoeting, Jennifer A.; Davis, Richard A.; Merton, Andrew A.; Thompson, Sandra E.
2006-02-01
We consider the problem of model selection for geospatial data. Spatial correlation is typically ignored in the selection of explanatory variables and this can influence model selection results. For example, the inclusion or exclusion of particular explanatory variables may not be apparent when spatial correlation is ignored. To address this problem, we consider the Akaike Information Criterion (AIC) as applied to a geostatistical model. We offer a heuristic derivation of the AIC in this context and provide simulation results that show that using AIC for a geostatistical model is superior to the often used approach of ignoring spatial correlation in the selection of explanatory variables. These ideas are further demonstrated via a model for lizard abundance. We also employ the principle of minimum description length (MDL) to variable selection for the geostatistical model. The effect of sampling design on the selection of explanatory covariates is also explored.
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.
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.
Biondini, Gino; Fagerstrom, Emily; Prinari, Barbara
2016-10-01
We formulate the inverse scattering transform (IST) for the defocusing nonlinear Schrödinger (NLS) equation with fully asymmetric non-zero boundary conditions (i.e., when the limiting values of the solution at space infinities have different non-zero moduli). The theory is formulated without making use of Riemann surfaces, and instead by dealing explicitly with the branched nature of the eigenvalues of the associated scattering problem. For the direct problem, we give explicit single-valued definitions of the Jost eigenfunctions and scattering coefficients over the whole complex plane, and we characterize their discontinuous behavior across the branch cut arising from the square root behavior of the corresponding eigenvalues. We pose the inverse problem as a Riemann-Hilbert Problem on an open contour, and we reduce the problem to a standard set of linear integral equations. Finally, for comparison purposes, we present the single-sheet, branch cut formulation of the inverse scattering transform for the initial value problem with symmetric (equimodular) non-zero boundary conditions, as well as for the initial value problem with one-sided non-zero boundary conditions, and we also briefly describe the formulation of the inverse scattering transform when a different choice is made for the location of the branch cuts.
Directory of Open Access Journals (Sweden)
Nemat Dalir
2014-01-01
Full Text Available Singular nonlinear initial-value problems (IVPs in first-order and second-order partial differential equations (PDEs arising in fluid mechanics are semianalytically solved. To achieve this, the modified decomposition method (MDM is used in conjunction with some new inverse differential operators. In other words, new inverse differential operators are developed for the MDM and used with the MDM to solve first- and second-order singular nonlinear PDEs. The results of the solutions by the MDM together with new inverse operators are compared with the existing exact analytical solutions. The comparisons show excellent agreement.
Institute of Scientific and Technical Information of China (English)
POUZO; Demian
2009-01-01
This paper considers the estimation of an unknown function h that can be characterized as a solution to a nonlinear operator equation mapping between two infinite dimensional Hilbert spaces. The nonlinear operator is unknown but can be consistently estimated, and its inverse is discontinuous, rendering the problem ill-posed. We establish the consistency for the class of estimators that are regularized using general lower semicompact penalty functions. We derive the optimal convergence rates of the estimators under the Hilbert scale norms. We apply our results to two important problems in economics and finance: (1) estimating the parameters of the pricing kernel of defaultable bonds; (2) recovering the volatility surface implied by option prices allowing for measurement error in the option prices and numerical error in the computation of the operator.
Institute of Scientific and Technical Information of China (English)
CHEN XiaoHong; POUZO Demian
2009-01-01
This paper considers the estimation of an unknown function h that can be characterized as a solution to a nonlinear operator equation mapping between two infinite dimensional Hilbert spaces.The nonlinear operator is unknown but can be consistently estimated, and its inverse is discontinuous,rendering the problem ill-posed. We establish the consistency for the class of estimators that are regularized using general lower semicompact penalty functions. We derive the optimal convergence rates of the estimators under the Hilbert scale norms. We apply our results to two important problems in economics and finance: (1) estimating the parameters of the pricing kernel of defaultable bonds; (2)recovering the volatility surface implied by option prices allowing for measurement error in the option prices and numerical error in the computation of the operator.
Romano, F.; Piatanesi, A.; Lorito, S.; Tolomei, C.; Atzori, S.; Murphy, S.
2016-11-01
Tsunami waveform inversion is often used to retrieve information about the causative seismic tsunami source. Tide gauges record tsunamis routinely; however, compared to deep-ocean sensor data, tide-gauge waveform modeling is more difficult due to coarse/inaccurate local bathymetric models resulting in a time mismatch between observed and predicted waveforms. This can affect the retrieved tsunami source model, thus limiting the use of tide-gauge data. A method for nonlinear inversion with an automatic optimal time alignment (OTA), calculated by including a time shift parameter in the cost function, is presented. The effectiveness of the method is demonstrated through a series of synthetic tests and is applied as part of a joint inversion with interferometric synthetic aperture radar data for the slip distribution of the 2015 Mw 8.3 Illapel earthquake. The results show that without OTA, the resolution on the slip model degrades significantly and that using this method for a real case strongly affects the retrieved slip pattern.
Liu, Pengcheng; Archuleta, Ralph J.
2004-02-01
We present a new procedure to invert for kinematic source parameters on a finite fault. On the basis of the reciprocity relation of the Green's functions, we use a newly developed fourth-order viscoelastic finite-difference algorithm to calculate three-dimensional (3-D) Green's functions (actually the tractions) on the fault. We invert the data for the unknown source parameters at the nodes (or corners) of the subfaults. The source parameters within a subfault area are allowed to vary; this variation is calculated through bilinear interpolation of the four nodal quantities. We have developed a global nonlinear inversion algorithm that is based on simulated annealing methods to solve efficiently for the nodal parameters. We apply this method to the 1989 Loma Prieta, California, M 6.9 earthquake for both a 1-D and 3-D velocity structure. We show (1) the bilinear interpolation technique reduces the dependence of inversion results on the subfault size by naturally including the effects of nearby subfaults. (2) While the number of synthetic seismograms that must be computed is greatly increased by the bilinear interpolation, the structure of the inversion method minimizes the actual numbers of computations. (3) As expected, complexity in the velocity structure is mapped into the source parameters that describe the rupture process; there are significant differences between faulting models derived from 1-D and 3-D structural models.
Directory of Open Access Journals (Sweden)
G. Forget
2015-10-01
Full Text Available This paper presents the ECCO v4 non-linear inverse modeling framework and its baseline solution for the evolving ocean state over the period 1992–2011. Both components are publicly available and subjected to regular, automated regression tests. The modeling framework includes sets of global conformal grids, a global model setup, implementations of data constraints and control parameters, an interface to algorithmic differentiation, as well as a grid-independent, fully capable Matlab toolbox. The baseline ECCO v4 solution is a dynamically consistent ocean state estimate without unidentified sources of heat and buoyancy, which any interested user will be able to reproduce accurately. The solution is an acceptable fit to most data and has been found to be physically plausible in many respects, as documented here and in related publications. Users are being provided with capabilities to assess model–data misfits for themselves. The synergy between modeling and data synthesis is asserted through the joint presentation of the modeling framework and the state estimate. In particular, the inverse estimate of parameterized physics was instrumental in improving the fit to the observed hydrography, and becomes an integral part of the ocean model setup available for general use. More generally, a first assessment of the relative importance of external, parametric and structural model errors is presented. Parametric and external model uncertainties appear to be of comparable importance and dominate over structural model uncertainty. The results generally underline the importance of including turbulent transport parameters in the inverse problem.
Towards adjoint-based inversion of time-dependent mantle convection with non-linear viscosity
Li, Dunzhu; Gurnis, Michael; Stadler, Georg
2017-01-01
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- 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 preconditioned 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.
Assessing the resolution-dependent utility of tomograms for geostatistics
Day-Lewis, F. D.; Lane, J.W.
2004-01-01
Geophysical tomograms are used increasingly as auxiliary data for geostatistical modeling of aquifer and reservoir properties. The correlation between tomographic estimates and hydrogeologic properties is commonly based on laboratory measurements, co-located measurements at boreholes, or petrophysical models. The inferred correlation is assumed uniform throughout the interwell region; however, tomographic resolution varies spatially due to acquisition geometry, regularization, data error, and the physics underlying the geophysical measurements. Blurring and inversion artifacts are expected in regions traversed by few or only low-angle raypaths. In the context of radar traveltime tomography, we derive analytical models for (1) the variance of tomographic estimates, (2) the spatially variable correlation with a hydrologic parameter of interest, and (3) the spatial covariance of tomographic estimates. Synthetic examples demonstrate that tomograms of qualitative value may have limited utility for geostatistics; moreover, the imprint of regularization may preclude inference of meaningful spatial statistics from tomograms.
Anchal, Abhishek; Kumar, Pradeep; Landais, Pascal
2016-10-01
We propose and numerically verify a scheme of frequency-shift free mid-span spectral inversion (MSSI) for nonlinearity mitigation in an optical transmission system. Spectral inversion is accomplished by optical phase conjugation, realized by counter-propagating dual pumped four-wave mixing in a highly nonlinear fiber. We examine the performance of MSSI due to critical parameters such as nonlinear fiber length, pump and signal power. We demonstrate the near complete nonlinearity mitigation of 40 Gbps DQPSK modulated data transmitted over 1000 km standard single mode fiber using our method of MSSI. We perform simulation of bit-error rate as a function of optical signal to noise ratio to corroborate the effect of frequency-shift free MSSI.
DEFF Research Database (Denmark)
Rubæk, Tonny; Meaney, P. M.; Meincke, Peter;
2007-01-01
Breast-cancer screening using microwave imaging is emerging as a new promising technique as a supplement to X-ray mammography. To create tomographic images from microwave measurements, it is necessary to solve a nonlinear inversion problem, for which an algorithm based on the iterative Gauss-Newton...... method has been developed at Dartmouth College. This algorithm determines the update values at each iteration by solving the set of normal equations of the problem using the Tikhonov algorithm. In this paper, a new algorithm for determining the iteration update values in the Gauss-Newton algorithm...... algorithm is compared to the Gauss-Newton algorithm with Tikhonov regularization and is shown to reconstruct images of similar quality using fewer iterations....
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.
Sakhnovich, Lev A; Roitberg, Inna Ya
2013-01-01
This monograph fits theclearlyneed for books with a rigorous treatment of theinverse problems for non-classical systems and that of initial-boundary-value problems for integrable nonlinear equations. The authorsdevelop a unified treatment of explicit and global solutions via the transfer matrix function in a form due to Lev A. Sakhnovich. The book primarily addresses specialists in the field. However, it is self-contained andstarts with preliminaries and examples, and hencealso serves as an introduction for advanced graduate students in the field.
Balkaya, Çağlayan; Ekinci, Yunus Levent; Göktürkler, Gökhan; Turan, Seçil
2017-01-01
3D non-linear inversion of total field magnetic anomalies caused by vertical-sided prismatic bodies has been achieved by differential evolution (DE), which is one of the population-based evolutionary algorithms. We have demonstrated the efficiency of the algorithm on both synthetic and field magnetic anomalies by estimating horizontal distances from the origin in both north and east directions, depths to the top and bottom of the bodies, inclination and declination angles of the magnetization, and intensity of magnetization of the causative bodies. In the synthetic anomaly case, we have considered both noise-free and noisy data sets due to two vertical-sided prismatic bodies in a non-magnetic medium. For the field case, airborne magnetic anomalies originated from intrusive granitoids at the eastern part of the Biga Peninsula (NW Turkey) which is composed of various kinds of sedimentary, metamorphic and igneous rocks, have been inverted and interpreted. Since the granitoids are the outcropped rocks in the field, the estimations for the top depths of two prisms representing the magnetic bodies were excluded during inversion studies. Estimated bottom depths are in good agreement with the ones obtained by a different approach based on 3D modelling of pseudogravity anomalies. Accuracy of the estimated parameters from both cases has been also investigated via probability density functions. Based on the tests in the present study, it can be concluded that DE is a useful tool for the parameter estimation of source bodies using magnetic anomalies.
Directory of Open Access Journals (Sweden)
G. Forget
2015-05-01
Full Text Available This paper presents the ECCO v4 non-linear inverse modeling framework and its baseline solution for the evolving ocean state over the period 1992–2011. Both components are publicly available and highly integrated with the MITgcm. They are both subjected to regular, automated regression tests. The modeling framework includes sets of global conformal grids, a global model setup, implementations of model-data constraints and adjustable control parameters, an interface to algorithmic differentiation, as well as a grid-independent, fully capable Matlab toolbox. The reference ECCO v4 solution is a dynamically consistent ocean state estimate (ECCO-Production, release 1 without un-identified sources of heat and buoyancy, which any interested user will be able to reproduce accurately. The solution is an acceptable fit to most data and has been found physically plausible in many respects, as documented here and in related publications. Users are being provided with capabilities to assess model-data misfits for themselves. The synergy between modeling and data synthesis is asserted through the joint presentation of the modeling framework and the state estimate. In particular, the inverse estimate of parameterized physics was instrumental in improving the fit to the observed hydrography, and becomes an integral part of the ocean model setup available for general use. More generally, a first assessment of the relative importance of external, parametric and structural model errors is presented. Parametric and external model uncertainties appear to be of comparable importance and dominate over structural model uncertainty. The results generally underline the importance of including turbulent transport parameters in the inverse problem.
Geodynamic inversion to constrain the non-linear rheology of the lithosphere
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
Weakly nonlinear models for internal waves: inverse scattering transform and solitary wave contents
Chen, Shengqian
2016-01-01
The time evolution emanating from ``internal dam-break'' initial conditions is studied for a class of models of stratified Euler fluids in configurations close to two-homogeneous layers separated by a thin diffused interface. Direct numerical simulations and experiments in wave tanks show that such initial conditions eventually give rise to coherent structures that are close to solitary-wave solutions moving ahead of a region of dispersive wave motion and turbulent mixing close to the location of the initial dam step. A priori theoretical predictions of the main features of these solitary waves, such as their amplitudes and speeds, appear to be unavailable, even for simplified models of wave evolution in stratified fluids. With the aim of providing estimates of the existence, amplitude and speed of such solitary waves, an approach based on Inverse Scattering Transform (IST) for completely integrable models is developed here and tested against direct numerical simulations of Euler fluids and some of their mode...
Waite, Gregory P.; Lanza, Federica
2016-10-01
Magmatic processes produce a rich variety of volcano seismic signals, ranging over several orders of magnitude in frequency and over a wide range of mechanism types. We examined signals from 400 to 10 s period associated with explosive eruptions at Fuego volcano, Guatemala, that were recorded over 19 days in 2009 on broadband stations with 30 s and 60 s corner periods. The raw data from the closest stations include tilt effects on the horizontal components but also have significant signal at periods below the instrument corners on the vertical components, where tilt effects should be negligible. We address the problems of tilt-affected horizontal waveforms through a joint waveform inversion of translation and rotation, which allows for an investigation of the varying influence of tilt with period. Using a phase-weighted stack of six similar events, we invert for source moment tensor using multiple bands. We use a grid search for source type and constrained inversions, which provides a quantitative measure of source mechanism reliability. The 30-10 s band-pass results are consistent with previous work that modeled data with a combined two crack or crack and pipe model. At the longest-period band examined, 400-60 s, the source mechanism is like a pipe that could represent the shallowest portion of the conduit. On the other hand, source mechanisms in some bands are unconstrained, presumably due to the combined tilt-dominated and translation-dominated signals, which are not coincident in space and have different time spans.
Serum α-Tocopherol Has a Nonlinear Inverse Association with Periodontitis among US Adults.
Zong, Geng; Scott, Ann E; Griffiths, Helen R; Zock, Peter L; Dietrich, Thomas; Newson, Rachel S
2015-05-01
Previous experimental models suggest that vitamin E may ameliorate periodontitis. However, epidemiologic studies show inconsistent evidence in supporting this plausible association. We investigated the association between serum α-tocopherol (αT) and γ-tocopherol (γT) and periodontitis in a large cross-sectional US population. This study included 4708 participants in the 1999-2001 NHANES. Serum tocopherols were measured by HPLC and values were adjusted by total cholesterol (TC). Periodontal status was assessed by mean clinical attachment loss (CAL) and probing pocket depth (PPD). Total periodontitis (TPD) was defined as the sum of mild, moderate, and severe periodontitis. All measurements were performed by NHANES. Means ± SDs of serum αT:TC ratio from low to high quartiles were 4.0 ± 0.4, 4.8 ± 0.2, 5.7 ± 0.4, and 9.1 ± 2.7 μmol/mmol. In multivariate regression models, αT:TC quartiles were inversely associated with mean CAL (P-trend = 0.06), mean PPD (P-trend periodontitis, which was restricted to adults with normal but relatively low αT status. These findings warrant further confirmation in longitudinal or intervention studies. © 2015 American Society for Nutrition.
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...... function and data noise level. In addition, we have tested the methodology on traveltime data collected at a field site in Denmark. There, inferred correlation structures indicate that structural differences exist between two areas located approximately 10 m apart, an observation confirmed by a GPR...
DEFF Research Database (Denmark)
Troldborg, Mads; Nowak, Wolfgang; Binning, Philip John
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, ii) measurement uncertainty, and iii...... 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......) uncertain source zone and transport parameters. The method generates multiple equally likely realisations of the spatial flow and concentration distribution, which all honour the measured data at the control plane. The flow realisations are generated by co-simulating the hydraulic conductivity...
Use of geostatistics for remediation planning to transcend urban political boundaries.
Milillo, Tammy M; Sinha, Gaurav; Gardella, Joseph A
2012-11-01
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.
Application of geostatistics to risk assessment.
Thayer, William C; Griffith, Daniel A; Goodrum, Philip E; Diamond, Gary L; Hassett, James M
2003-10-01
Geostatistics offers two fundamental contributions to environmental contaminant exposure assessment: (1) a group of methods to quantitatively describe the spatial distribution of a pollutant and (2) the ability to improve estimates of the exposure point concentration by exploiting the geospatial information present in the data. The second contribution is particularly valuable when exposure estimates must be derived from small data sets, which is often the case in environmental risk assessment. This article addresses two topics related to the use of geostatistics in human and ecological risk assessments performed at hazardous waste sites: (1) the importance of assessing model assumptions when using geostatistics and (2) the use of geostatistics to improve estimates of the exposure point concentration (EPC) in the limited data scenario. The latter topic is approached here by comparing design-based estimators that are familiar to environmental risk assessors (e.g., Land's method) with geostatistics, a model-based estimator. In this report, we summarize the basics of spatial weighting of sample data, kriging, and geostatistical simulation. We then explore the two topics identified above in a case study, using soil lead concentration data from a Superfund site (a skeet and trap range). We also describe several areas where research is needed to advance the use of geostatistics in environmental risk assessment.
Inverse problems with non-trivial priors: efficient solution through sequential Gibbs sampling
DEFF Research Database (Denmark)
Hansen, Thomas Mejer; Cordua, Knud Skou; Mosegaard, Klaus
2012-01-01
Markov chain Monte Carlo methods such as the Gibbs sampler and the Metropolis algorithm can be used to sample solutions to non-linear inverse problems. In principle, these methods allow incorporation of prior information of arbitrary complexity. If an analytical closed form description of the pri...... also reduce the computation time for the inversion dramatically. The method works for any statistical model for which sequential simulation can be used to generate realizations. This applies to most algorithms developed in the geostatistical community.......Markov chain Monte Carlo methods such as the Gibbs sampler and the Metropolis algorithm can be used to sample solutions to non-linear inverse problems. In principle, these methods allow incorporation of prior information of arbitrary complexity. If an analytical closed form description of the prior...... for applying the sequential Gibbs sampler and illustrate how it works. Through two case studies, we demonstrate the application of the method to a linear image restoration problem and to a non-linear cross-borehole inversion problem. We demonstrate how prior information can reduce the complexity of an inverse...
Energy Technology Data Exchange (ETDEWEB)
Daouas, N.; Radhouani, M.S. [Ecole Nationale d' Ingenieurs de Monastir, Dept. de Genie-Energetique, Monastir (Tunisia)
2000-02-01
Nonlinear inverse heat conduction problem is resolved by using a formulation of the Kalman filter based on a statistical approach and extended to nonlinear systems. The time evolution of a surface heat flux density is reconstructed from a numerical simulation which allowed us to analyse the influence of some parameters, that condition the running of the filter, on the estimation result. A suitable choice of these parameters, guided by the filter behaviour observations, leads to a solution that remains stable when using noisy data, but that is slightly time-lagged compared to the exact function. This time-lag depends on the location of the interior temperature measurement needed for the inversion and on the model error caused by the approximation of the heat flux with a piece-wide constant function. The application of the extended Kalman filter with real measurements recorded from an experimental set-up, shows that this technique fits the stochastic structure of experimental measurements. The provided results are validated by using the Raynaud's and Bransier's inverse method and are in good agreement with the flux density estimated with this method. (authors)
Assessment of spatial distribution of fallout radionuclides through geostatistics concept.
Mabit, L; Bernard, C
2007-01-01
After introducing geostatistics concept and its utility in environmental science and especially in Fallout Radionuclide (FRN) spatialisation, a case study for cesium-137 ((137)Cs) redistribution at the field scale using geostatistics is presented. On a Canadian agricultural field, geostatistics coupled with a Geographic Information System (GIS) was used to test three different techniques of interpolation [Ordinary Kriging (OK), Inverse Distance Weighting power one (IDW1) and two (IDW2)] to create a (137)Cs map and to establish a radioisotope budget. Following the optimization of variographic parameters, an experimental semivariogram was developed to determine the spatial dependence of (137)Cs. It was adjusted to a spherical isotropic model with a range of 30 m and a very small nugget effect. This (137)Cs semivariogram showed a good autocorrelation (R(2)=0.91) and was well structured ('nugget-to-sill' ratio of 4%). It also revealed that the sampling strategy was adequate to reveal the spatial correlation of (137)Cs. The spatial redistribution of (137)Cs was estimated by Ordinary Kriging and IDW to produce contour maps. A radioisotope budget was established for the 2.16 ha agricultural field under investigation. It was estimated that around 2 x 10(7)Bq of (137)Cs were missing (around 30% of the total initial fallout) and were exported by physical processes (runoff and erosion processes) from the area under investigation. The cross-validation analysis showed that in the case of spatially structured data, OK is a better interpolation method than IDW1 or IDW2 for the assessment of potential radioactive contamination and/or pollution.
Jiang, Yi; Li, Guo-Yang; Qian, Lin-Xue; Hu, Xiang-Dong; Liu, Dong; Liang, Si; Cao, Yanping
2015-02-01
Dynamic elastography has become a new clinical tool in recent years to characterize the elastic properties of soft tissues in vivo, which are important for the disease diagnosis, e.g., the detection of breast and thyroid cancer and liver fibrosis. This paper investigates the supersonic shear imaging (SSI) method commercialized in recent years with the purpose to determine the nonlinear elastic properties based on this promising technique. Particularly, we explore the propagation of the shear wave induced by the acoustic radiation force in a stressed hyperelastic soft tissue described via the Demiray-Fung model. Based on the elastodynamics theory, an analytical solution correlating the wave speed with the hyperelastic parameters of soft tissues is first derived. Then an inverse approach is established to determine the hyperelastic parameters of biological soft tissues based on the measured wave speeds at different stretch ratios. The property of the inverse method, e.g., the existence, uniqueness and stability of the solution, has been investigated. Numerical experiments based on finite element simulations and the experiments conducted on the phantom and pig livers have been employed to validate the new method. Experiments performed on the human breast tissue and human heel fat pads have demonstrated the capability of the proposed method for measuring the in vivo nonlinear elastic properties of soft tissues. Generalization of the inverse analysis to other material models and the implication of the results reported here for clinical diagnosis have been discussed. Copyright © 2014 Elsevier B.V. All rights reserved.
An Interactive Bayesian Geostatistical Inverse Protocol for Hydraulic Tomography
2008-07-25
Boise State University, Boise, Idaho, USA. 3Civil and Environmental Engineering , Stanford University, Stanford, California, USA. Copyright 2008 by...probabilistic approach acknowledges the nonuniqueness of the parameter estimation problem and incorporates uncertainty from multiple sources into the...compression and image focusing, Geophysics, 67(5), 1532–1541, doi:10.1190/1.1512749. Sharma, P. V. (1997), Environmental and Engineering Geophysics, Cam
Reservoir Modeling Combining Geostatistics with Markov Chain Monte Carlo Inversion
DEFF Research Database (Denmark)
Zunino, Andrea; Lange, Katrine; Melnikova, Yulia;
2014-01-01
, multi-step forward model (rock physics and seismology) and to provide realistic estimates of uncertainties. To generate realistic models which represent samples of the prior distribution, and to overcome the high computational demand, we reduce the search space utilizing an algorithm drawn from...
Geostatistics and spatial analysis in biological anthropology.
Relethford, John H
2008-05-01
A variety of methods have been used to make evolutionary inferences based on the spatial distribution of biological data, including reconstructing population history and detection of the geographic pattern of natural selection. This article provides an examination of geostatistical analysis, a method used widely in geology but which has not often been applied in biological anthropology. Geostatistical analysis begins with the examination of a variogram, a plot showing the relationship between a biological distance measure and the geographic distance between data points and which provides information on the extent and pattern of spatial correlation. The results of variogram analysis are used for interpolating values of unknown data points in order to construct a contour map, a process known as kriging. The methods of geostatistical analysis and discussion of potential problems are applied to a large data set of anthropometric measures for 197 populations in Ireland. The geostatistical analysis reveals two major sources of spatial variation. One pattern, seen for overall body and craniofacial size, shows an east-west cline most likely reflecting the combined effects of past population dispersal and settlement. The second pattern is seen for craniofacial height and shows an isolation by distance pattern reflecting rapid spatial changes in the midlands region of Ireland, perhaps attributable to the genetic impact of the Vikings. The correspondence of these results with other analyses of these data and the additional insights generated from variogram analysis and kriging illustrate the potential utility of geostatistical analysis in biological anthropology.
Legaie, D.; Pron, H.; Bissieux, C.
2008-11-01
Integral transforms (Laplace, Fourier, Hankel) are widely used to solve the heat diffusion equation. Moreover, it often appears relevant to realize the estimation of thermophysical properties in the transformed space. Here, an analytical model has been developed, leading to a well-posed inverse problem of parameter identification. Two black coatings, a thin black paint layer and an amorphous carbon film, were studied by photothermal infrared thermography. A Hankel transform has been applied on both thermal model and data and the estimation of thermal diffusivity has been achieved in the Hankel space. The inverse problem is formulated as a non-linear least square problem and a Gauss-Newton algorithm is used for the parameter identification.
GEOPACK, a comprehensive user-friendly geostatistical software system, was developed to help in the analysis of spatially correlated data. The software system was developed to be used by scientists, engineers, regulators, etc., with little experience in geostatistical techniques...
DEFF Research Database (Denmark)
Sackey, Isaac; Da Ros, Francesco; Karl Fischer, Johannes;
2015-01-01
We experimentally investigate Kerr nonlinearity mitigation of a 28-GBd polarization-multiplexed 16-QAM signal in a five-channel 50-GHz spaced wavelength-division multiplexing (WDM) system. Optical phase conjugation (OPC) employing the mid-link spectral inversion technique is implemented by using...... a dual-pump polarization-independent fiber-optic parametric amplifier and compared to digital backpropagation (DBP) compensation over up to 800-km in a dispersion-managed link. In the single-channel case, the use of the DBP algorithm outperformed the OPC with a Q-factor improvement of 0.9 dB after 800-km...
DEFF Research Database (Denmark)
Sackey, Isaac; Da Ros, Francesco; Karl Fischer, Johannes
2015-01-01
a dual-pump polarization-independent fiber-optic parametric amplifier and compared to digital backpropagation (DBP) compensation over up to 800-km in a dispersion-managed link. In the single-channel case, the use of the DBP algorithm outperformed the OPC with a Q-factor improvement of 0.9 dB after 800-km......We experimentally investigate Kerr nonlinearity mitigation of a 28-GBd polarization-multiplexed 16-QAM signal in a five-channel 50-GHz spaced wavelength-division multiplexing (WDM) system. Optical phase conjugation (OPC) employing the mid-link spectral inversion technique is implemented by using...
Stelzenmüller, Vanessa; Maynou, Francesc; Ehrich, Siegfried; Zauke, Gerd-Peter
2004-09-01
This study aims to evaluate the suitability of non-linear geostatistics and indicator kriging (IK) as a tool in environmental impact assessment and nature conservation, in particular to search for potential Special Areas of Conservation (SAC) for the endangered fish species twaite shad, Alosa fallax (Lacepède, 1803) within the German Exclusive Economical Zone (EEZ) of the North Sea. To analyse the spatial distribution of this fish species, data on standardised biomass index (catch per unit effort, c.p.u.e., kg × 30 min-1) from 1996 to 2001 were used, regarding the third and fourth quarters of each year, respectively. Thereby we assume that the spatial distribution can be described as a time-invariant process. This assumption is supported by information on annual sampling effort, allocation of hauls and spatial distribution of the positive catches. All indicator variograms obtained for different c.p.u.e. cut-off values displayed distinct spatial structures, clearly indicating that the indicator variables were spatially autocorrelated. Gaussian models were fitted by least-squares methods and were evaluated with a goodness-of-fit statistic. Subsequently, IK was employed to estimate the probability of exceeding the c.p.u.e. cut-off values for the twaite shad in the investigation area. These were highest in the Weser- and Elbe-estuary, probably because of migrations of twaite shad to and from estuaries at the time of investigation due to spawning, while within the German EEZ of the North Sea no such areas with increased probabilities could be discerned. Thus, although available data did not allow to identify and implement any SAC in the German EEZ, the methods employed here can be regarded as a promising management tool in biological conservation issues. (
Voorhies, Coerte V.
1993-01-01
The problem of estimating a steady fluid velocity field near the top of Earth's core which induces the secular variation (SV) indicated by models of the observed geomagnetic field is examined in the source-free mantle/frozen-flux core (SFI/VFFC) approximation. This inverse problem is non-linear because solutions of the forward problem are deterministically chaotic. The SFM/FFC approximation is inexact, and neither the models nor the observations they represent are either complete or perfect. A method is developed for solving the non-linear inverse motional induction problem posed by the hypothesis of (piecewise, statistically) steady core surface flow and the supposition of a complete initial geomagnetic condition. The method features iterative solution of the weighted, linearized least-squares problem and admits optional biases favoring surficially geostrophic flow and/or spatially simple flow. Two types of weights are advanced radial field weights for fitting the evolution of the broad-scale portion of the radial field component near Earth's surface implied by the models, and generalized weights for fitting the evolution of the broad-scale portion of the scalar potential specified by the models.
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...
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...
Geostatistical modeling of topography using auxiliary maps
Hengl, T.; Bajat, B.; Blagojević, D.; Reuter, H.I.
2008-01-01
This paper recommends computational procedures for employing auxiliary maps, such as maps of drainage patterns, land cover and remote-sensing-based indices, directly in the geostatistical modeling of topography. The methodology is based on the regression-kriging technique, as implemented in the R pa
Oosterhuis, Ekke J.; Eidhof, Wouter B.; Hoogt, van der Peter J.M.; Boer, de André
2006-01-01
Force prediction can basically be done by two methods: direct methods and optimization methods. Direct methods use the inverse of the forward system model to calculate the excitation directly from the measured responses. Optimization methods use a forward model in an optimization loop wherein the in
Directory of Open Access Journals (Sweden)
A. Belmiloudi
2014-01-01
Full Text Available The paper investigates boundary optimal controls and parameter estimates to the well-posedness nonlinear model of dehydration of thermic problems. We summarize the general formulations for the boundary control for initial-boundary value problem for nonlinear partial differential equations modeling the heat transfer and derive necessary optimality conditions, including the adjoint equation, for the optimal set of parameters minimizing objective functions J. Numerical simulations illustrate several numerical optimization methods, examples, and realistic cases, in which several interesting phenomena are observed. A large amount of computational effort is required to solve the coupled state equation and the adjoint equation (which is backwards in time, and the algebraic gradient equation (which implements the coupling between the adjoint and control variables. The state and adjoint equations are solved using the finite element method.
Energy Technology Data Exchange (ETDEWEB)
Romero, MarIa de los Angeles Sandoval; Weder, Ricardo [Instituto de Investigaciones en Matematicas Aplicadas y en Sistemas, Universidad Nacional Autonoma de Mexico, Apartado Postal 20-726, Mexico DF 01000 (Mexico)
2006-09-15
We consider nonlinear Schroedinger equations with a potential, and non-local nonlinearities, that are models in mesoscopic physics, for example of a quantum capacitor, and that are also models of molecular structure. We study in detail the initial value problem for these equations, in particular, existence and uniqueness of local and global solutions, continuous dependence on the initial data and regularity. We allow for a large class of unbounded potentials. We have no restriction on the growth at infinity of the positive part of the potential. We also construct the scattering operator in the case of potentials that go to zero at infinity. Furthermore, we give a method for the unique reconstruction of the potential from the small amplitude limit of the scattering operator. In the case of the quantum capacitor, our method allows us to uniquely reconstruct all the physical parameters from the small amplitude limit of the scattering operator.
Mixed-point geostatistical simulation: A combination of two- and multiple-point geostatistics
Cordua, Knud Skou; Hansen, Thomas Mejer; Gulbrandsen, Mats Lundh; Barnes, Christophe; Mosegaard, Klaus
2016-09-01
Multiple-point-based geostatistical methods are used to model complex geological structures. However, a training image containing the characteristic patterns of the Earth model has to be provided. If no training image is available, two-point (i.e., covariance-based) geostatistical methods are typically applied instead because these methods provide fewer constraints on the Earth model. This study is motivated by the case where 1-D vertical training images are available through borehole logs, whereas little or no information about horizontal dependencies exists. This problem is solved by developing theory that makes it possible to combine information from multiple- and two-point geostatistics for different directions, leading to a mixed-point geostatistical model. An example of combining information from the multiple-point-based single normal equation simulation algorithm and two-point-based sequential indicator simulation algorithm is provided. The mixed-point geostatistical model is used for conditional sequential simulation based on vertical training images from five borehole logs and a range parameter describing the horizontal dependencies.
Yu, XiaoChun; Bai, YuGuang; Cui, Miao; Gao, XiaoWei
2013-05-01
This paper presents a new inverse analysis approach to sensitivity analysis and material property identification in transient non-homogeneous and non-linear heat conduction Boundary Element Method (BEM) analysis based on Complex Variable Differentiation Method (CVDM). In this approach, the material properties are taken as the optimization variables, and the sensitivity coefficients are computed by CVDM. The advantages of using CVDM are that the computation of partial derivatives of an implicit function is reduced to function calculation in a complex domain, and the parameter sensitivity coefficients can be determined in a more accurate way than the traditional Finite Difference Method (FDM). Based on BEM and CVDM in evaluation of the sensitivity matrix of heat flux, the parameter such as thermal conductivity can be accurately identified. Six numerical examples are given to demonstrate the potential of the proposed approach. The results indicate that the presented method is efficient for identifying the thermal conductivity with single or multiple parameters.
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...
Applications of geostatistics in plant nematology.
Wallace, M K; Hawkins, D M
1994-12-01
The application of geostatistics to plant nematology was made by evaluating soil and nematode data acquired from 200 soil samples collected from the A(p) horizon of a reed canary-grass field in northern Minnesota. Geostatistical concepts relevant to nematology include semi-variogram modelling, kriging, and change of support calculations. Soil and nematode data generally followed a spherical semi-variogram model, with little random variability associated with soil data and large inherent variability for nematode data. Block kriging of soil and nematode data provided useful contour maps of the data. Change of snpport calculations indicated that most of the random variation in nematode data was due to short-range spatial variability in the nematode population densities.
The application of geostatistics in erosion hazard mapping
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 minim
Bayesian Analysis of Geostatistical Models With an Auxiliary Lattice
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.
A comprehensive, user-friendly geostatistical software system called GEOPACk has been developed. The purpose of this software is to make available the programs necessary to undertake a geostatistical analysis of spatially correlated data. The programs were written so that they ...
Studies on Inverse Opal and Two-Dimensional Nonlinear Photonic Crystals%反Opal及二维非线性光子晶体的研究
Institute of Scientific and Technical Information of China (English)
倪培根; 程丙英; 张道中
2006-01-01
通过向SiO2 Opal模板中填充钛酸乙酯制备TiO2光子晶体,观测到光子晶体带隙位置的移动达62nm,并发现光子晶体的有序度随填充率的升高而下降.向聚苯乙烯Opal模板中填充钛酸乙酯,制备成当时填充率最高、带隙最短的紫外波段TiO2反Opal光子晶体(中心波长～380nm),并根据测量的其透射谱估算出其填充率约为12%,即Opal模板孔隙的50%被填充.本文还对二维PPLN光子晶体进行了研究.建立了一套高压极化装置和电压数据采集装置,通过外加电场极化法成功制备出了具有正方形和矩形两种晶格形状二维PPLN光子晶体.利用二维PPLN的二阶准相位匹配,测量了其对1.064μm激光的二次谐波转换效率,并研究了晶体的温度、激光的入射角度及占空比对二次谐波转换效率的影响.利用矩形晶格实现了多方向、多波长倍频高效输出.%In this paper, we report some results on inverse opal photonic crystal and two-dimensional periodically poled lithium niobate photonic crystal. First, the process of infiltrating TiO2 into SiO2 Opal was systematically studied. Because of the infiltration of TiO2, the gap of SiO2 Opal was shifted to longer wavelength and a maximum shift of 62nm was observed. Furthermore, an inverse TiO2 Opal with larger filling fraction, ～ 12%, was fabricated, whose band gap in the Γ-L direction is located in the ultraviolet region ( ～ 380nm). Then two-dimensional nonlinear photonic crystals of lithium nlobate with uniform square lattices were fabricated by applying external electric fields. The variations of second-harmonic output with crystal temperatures, incident angles and reversed duty cycles were measured. Red, yellow,green, blue, and violet coherent radiations were generated in the nonlinear photonic crystal with rectangular lattice in the collinearly and non-collinearly quasi-phase matching geometries. The results showed that two-dimensional nonlinear photonic crystal
Geostatistical enhancement of european hydrological predictions
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
Petra, N.; Alexanderian, A.; Stadler, G.; Ghattas, O.
2015-12-01
We address the problem of optimal experimental design (OED) for Bayesian nonlinear inverse problems governed by partial differential equations (PDEs). The inverse problem seeks to infer a parameter field (e.g., the log permeability field in a porous medium flow model problem) from synthetic observations at a set of sensor locations and from the governing PDEs. The goal of the OED problem is to find an optimal placement of sensors so as to minimize the uncertainty in the inferred parameter field. We formulate the OED objective function by generalizing the classical A-optimal experimental design criterion using the expected value of the trace of the posterior covariance. This expected value is computed through sample averaging over the set of likely experimental data. Due to the infinite-dimensional character of the parameter field, we seek an optimization method that solves the OED problem at a cost (measured in the number of forward PDE solves) that is independent of both the parameter and the sensor dimension. To facilitate this goal, we construct a Gaussian approximation to the posterior at the maximum a posteriori probability (MAP) point, and use the resulting covariance operator to define the OED objective function. We use randomized trace estimation to compute the trace of this covariance operator. The resulting OED problem includes as constraints the system of PDEs characterizing the MAP point, and the PDEs describing the action of the covariance (of the Gaussian approximation to the posterior) to vectors. We control the sparsity of the sensor configurations using sparsifying penalty functions, and solve the resulting penalized bilevel optimization problem via an interior-point quasi-Newton method, where gradient information is computed via adjoints. We elaborate our OED method for the problem of determining the optimal sensor configuration to best infer the log permeability field in a porous medium flow problem. Numerical results show that the number of PDE
Geostatistics, remote sensing and precision farming.
Mulla, D J
1997-01-01
Precision farming is possible today because of advances in farming technology, procedures for mapping and interpolating spatial patterns, and geographic information systems for overlaying and interpreting several soil, landscape and crop attributes. The key component of precision farming is the map showing spatial patterns in field characteristics. Obtaining information for this map is often achieved by soil sampling. This approach, however, can be cost-prohibitive for grain crops. Soil sampling strategies can be simplified by use of auxiliary data provided by satellite or aerial photo imagery. This paper describes geostatistical methods for estimating spatial patterns in soil organic matter, soil test phosphorus and wheat grain yield from a combination of Thematic Mapper imaging and soil sampling.
Bayesian modelling of geostatistical malaria risk data
Directory of Open Access Journals (Sweden)
L. Gosoniu
2006-11-01
Full Text Available Bayesian geostatistical models applied to malaria risk data quantify the environment-disease relations, identify significant environmental predictors of malaria transmission and provide model-based predictions of malaria risk together with their precision. These models are often based on the stationarity assumption which implies that spatial correlation is a function of distance between locations and independent of location. We relax this assumption and analyse malaria survey data in Mali using a Bayesian non-stationary model. Model fit and predictions are based on Markov chain Monte Carlo simulation methods. Model validation compares the predictive ability of the non-stationary model with the stationary analogue. Results indicate that the stationarity assumption is important because it influences the significance of environmental factors and the corresponding malaria risk maps.
Bayesian modelling of geostatistical malaria risk data.
Gosoniu, L; Vounatsou, P; Sogoba, N; Smith, T
2006-11-01
Bayesian geostatistical models applied to malaria risk data quantify the environment-disease relations, identify significant environmental predictors of malaria transmission and provide model-based predictions of malaria risk together with their precision. These models are often based on the stationarity assumption which implies that spatial correlation is a function of distance between locations and independent of location. We relax this assumption and analyse malaria survey data in Mali using a Bayesian non-stationary model. Model fit and predictions are based on Markov chain Monte Carlo simulation methods. Model validation compares the predictive ability of the non-stationary model with the stationary analogue. Results indicate that the stationarity assumption is important because it influences the significance of environmental factors and the corresponding malaria risk maps.
Geostatistical Estimations of Regional Hydraulic Conductivity Fields
Patriarche, D.; Castro, M. C.; Goovaerts, P.
2004-12-01
Direct and indirect measurements of hydraulic conductivity (K) are commonly performed, providing information on the magnitude of this parameter at the local scale (tens of centimeters to hundreds of meters) and at shallow depths. By contrast, field information on hydraulic conductivities at regional scales of tens to hundreds of kilometers and at greater depths is relatively scarce. Geostatistical methods allow for sparsely sampled observations of a variable (primary information) to be complemented by a more densely sampled secondary attribute. Geostatistical estimations of the hydraulic conductivity field in the Carrizo aquifer, a major groundwater flow system extending along Texas, are performed using available primary (e.g., transmissivity, hydraulic conductivity) and secondary (specific capacity) information, for depths up to 2.2 km, and over three regional domains of increasing extent: 1) the domain corresponding to a three-dimensional groundwater flow model previously built (model domain); 2) the area corresponding to the ten counties encompassing the model domain (County domain), and; 3) the full extension of the Carrizo aquifer within Texas (Texas domain). Two different approaches are used: 1) an indirect approach are transmissivity (T) is estimated first and (K) is retrieved through division of the T estimate by the screening length of the wells, and; 2) a direct approach where K data are kriged directly. Prediction performances of the tested geostatistical procedures (kriging combined with linear regression, kriging with known local means, kriging of residuals, and cokriging) are evaluated through cross validation for both log-transformed variables and back-transformed ones. For the indirect approach, kriging of log T residuals yields the best estimates for both log-transformed and back-transformed variables in the model domain. For larger regional scales (County and Texas domains), cokriging performs generally better than univariate kriging procedures
Fukahata, Yukitoshi; Hashimoto, Manabu
2016-12-01
At the 2016 Kumamoto earthquake, surface ruptures were observed not only along the Futagawa fault, where main ruptures occurred, but also along the Hinagu fault. To estimate the slip distribution on these faults, we extend a method of nonlinear inversion analysis (Fukahata and Wright in Geophys J Int 173:353-364, 2008) to a two-fault system. With the method of Fukahata and Wright (2008), we can simultaneously determine the optimal dip angle of a fault and the slip distribution on it, based on Akaike's Bayesian information criterion by regarding the dip angle as an hyperparameter. By inverting the InSAR data with the developed method, we obtain the dip angles of the Futagawa and Hinagu faults as 61° ± 6° and 74° ± 12°, respectively. The slip on the Futagawa fault is mainly strike slip. The largest slip on it is over 5 m around the center of the model fault (130.9° in longitude) with a significant normal slip component. The slip on the Futagawa fault quickly decreases to zero beyond the intersection with the Hinagu fault. On the other hand, the slip has a local peak just inside Aso caldera, which would be a cause of severe damage in this area. A relatively larger reverse fault slip component on a deeper part around the intersection with Aso caldera suggests that something complicated happened there. The slip on the Hinagu fault is almost a pure strike slip with a peak of about 2.4 m. The developed method is useful in clarifying the slip distribution, when a complicated rupture like the Kumamoto earthquake happens in a remote area.[Figure not available: see fulltext.
Hybrid modeling of spatial continuity for application to numerical inverse problems
Friedel, Michael J.; Iwashita, Fabio
2013-01-01
A novel two-step modeling approach is presented to obtain optimal starting values and geostatistical constraints for numerical inverse problems otherwise characterized by spatially-limited field data. First, a type of unsupervised neural network, called the self-organizing map (SOM), is trained to recognize nonlinear relations among environmental variables (covariates) occurring at various scales. The values of these variables are then estimated at random locations across the model domain by iterative minimization of SOM topographic error vectors. Cross-validation is used to ensure unbiasedness and compute prediction uncertainty for select subsets of the data. Second, analytical functions are fit to experimental variograms derived from original plus resampled SOM estimates producing model variograms. Sequential Gaussian simulation is used to evaluate spatial uncertainty associated with the analytical functions and probable range for constraining variables. The hybrid modeling of spatial continuity is demonstrated using spatially-limited hydrologic measurements at different scales in Brazil: (1) physical soil properties (sand, silt, clay, hydraulic conductivity) in the 42 km2 Vargem de Caldas basin; (2) well yield and electrical conductivity of groundwater in the 132 km2 fractured crystalline aquifer; and (3) specific capacity, hydraulic head, and major ions in a 100,000 km2 transboundary fractured-basalt aquifer. These results illustrate the benefits of exploiting nonlinear relations among sparse and disparate data sets for modeling spatial continuity, but the actual application of these spatial data to improve numerical inverse modeling requires testing.
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.
Bayesian geostatistical modeling of Malaria Indicator Survey data in Angola.
Directory of Open Access Journals (Sweden)
Laura Gosoniu
Full Text Available 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.
Inverse problem in hydrogeology
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
The role of geostatistics in medical geology
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 < 50 μg/L) most commonly found in drinking 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
On the geostatistical characterization of hierarchical media
Neuman, Shlomo P.; Riva, Monica; Guadagnini, Alberto
2008-02-01
The subsurface consists of porous and fractured materials exhibiting a hierarchical geologic structure, which gives rise to systematic and random spatial and directional variations in hydraulic and transport properties on a multiplicity of scales. Traditional geostatistical moment analysis allows one to infer the spatial covariance structure of such hierarchical, multiscale geologic materials on the basis of numerous measurements on a given support scale across a domain or "window" of a given length scale. The resultant sample variogram often appears to fit a stationary variogram model with constant variance (sill) and integral (spatial correlation) scale. In fact, some authors, who recognize that hierarchical sedimentary architecture and associated log hydraulic conductivity fields tend to be nonstationary, nevertheless associate them with stationary "exponential-like" transition probabilities and variograms, respectively, the latter being a consequence of the former. We propose that (1) the apparent ability of stationary spatial statistics to characterize the covariance structure of nonstationary hierarchical media is an artifact stemming from the finite size of the windows within which geologic and hydrologic variables are ubiquitously sampled, and (2) the artifact is eliminated upon characterizing the covariance structure of such media with the aid of truncated power variograms, which represent stationary random fields obtained upon sampling a nonstationary fractal over finite windows. To support our opinion, we note that truncated power variograms arise formally when a hierarchical medium is sampled jointly across all geologic categories and scales within a window; cite direct evidence that geostatistical parameters (variance and integral scale) inferred on the basis of traditional variograms vary systematically with support and window scales; demonstrate the ability of truncated power models to capture these variations in terms of a few scaling parameters
Robust geostatistical analysis of spatial data
Papritz, Andreas; Künsch, Hans Rudolf; Schwierz, Cornelia; Stahel, Werner A.
2013-04-01
Most of the geostatistical software tools rely on non-robust algorithms. This is unfortunate, because outlying observations are rather the rule than the exception, in particular in environmental data sets. Outliers affect the modelling of the large-scale spatial trend, the estimation of the spatial dependence of the residual variation and the predictions by kriging. Identifying outliers manually is cumbersome and requires expertise because one needs parameter estimates to decide which observation is a potential outlier. Moreover, inference after the rejection of some observations is problematic. A better approach is to use robust algorithms that prevent automatically that outlying observations have undue influence. Former studies on robust geostatistics focused on robust estimation of the sample variogram and ordinary kriging without external drift. Furthermore, Richardson and Welsh (1995) proposed a robustified version of (restricted) maximum likelihood ([RE]ML) estimation for the variance components of a linear mixed model, which was later used by Marchant and Lark (2007) for robust REML estimation of the variogram. We propose here a novel method for robust REML estimation of the variogram of a Gaussian random field that is possibly contaminated by independent errors from a long-tailed distribution. It is based on robustification of estimating equations for the Gaussian REML estimation (Welsh and Richardson, 1997). Besides robust estimates of the parameters of the external drift and of the variogram, the method also provides standard errors for the estimated parameters, robustified kriging predictions at both sampled and non-sampled locations and kriging variances. Apart from presenting our modelling framework, we shall present selected simulation results by which we explored the properties of the new method. This will be complemented by an analysis a data set on heavy metal contamination of the soil in the vicinity of a metal smelter. Marchant, B.P. and Lark, R
High Performance Geostatistical Modeling of Biospheric Resources
Pedelty, J. A.; Morisette, J. T.; Smith, J. A.; Schnase, J. L.; Crosier, C. S.; Stohlgren, T. J.
2004-12-01
We are using parallel geostatistical codes to study spatial relationships among biospheric resources in several study areas. For example, spatial statistical models based on large- and small-scale variability have been used to predict species richness of both native and exotic plants (hot spots of diversity) and patterns of exotic plant invasion. However, broader use of geostastics in natural resource modeling, especially at regional and national scales, has been limited due to the large computing requirements of these applications. To address this problem, we implemented parallel versions of the kriging spatial interpolation algorithm. The first uses the Message Passing Interface (MPI) in a master/slave paradigm on an open source Linux Beowulf cluster, while the second is implemented with the new proprietary Xgrid distributed processing system on an Xserve G5 cluster from Apple Computer, Inc. These techniques are proving effective and provide the basis for a national decision support capability for invasive species management that is being jointly developed by NASA and the US Geological Survey.
Preferential sampling and Bayesian geostatistics: Statistical modeling and examples.
Cecconi, Lorenzo; Grisotto, Laura; Catelan, Dolores; Lagazio, Corrado; Berrocal, Veronica; Biggeri, Annibale
2016-08-01
Preferential sampling refers to any situation in which the spatial process and the sampling locations are not stochastically independent. In this paper, we present two examples of geostatistical analysis in which the usual assumption of stochastic independence between the point process and the measurement process is violated. To account for preferential sampling, we specify a flexible and general Bayesian geostatistical model that includes a shared spatial random component. We apply the proposed model to two different case studies that allow us to highlight three different modeling and inferential aspects of geostatistical modeling under preferential sampling: (1) continuous or finite spatial sampling frame; (2) underlying causal model and relevant covariates; and (3) inferential goals related to mean prediction surface or prediction uncertainty.
Geostatistics and GIS: tools for characterizing environmental contamination.
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.
Directory of Open Access Journals (Sweden)
Ibrahim Hassan
2016-06-01
Full Text Available Various geostatistical and deterministic techniques were used to analyse the spatial variations of groundwater depths. Two different geostatistical methods of ordinary kriging and co-kriging with four semivariogram models, spherical, exponential, circular, Gaussian, and four deterministic methods which are inverse distance weighted (IDW, global polynomial interpolation (GPI, local Polynomial Interpolation (LPI, radial basis function (RBF were used for the estimation of groundwater depths. The study area is in the three Northwestern districts of Bangladesh. Groundwater depth data were recorded from 132 observation wells in the study area over a period of 6 years (2004 to 2009 was considered for the analysis. The spatial interpolation of groundwater depths was then performed using the best-fit model which is geostatistical model selected by comparing the observed RMSE values predicted by the geostatistical and deterministic models and the empirical semi-variogram models. Out of the four semi-variogram models, spherical semi-variogram with cokriging model was considered as the best fitted model for the study area. Result of sensitivity analysis conducted on the input parameters shows that inputs have a strong influence on groundwater levels and the statistical indicators of RMSE and ME suggest that the Co-kriging work best with percolation in predicting the average groundwater table of the study area.
Hydrogeologic unit flow characterization using transition probability geostatistics.
Jones, Norman L; Walker, Justin R; Carle, Steven F
2005-01-01
This paper describes a technique for applying the transition probability geostatistics method for stochastic simulation to a MODFLOW model. Transition probability geostatistics has some advantages over traditional indicator kriging methods including a simpler and more intuitive framework for interpreting geologic relationships and the ability to simulate juxtapositional tendencies such as fining upward sequences. The indicator arrays generated by the transition probability simulation are converted to layer elevation and thickness arrays for use with the new Hydrogeologic Unit Flow package in MODFLOW 2000. This makes it possible to preserve complex heterogeneity while using reasonably sized grids and/or grids with nonuniform cell thicknesses.
Random spatial processes and geostatistical models for soil variables
Lark, R. M.
2009-04-01
Geostatistical models of soil variation have been used to considerable effect to facilitate efficient and powerful prediction of soil properties at unsampled sites or over partially sampled regions. Geostatistical models can also be used to investigate the scaling behaviour of soil process models, to design sampling strategies and to account for spatial dependence in the random effects of linear mixed models for spatial variables. However, most geostatistical models (variograms) are selected for reasons of mathematical convenience (in particular, to ensure positive definiteness of the corresponding variables). They assume some underlying spatial mathematical operator which may give a good description of observed variation of the soil, but which may not relate in any clear way to the processes that we know give rise to that observed variation in the real world. In this paper I shall argue that soil scientists should pay closer attention to the underlying operators in geostatistical models, with a view to identifying, where ever possible, operators that reflect our knowledge of processes in the soil. I shall illustrate how this can be done in the case of two problems. The first exemplar problem is the definition of operators to represent statistically processes in which the soil landscape is divided into discrete domains. This may occur at disparate scales from the landscape (outcrops, catchments, fields with different landuse) to the soil core (aggregates, rhizospheres). The operators that underly standard geostatistical models of soil variation typically describe continuous variation, and so do not offer any way to incorporate information on processes which occur in discrete domains. I shall present the Poisson Voronoi Tessellation as an alternative spatial operator, examine its corresponding variogram, and apply these to some real data. The second exemplar problem arises from different operators that are equifinal with respect to the variograms of the
Geostatistical Solutions for Downscaling Remotely Sensed Land Surface Temperature
Wang, Q.; Rodriguez-Galiano, V.; Atkinson, P. M.
2017-09-01
Remotely sensed land surface temperature (LST) downscaling is an important issue in remote sensing. Geostatistical methods have shown their applicability in downscaling multi/hyperspectral images. In this paper, four geostatistical solutions, including regression kriging (RK), downscaling cokriging (DSCK), kriging with external drift (KED) and area-to-point regression kriging (ATPRK), are applied for downscaling remotely sensed LST. Their differences are analyzed theoretically and the performances are compared experimentally using a Landsat 7 ETM+ dataset. They are also compared to the classical TsHARP method.
Local Geostatistical Models and Big Data in Hydrological and Ecological Applications
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
Direct Waveform Inversion by Iterative Inverse Propagation
Schlottmann, R B
2009-01-01
Seismic waves are the most sensitive probe of the Earth's interior we have. With the dense data sets available in exploration, images of subsurface structures can be obtained through processes such as migration. Unfortunately, relating these surface recordings to actual Earth properties is non-trivial. Tomographic techniques use only a small amount of the information contained in the full seismogram and result in relatively low resolution images. Other methods use a larger amount of the seismogram but are based on either linearization of the problem, an expensive statistical search over a limited range of models, or both. We present the development of a new approach to full waveform inversion, i.e., inversion which uses the complete seismogram. This new method, which falls under the general category of inverse scattering, is based on a highly non-linear Fredholm integral equation relating the Earth structure to itself and to the recorded seismograms. An iterative solution to this equation is proposed. The res...
Gstat: a program for geostatistical modelling, prediction and simulation
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.
Geostatistical Modeling of Evolving Landscapes by Means of Image Quilting
Mendes, J. H.; Caers, J.; Scheidt, C.
2015-12-01
Realistic geological representation of subsurface heterogeneity remains an important outstanding challenge. While many geostatistical methods exist for representing sedimentary systems, such as multiple-point geostatistics, rule-based methods or Boolean methods, the question of what the prior uncertainty on parameters (or training images) of such algorithms are, remains outstanding. In this initial work, we investigate the use of flume experiments to constrain better such prior uncertainty and to start understanding what information should be provided to geostatistical algorithms. In particular, we study the use of image quilting as a novel multiple-point method for generating fast geostatistical realizations once a training image is provided. Image quilting is a method emanating from computer graphics where patterns are extracted from training images and then stochastically quilted along a raster path to create stochastic variation of the stated training image. In this initial study, we use a flume experiment and extract 10 training images as representative for the variability of the evolving landscape over a period of 136 minutes. The training images consists of wet/dry regions obtained from overhead shots taken over the flume experiment. To investigate whether such image quilting reproduces the same variability of the evolving landscape in terms of wet/dry regions, we generate multiple realizations with all 10 training images and compare that variability with the variability seen in the entire flume experiment. By proper tuning of the quilting parameters we find generally reasonable agreement with the flume experiment.
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
Multiple Point Geostatistics for automated landform mapping
Karssenberg, D.; Vannametee, E.; Babel, L.; Schuur, J.; Hendriks, M.; Bierkens, M. F.
2011-12-01
Land-surface processes are often studied at the level of elementary landform units, e.g. geomorphological units. To avoid expensive and difficult field surveys and to ensure a consistent mapping scheme, automated derivation of these units is desirable. However, automated classification based on two-point statistics of topographical attributes (e.g. semivarigram) is inadequate in reproducing complex, curvilinear landform patterns. Therefore, the spatial structure and configuration of terrain characteristics suitable for landform classification should be based on statistics from multiple points. In this study, a generic automated landform classification routine is developed which is based on Multiple Point Geostatistics (MPG) using information from a field map of geomorphology in a training area and a gridded Digital Elevation Model (DEM). Focus is on classification of geomorphologic units; e.g. alluvial fan, river terrace. The approach is evaluated using data from the French Alps. In the first procedural step, spatial statistics of the geomorphologic units are retrieved from a training data set, consisting of a digital elevation model and a geomorphologic map, created using field observations and 37.5 x 37.5 m2 cells. For each grid cell in the training data set, the geomorphological unit of the grid cell and a set of topographical attributes (i.e. a pattern) of the grid cell is stored in a frequency database. The set of topographical attributes stored is chosen such that it represents criteria used in field mapping. These are, for instance, topographical slope gradient, upstream area, or geomorphological units mapped in the neighborhood of the cell. Continuous information (e.g. slope) is converted to categorical data (slope class), which is required in the MPG approach. The second step is to use the knowledge stored in the frequency database for mapping. The algorithm reads a set of attribute classes from a classification target cell and its surrounding cells taking
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
Institute of Scientific and Technical Information of China (English)
臧强; 张凯锋; 戴先中; 周颖
2012-01-01
For a class of nonlinear differential - algebraic equations ( DAE) subsystems: whose index is one and interconnection is local measurable, the inverse system control method is studied in this paper. The result is applied to the components control of power systems. At first the background and the particularities of such systems are expatiated. Then the definition of - order right inverse system is put forward. A recursive algorithm is given, with which to identify whether the nonlinear DAE subsystems are invertible. An - order right inverse system is realized by both state - feedback and dynamic compensation, with which the nonlinear DAE subsystems are decoupled and linearized. Finally, an excitation controller is designed for one of the synchronous generators in the multi - machine power systems based on the proposed method in this paper. The simulation is conducted and the results demonstrate the effectiveness of the proposed control scheme.%对于指数1且关联可测的非线性微分-代数子系统,研究其逆系统控制方法,并将结果应用于电力系统元件分散控制.首先描述了此类非线性微分-代数子系统的物理背景和系统特性,并给出了非线性微分-代数子系统的α阶积分右逆系统和可逆的定义;然后给出了一种递归算法,以此来判别被控系统的可逆性,并构造出由状态反馈和动态补偿实现的α阶积分右逆系统,实现了复合系统的线性化解耦；最后针对多机电力系统中的一台同步发电机,应用所提出的方法研究其励磁控制电压问题.仿真结果验证了所提出方法的有效性.
Muthusamy, Manoranjan; Schellart, Alma; Tait, Simon; Heuvelink, Gerard B. M.
2017-02-01
In this study we develop a method to estimate the spatially averaged rainfall intensity together with associated level of uncertainty using geostatistical upscaling. Rainfall data collected from a cluster of eight paired rain gauges in a 400 m × 200 m urban catchment are used in combination with spatial stochastic simulation to obtain optimal predictions of the spatially averaged rainfall intensity at any point in time within the urban catchment. The uncertainty in the prediction of catchment average rainfall intensity is obtained for multiple combinations of intensity ranges and temporal averaging intervals. The two main challenges addressed in this study are scarcity of rainfall measurement locations and non-normality of rainfall data, both of which need to be considered when adopting a geostatistical approach. Scarcity of measurement points is dealt with by pooling sample variograms of repeated rainfall measurements with similar characteristics. Normality of rainfall data is achieved through the use of normal score transformation. Geostatistical models in the form of variograms are derived for transformed rainfall intensity. Next spatial stochastic simulation which is robust to nonlinear data transformation is applied to produce realisations of rainfall fields. These realisations in transformed space are first back-transformed and next spatially aggregated to derive a random sample of the spatially averaged rainfall intensity. Results show that the prediction uncertainty comes mainly from two sources: spatial variability of rainfall and measurement error. At smaller temporal averaging intervals both these effects are high, resulting in a relatively high uncertainty in prediction. With longer temporal averaging intervals the uncertainty becomes lower due to stronger spatial correlation of rainfall data and relatively smaller measurement error. Results also show that the measurement error increases with decreasing rainfall intensity resulting in a higher
Hevesi, Joseph A.; Istok, Jonathan D.; Flint, Alan L.
1992-01-01
Values of average annual precipitation (AAP) are desired for hydrologic studies within a watershed containing Yucca Mountain, Nevada, a potential site for a high-level nuclear-waste repository. Reliable values of AAP are not yet available for most areas within this watershed because of a sparsity of precipitation measurements and the need to obtain measurements over a sufficient length of time. To estimate AAP over the entire watershed, historical precipitation data and station elevations were obtained from a network of 62 stations in southern Nevada and southeastern California. Multivariate geostatistics (cokriging) was selected as an estimation method because of a significant (p = 0.05) correlation of r = .75 between the natural log of AAP and station elevation. A sample direct variogram for the transformed variable, TAAP = ln [(AAP) 1000], was fitted with an isotropic, spherical model defined by a small nugget value of 5000, a range of 190 000 ft, and a sill value equal to the sample variance of 163 151. Elevations for 1531 additional locations were obtained from topographic maps to improve the accuracy of cokriged estimates. A sample direct variogram for elevation was fitted with an isotropic model consisting of a nugget value of 5500 and three nested transition structures: a Gaussian structure with a range of 61 000 ft, a spherical structure with a range of 70 000 ft, and a quasi-stationary, linear structure. The use of an isotropic, stationary model for elevation was considered valid within a sliding-neighborhood radius of 120 000 ft. The problem of fitting a positive-definite, nonlinear model of coregionalization to an inconsistent sample cross variogram for TAAP and elevation was solved by a modified use of the Cauchy-Schwarz inequality. A selected cross-variogram model consisted of two nested structures: a Gaussian structure with a range of 61 000 ft and a spherical structure with a range of 190 000 ft. Cross validation was used for model selection and for
Institute of Scientific and Technical Information of China (English)
孙宇新; 杨玉伟
2016-01-01
For agricultural motor drive applications, reliability and stability are very significant, and even under disturbance condition, stable drive operation is essential. In view of the characteristics of the bearingless induction motor, which includes multi -variables, nonlinearity and high coupling, an adaptive inverse decoupling control strategy for the bearingless induction motor based on the nonlinear adaptive filter was proposed to improve the efficiency and reliability of the motor drives. First, the mathematical model of a bearingless induction motor was deduced through analyzing the generation mechanism of a bearingless induction motor’s radial levitation force. By adopting the control theory of an adaptive inverse control system and the principle of a nonlinear adaptive filter, the model and inverse model of the torque system and levitation system were established respectively, including the option of the structure of nonlinear adaptive filter and the adaptive algorithm. Based on the inverse model, the adaptive inverse controller which cascaded in front of the corresponding system was designed by making use of the algorithm of variable step size least mean square (LMS) to adjust the weighting factors online. The difference between the given input signal and the system output signal was used as the error signal of the adaptive algorithm of variable step size LMS. In addition, compared to the traditional field oriented control method, this method did not need to rely on torque system to transfer flux information, which avoided the mutual restriction among the control strategies, and solved the coupling problem between the variables in the modeling process. Then, aiming at the performances of rotor flux, speed, torque and levitation response, the simulation and analysis of the adaptive inverse control system for the bearingless induction motor wew carried out on the basis of MATLAB/Simulink simulation platform. Moreover, the initial given value of motor speed
Seismic Waveform Inversion Using the Finite-Difference Contrast Source Inversion Method
Bo Han; Qinglong He; Yong Chen; Yixin Dou
2014-01-01
This paper extends the finite-difference contrast source inversion method to reconstruct the mass density for two-dimensional elastic wave inversion in the framework of the full-waveform inversion. The contrast source inversion method is a nonlinear iterative method that alternatively reconstructs contrast sources and contrast function. One of the most outstanding advantages of this inversion method is the highly computational efficiency, since it does not need to simulate a fu...
Usage of multivariate geostatistics in interpolation processes for meteorological precipitation maps
Gundogdu, Ismail Bulent
2017-01-01
Long-term meteorological data are very important both for the evaluation of meteorological events and for the analysis of their effects on the environment. Prediction maps which are constructed by different interpolation techniques often provide explanatory information. Conventional techniques, such as surface spline fitting, global and local polynomial models, and inverse distance weighting may not be adequate. Multivariate geostatistical methods can be more significant, especially when studying secondary variables, because secondary variables might directly affect the precision of prediction. In this study, the mean annual and mean monthly precipitations from 1984 to 2014 for 268 meteorological stations in Turkey have been used to construct country-wide maps. Besides linear regression, the inverse square distance and ordinary co-Kriging (OCK) have been used and compared to each other. Also elevation, slope, and aspect data for each station have been taken into account as secondary variables, whose use has reduced errors by up to a factor of three. OCK gave the smallest errors (1.002 cm) when aspect was included.
Ali, Azizi; Mohd Muslim, Aidy; Lokman Husain, Mohd; Fadzil Akhir, Mohd
2013-04-01
Sea surface temperature (SST) variation provides vital information for weather and ocean forecasting especially when studying climate change. Conventional methods of collecting ocean parameters such as SST, remains expensive and labor intensive due to the large area coverage and complex analytical procedure required. Therefore, some studies need to be conducted on the spatial and temporal distribution of ocean parameters. This study looks at Geo-statisctical methods in interpolating SST values and its impact on accuracy. Two spatial Geo-statistical techniques, mainly kriging and inverse distance functions (IDW) were applied to create variability distribution maps of SST for the Southern South China Sea (SCS). Data from 72 sampling station was collected in July 2012 covering an area of 270 km x 100 km and 263 km away from shore. This data provide the basis for the interpolation and accuracy analysis. After normalization, variograms were computed to fit the data sets producing models with the least RSS value. The accuracy were later evaluated based on on root mean squared error (RMSE) and root mean kriging variance (RMKV). Results show that Kriging with exponential model produced most accuracy estimates, reducing error in 17.3% compared with inverse distance functions.
Institute of Scientific and Technical Information of China (English)
王正齐; 刘贤兴
2013-01-01
The bearingless induction motor is a nonlinear, multi-variable and strongly coupled system. For this system, a novel internal model control strategy based on neural network αth-order inverse system theory is proposed in this paper to realize the decoupling control. By cascading the ath-order inverse model approximated by the dynamic neural network with the original system, the nonlinear bearingless induction motor system is decoupled into four independent pseudo-linear subsystems, that is, two radial displacement subsystems, a speed subsystem and a rotor flux subsystem. Then, the internal model control method is introduced to the four pseudo-linear subsystems to ensure the robustness and antijamming ability of the closed-loop system. The effectiveness and superiority of the proposed strategy are demonstrated by simulation and experiment.%针对无轴承异步电机非线性、多变量、强耦合的特点,提出一种基于神经网络α阶逆系统方法的非线性内模控制策略.将用动态神经网络逼近的无轴承异步电机α阶逆模型与原系统复合,将非线性的无轴承异步电机原系统解耦成转子径向位移、转速和转子磁链四个独立的伪线性子系统.为了保证系统的鲁棒性,对伪线性系统引入内模控制,仿真和实验研究验证了所提控制方法的有效性.
The Method of Fixed Point on the Nonlinear Inversion for Seismic Scattering%地震波散射非线性反演的不动点方法
Institute of Scientific and Technical Information of China (English)
杨晓春; 李小凡; 张美根
2007-01-01
旨在构造一种新的地震波散射非线性反演方法.将函数论中的不动点理论引入到地震波散射非线性反演中,并构造出了波相空间里关于速度参数的具体的压缩映射算子,从而从理论上保证了速度参数不动点的存在性和寻找途径.在此基础上还证明了利用此速度参数的不动点和正演所得到的相应的波值也是波函数本身的不动点,并利用不动点的稳定属性得出此不动点是一个最优的点.最后,文中还用该方法给出了具体的数值算例,间接地证实了本方法的实用性.%The work described in this paper focuses on making a new method of nonlinear inversion for seismic scattering. The fixed-point theory is incorporated into the nonlinear seismic scattering inversion and the method to create a series of contractive mappings of velocity parameter's in the mapping space of wave is given. The existence of fixed point of velocity parameter is testified by the results and the method to find it is given. Furthermore, it is proved that the value obtained by taking the fixed point of velocity parameter into wave equation is the fixed point of the wave of the contractive mapping. Because of the stabilities quality of the fixed point, it is the global optimum. The given numerical example shows the validity of the method.
4th European Conference on Geostatistics for Environmental Applications
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...
Mapping malaria risk in Bangladesh using Bayesian geostatistical models.
Reid, Heidi; Haque, Ubydul; Clements, Archie C A; Tatem, Andrew J; Vallely, Andrew; Ahmed, Syed Masud; Islam, Akramul; Haque, Rashidul
2010-10-01
Background malaria-control programs are increasingly dependent on accurate risk maps to effectively guide the allocation of interventions and resources. Advances in model-based geostatistics and geographical information systems (GIS) have enabled researchers to better understand factors affecting malaria transmission and thus, more accurately determine the limits of malaria transmission globally and nationally. Here, we construct Plasmodium falciparum risk maps for Bangladesh for 2007 at a scale enabling the malaria-control bodies to more accurately define the needs of the program. A comprehensive malaria-prevalence survey (N = 9,750 individuals; N = 354 communities) was carried out in 2007 across the regions of Bangladesh known to be endemic for malaria. Data were corrected to a standard age range of 2 to less than 10 years. Bayesian geostatistical logistic regression models with environmental covariates were used to predict P. falciparum prevalence for 2- to 10-year-old children (PfPR(2-10)) across the endemic areas of Bangladesh. The predictions were combined with gridded population data to estimate the number of individuals living in different endemicity classes. Across the endemic areas, the average PfPR(2-10) was 3.8%. Environmental variables selected for prediction were vegetation cover, minimum temperature, and elevation. Model validation statistics revealed that the final Bayesian geostatistical model had good predictive ability. Risk maps generated from the model showed a heterogeneous distribution of PfPR(2-10) ranging from 0.5% to 50%; 3.1 million people were estimated to be living in areas with a PfPR(2-10) greater than 1%. Contemporary GIS and model-based geostatistics can be used to interpolate malaria risk in Bangladesh. Importantly, malaria risk was found to be highly varied across the endemic regions, necessitating the targeting of resources to reduce the burden in these areas.
Rucker, Dale F.; Ferré, Ty P. A.
2004-08-01
A MATLAB program was developed to invert first arrival travel time picks from zero offset profiling borehole ground penetrating radar traces to obtain the electromagnetic wave propagation velocities in soil. Zero-offset profiling refers to a mode of operation wherein the centers of the bistatic antennae being lowered to the same depth below ground for each measurement. The inversion uses a simulated annealing optimization routine, whereby the model attempts to reduce the root mean square error between the measured and modeled travel time by perturbing the velocity in a ray tracing routine. Measurement uncertainty is incorporated through the presentation of the ensemble mean and standard deviation from the results of a Monte Carlo simulation. The program features a pre-processor to modify or delete travel time information from the profile before inversion and post-processing through presentation of the ensemble statistics of the water contents inferred from the velocity profile. The program includes a novel application of a graphical user interface to animate the velocity fitting routine.
Reducing spatial uncertainty in climatic maps through geostatistical analysis
Pesquer, Lluís; Ninyerola, Miquel; Pons, Xavier
2014-05-01
Climatic maps from meteorological stations and geographical co-variables can be obtained through correlative models (Ninyerola et al., 2000)*. Nevertheless, the spatial uncertainty of the resulting maps could be reduced. The present work is a new stage over those approaches aiming to study how to obtain better results while characterizing spatial uncertainty. The study area is Catalonia (32000 km2), a region with highly variable relief (0 to 3143 m). We have used 217 stations (321 to 1244 mm) to model the annual precipitation in two steps: 1/ multiple regression using geographical variables (elevation, distance to the coast, latitude, etc) and 2/ refinement of the results by adding the spatial interpolation of the regression residuals with inverse distance weighting (IDW), regularized splines with tension (SPT) or ordinary kriging (OK). Spatial uncertainty analysis is based on an independent subsample (test set), randomly selected in previous works. The main contribution of this work is the analysis of this test set as well as the search for an optimal process of division (split) of the stations in two sets, one used to perform the multiple regression and residuals interpolation (fit set), and another used to compute the quality (test set); optimal division should reduce spatial uncertainty and improve the overall quality. Two methods have been evaluated against classical methods: (random selection RS and leave-one-out cross-validation LOOCV): selection by Euclidian 2D-distance, and selection by anisotropic 2D-distance combined with a 3D-contribution (suitable weighted) from the most representative independent variable. Both methods define a minimum threshold distance, obtained by variogram analysis, between samples. Main preliminary results for LOOCV, RS (average from 10 executions), Euclidian criterion (EU), and for anisotropic criterion (with 1.1 value, UTMY coordinate has a bit more weight than UTMX) combined with 3D criteria (A3D) (1000 factor for elevation
A reservoir skeleton-based multiple point geostatistics method
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
Traditional stochastic reservoir modeling,including object-based and pixel-based methods,cannot solve the problem of reproducing continuous and curvilinear reservoir objects. The paper first dives into the various stochastic modeling methods and extracts their merits,then proposes the skeleton-based multiple point geostatistics(SMPS) for the fluvial reservoir. The core idea is using the skeletons of reservoir objects to restrict the selection of data patterns. The skeleton-based multiple point geostatistics consists of two steps. First,predicting the channel skeleton(namely,channel centerline) by using the method in object-based modeling. The paper proposes a new method of search window to predict the skeleton. Then forecasting the distributions of reservoir objects using multiple point geostatistics with the restriction of channel skeleton. By the restriction of channel centerline,the selection of data events will be more reasonable and the realization will be achieved more really. The checks by the conceptual model and the real reservoir show that SMPS is much better than Sisim(sequential indicator simulation) ,Snesim(Single Normal Equation Simulation) and Simpat(simulation with patterns) in building the fluvial reservoir model. This new method will contribute to both the theoretical research of stochastic modeling and the oilfield developments of constructing highly precise reservoir geological models.
Breast carcinoma, intratumour heterogeneity and histological grading, using geostatistics.
Sharifi-Salamatian, V; de Roquancourt, A; Rigaut, J P
2000-01-01
Tumour progression is currently believed to result from genetic instability. Chromosomal patterns specific of a type of cancer are frequent even though phenotypic spatial heterogeneity is omnipresent. The latter is the usual cause of histological grading imprecision, a well documented problem, without any fully satisfactory solution up to now. The present article addresses this problem in breast carcinoma. The assessment of a genetic marker for human tumours requires quantifiable measures of intratumoral heterogeneity. If any invariance paradigm representing a stochastic or geostatistic function could be discovered, this might help in solving the grading problem. A novel methodological approach using geostatistics to measure heterogeneity is used. Twenty tumours from the three usual (Scarff-Bloom and Richardson) grades were obtained and paraffin sections stained by MIB-1 (Ki-67) and peroxidase staining. Whole two-dimensional sections were sampled. Morphometric grids of variable sizes allowed a simple and fast recording of positions of epithelial nuclei, marked or not by MIB-1. The geostatistical method is based here upon the asymptotic behaviour of dispersion variance. Measure of asymptotic exponent of dispersion variance shows an increase from grade 1 to grade 3. Preliminary results are encouraging: grades 1 and 3 on one hand and 2 and 3 on the other hand are totally separated. The final proof of an improved grading using this measure will of course require a confrontation with the results of survival studies.
2nd European Conference on Geostatistics for Environmental Applications
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...
Institute of Scientific and Technical Information of China (English)
陈亚文; 邹学文
2012-01-01
为了克服观测数据有限以及数据存在一定误差对参数反演结果的影响,提出了一种参数反演的有效算法.根据已知参数的先验分布和已经获得的有误差的监测数据,以贝叶斯推理作为理论基础,获得参数的联合后验概率密度函数,再利用马尔科夫链蒙特卡罗模拟对后验分布进行采样,获得参数的后验边缘概率密度,由此得到了参数的数学期望等有效的统计量.数值模拟结果表明,此算法能够有效地解决二维非线性抛物型方程的参数识别反问题,且具有较高的精度.%In order to overcome the limited observation data with noise, an inversion of the effective parameters algorithm is presented. First, according to the parameters,a priori distribution and the limited observation data with noise, Bayesian inference as a theoretical foundation,parameters of the joint posterior probability density function are obtained. Markov chain Monte Carlo simulation was taken to sample the posterior distribution to get the marginal posterior probability function of the parameters, and the statistical quantities such as the mathematic expectation were calculated. Experimental results show that this algorithm can successfully solve the problem of two-dimensional nonlinear parabolic equation parameter inversion and inversion results have higher accuracy.
Institute of Scientific and Technical Information of China (English)
江念; 王召巴; 陈友兴
2015-01-01
Based on correlation of the multi-level wavelet coefficients, a new algorithm combined with pulse-inversion tech-nique was proposed to improve the accuracy and robustness of defects for nonlinear ultrasonic nondestructive testing.The pulse-in-version technique was used to inhibit the odd harmonics due to nonlinearity of the input instrumentation.By employing the wavelet transform method, adhesive joints tested ultrasonic signal were de-noising processed.The experimental results show that proposed method can efficiently extract the pure second harmonic and enhance ability to characterize the adhesive strength by ultrasonic non-linear coefficient.%为提高非线性超声检测技术的准确性和鲁棒性，文中将脉冲反转技术和信号小波系数相关性滤波算法结合用于处理非线性超声检测信号。利用脉冲反转技术抑制实验仪器产生的奇数次谐波信号，再根据信号小波系数相关性算法滤除噪声。实验结果表明：上述信号处理方法能有效提取频率纯净的二次谐波，提高了超声非线性系数表征试件粘接强度的能力。
National Research Council Canada - National Science Library
Freire, J; Fernandez, L; Gonzalez-Gurriaran, E
1991-01-01
Geostatistical methodology was applied to analyze spatial structure and distribution of the epibenthic crustaceans Liocarcinus depurator, Macropipus tuberculatus, Polybius henslowii, Munida intermedia...
Institute of Scientific and Technical Information of China (English)
Bill X Hu; Jiang Xiaowei; Wan Li
2007-01-01
On the basis of local measurements of hydraulic conductivity, geostatistical methods have been found to be useful in heterogeneity characterization of a hydraulic conductivity field on a regional scale. However, the methods are not suited to directly integrate dynamic production data, such as,hydraulic head and solute concentration, into the study of conductivity distribution. These data, which record the flow and transport processes in the medium, are closely related to the spatial distribution of hydraulic conductivity. In this study, a three-dimensional gradient-based inverse method-the sequential self-calibration (SSC) method-is developed to calibrate a hydraulic conductivity field,initially generated by a geostatistical simulation method, conditioned on tracer test results. The SSC method can honor both local hydraulic conductivity measurements and tracer test data. The mismatch between the simulated hydraulic conductivity field and the reference true one, measured by its mean square error (MSE), is reduced through the SSC conditional study. In comparison with the unconditional results, the SSC conditional study creates the mean breakthrough curve much closer to the reference true curve, and significantly reduces the prediction uncertainty of the solute transport in the observed locations. Further, the reduction of uncertainty is spatially dependent, which indicates that good locations, geological structure, and boundary conditions will affect the efficiency of the SSC study results.
Energy Technology Data Exchange (ETDEWEB)
Lanyon, G.W. [GeoScience Ltd., Falmouth (United Kingdom); Marschall, P.; Vomvoris, S. [NAGRA, Wettingen (Switzerland); Jaquet, O. [Colenco Power Engineering AG, Baden (Switzerland); Mazurek, M. [Bern Univ. (Switzerland). Mineralogisch-petrographisches Inst.
1998-09-01
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 14 refs, 9 figs
Juang, K W; Lee, D Y; Ellsworth, T R
2001-01-01
The spatial distribution of a pollutant in contaminated soils is usually highly skewed. As a result, the sample variogram often differs considerably from its regional counterpart and the geostatistical interpolation is hindered. In this study, rank-order geostatistics with standardized rank transformation was used for the spatial interpolation of pollutants with a highly skewed distribution in contaminated soils when commonly used nonlinear methods, such as logarithmic and normal-scored transformations, are not suitable. A real data set of soil Cd concentrations with great variation and high skewness in a contaminated site of Taiwan was used for illustration. The spatial dependence of ranks transformed from Cd concentrations was identified and kriging estimation was readily performed in the standardized-rank space. The estimated standardized rank was back-transformed into the concentration space using the middle point model within a standardized-rank interval of the empirical distribution function (EDF). The spatial distribution of Cd concentrations was then obtained. The probability of Cd concentration being higher than a given cutoff value also can be estimated by using the estimated distribution of standardized ranks. The contour maps of Cd concentrations and the probabilities of Cd concentrations being higher than the cutoff value can be simultaneously used for delineation of hazardous areas of contaminated soils.
Ingram, WT
2012-01-01
Inverse limits provide a powerful tool for constructing complicated spaces from simple ones. They also turn the study of a dynamical system consisting of a space and a self-map into a study of a (likely more complicated) space and a self-homeomorphism. In four chapters along with an appendix containing background material the authors develop the theory of inverse limits. The book begins with an introduction through inverse limits on [0,1] before moving to a general treatment of the subject. Special topics in continuum theory complete the book. Although it is not a book on dynamics, the influen
Ding, J. Y.
2013-12-01
This note illustrates, in the context of Brutsaert-Nieber (1977) model: -dQ/dt = aQb, the utility of a newly rediscovered inverse fractional power (IFP) transform of the flow rates. This method of streamflow recession analysis dates back a half-century. The IFP transform Δb on an operand Q is defined as Δb Q = 1/Qb-1. Brutsaert-Nieber model by IFP transform thus becomes: ΔbQ(t) = ΔbQ(0) + (b-1) at, if b ≠ 1. The IFP transformed recession curve appears as a straight line on a semi-IFP plot. The method has both the advantage of being independent of the size of computational time step, and the disadvantage of being depending on the parameter b value. This is used to calibrate the Brutsaert-Nieber recession flow model in which b is a slope (or shape) parameter, and a is an intercept (or a scale parameter). It is applied to four observed events on the Spoon River in Illinois (4237 km2). The results show that the IFP transform method gives a narrower range of parameter b values than the regression method in a recession plot. Theoretically, an IFP transformed recession curve for large watersheds falls between those performed by the reciprocal of the cubic root (RoCR) transform and the reciprocal of the square root (RoSR) one. In general, the forgotten IFP transform method merits a fresh look, especially for hillslopes and zero-order catchments, the building blocks of a watershed system. In particular, because of its origin in hillslope hydrology, the 1-parameter RoSR transform need be falsified or verified for application to headwater catchments.
Energy Technology Data Exchange (ETDEWEB)
Finsterle, S.; Kowalsky, M.B.
2010-10-15
We propose a modification to the Levenberg-Marquardt minimization algorithm for a more robust and more efficient calibration of highly parameterized, strongly nonlinear models of multiphase flow through porous media. The new method combines the advantages of truncated singular value decomposition with those of the classical Levenberg-Marquardt algorithm, thus enabling a more robust solution of underdetermined inverse problems with complex relations between the parameters to be estimated and the observable state variables used for calibration. The truncation limit separating the solution space from the calibration null space is re-evaluated during the iterative calibration process. In between these re-evaluations, fewer forward simulations are required, compared to the standard approach, to calculate the approximate sensitivity matrix. Truncated singular values are used to calculate the Levenberg-Marquardt parameter updates, ensuring that safe small steps along the steepest-descent direction are taken for highly correlated parameters of low sensitivity, whereas efficient quasi-Gauss-Newton steps are taken for independent parameters with high impact. The performance of the proposed scheme is demonstrated for a synthetic data set representing infiltration into a partially saturated, heterogeneous soil, where hydrogeological, petrophysical, and geostatistical parameters are estimated based on the joint inversion of hydrological and geophysical data.
Geospatial Interpolation and Mapping of Tropospheric Ozone Pollution Using Geostatistics
Directory of Open Access Journals (Sweden)
Swatantra R. Kethireddy
2014-01-01
Full Text Available Tropospheric ozone (O3 pollution is a major problem worldwide, including in the United States of America (USA, particularly during the summer months. Ozone oxidative capacity and its impact on human health have attracted the attention of the scientific community. In the USA, sparse spatial observations for O3 may not provide a reliable source of data over a geo-environmental region. Geostatistical Analyst in ArcGIS has the capability to interpolate values in unmonitored geo-spaces of interest. In this study of eastern Texas O3 pollution, hourly episodes for spring and summer 2012 were selectively identified. To visualize the O3 distribution, geostatistical techniques were employed in ArcMap. Using ordinary Kriging, geostatistical layers of O3 for all the studied hours were predicted and mapped at a spatial resolution of 1 kilometer. A decent level of prediction accuracy was achieved and was confirmed from cross-validation results. The mean prediction error was close to 0, the root mean-standardized-prediction error was close to 1, and the root mean square and average standard errors were small. O3 pollution map data can be further used in analysis and modeling studies. Kriging results and O3 decadal trends indicate that the populace in Houston-Sugar Land-Baytown, Dallas-Fort Worth-Arlington, Beaumont-Port Arthur, San Antonio, and Longview are repeatedly exposed to high levels of O3-related pollution, and are prone to the corresponding respiratory and cardiovascular health effects. Optimization of the monitoring network proves to be an added advantage for the accurate prediction of exposure levels.
Geospatial interpolation and mapping of tropospheric ozone pollution using geostatistics.
Kethireddy, Swatantra R; Tchounwou, Paul B; Ahmad, Hafiz A; Yerramilli, Anjaneyulu; Young, John H
2014-01-10
Tropospheric ozone (O3) pollution is a major problem worldwide, including in the United States of America (USA), particularly during the summer months. Ozone oxidative capacity and its impact on human health have attracted the attention of the scientific community. In the USA, sparse spatial observations for O3 may not provide a reliable source of data over a geo-environmental region. Geostatistical Analyst in ArcGIS has the capability to interpolate values in unmonitored geo-spaces of interest. In this study of eastern Texas O3 pollution, hourly episodes for spring and summer 2012 were selectively identified. To visualize the O3 distribution, geostatistical techniques were employed in ArcMap. Using ordinary Kriging, geostatistical layers of O3 for all the studied hours were predicted and mapped at a spatial resolution of 1 kilometer. A decent level of prediction accuracy was achieved and was confirmed from cross-validation results. The mean prediction error was close to 0, the root mean-standardized-prediction error was close to 1, and the root mean square and average standard errors were small. O3 pollution map data can be further used in analysis and modeling studies. Kriging results and O3 decadal trends indicate that the populace in Houston-Sugar Land-Baytown, Dallas-Fort Worth-Arlington, Beaumont-Port Arthur, San Antonio, and Longview are repeatedly exposed to high levels of O3-related pollution, and are prone to the corresponding respiratory and cardiovascular health effects. Optimization of the monitoring network proves to be an added advantage for the accurate prediction of exposure levels.
Mercury emissions from coal combustion in Silesia, analysis using geostatistics
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
Interface-wave dispersion curves inversion based on nonlinear Bayesian theory%根据非线性贝叶斯理论的界面波频散曲线反演
Institute of Scientific and Technical Information of China (English)
李翠琳; Stan E Dosso; Hefeng Dong
2012-01-01
通过时频分析法从海底环境噪声数据中提取界面波频散曲线,进而采用非线性贝叶斯反演方法估算海底沉积物厚度、剪切波速度、压缩波速度和密度等参数及其不确定性.参数的最大后验概率(MAP)估计值和边缘概率分布分别通过自适应单纯形模拟退火法和Metropolis-Hastings采样法在各参数先验区间内搜索获得,采用贝叶斯信息准则(BIC)从不同参数化模型中选择最优模型.界面波频散曲线反演结果表明:满足实测数据的最优海底模型结构为3层均匀分布剪切波速度剖面结构,海底深度的反演精度在800 m以内,比起压缩波速度和密度,剪切波速度的不确定性更小,对界面波频散曲线更敏感.%This paper applies a dataset of ocean ambient noise data to extract interface-wave dispersion curves using time-frequency analysis. The nonlinear Bayesian inversion is applied to estimate seabed sediment parameters such as thickness, shear-wave velocity, compression wave velocity and density, and their uncertainties from interface-wave dispersion curves. The maximum a posterior (MAP) model and marginal probability distributions of parameters are estimated using posterior probability densities computed by adaptive simplex simulated annealing and Metropolis-Hastings sampling methods. The Bayesian information criterion is applied to determine the optimal model that fully explains the observed data by the different parameterizations. The inversion results indicate that 3-uniform-layer model is chosen as the preferred parameterization. The resolution of inversion is up to 800 m-depth. The shear-wave velocity and layer thickness have fewer uncertainties and are more sensitive to the interface wave dispersion than the compression wave velocity and density.
Spatial analysis of lettuce downy mildew using geostatistics and geographic information systems.
Wu, B M; van Bruggen, A H; Subbarao, K V; Pennings, G G
2001-02-01
ABSTRACT The epidemiology of lettuce downy mildew has been investigated extensively in coastal California. However, the spatial patterns of the disease and the distance that Bremia lactucae spores can be transported have not been determined. During 1995 to 1998, we conducted several field- and valley-scale surveys to determine spatial patterns of this disease in the Salinas valley. Geostatistical analyses of the survey data at both scales showed that the influence range of downy mildew incidence at one location on incidence at other locations was between 80 and 3,000 m. A linear relationship was detected between semivariance and lag distance at the field scale, although no single statistical model could fit the semi-variograms at the valley scale. Spatial interpolation by the inverse distance weighting method with a power of 2 resulted in plausible estimates of incidence throughout the valley. Cluster analysis in geographic information systems on the interpolated disease incidence from different dates demonstrated that the Salinas valley could be divided into two areas, north and south of Salinas City, with high and low disease pressure, respectively. Seasonal and spatial trends along the valley suggested that the distinction between the downy mildew conducive and nonconducive areas might be determined by environmental factors.
A Resampling-Based Stochastic Approximation Method for Analysis of Large Geostatistical Data
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.
Zhang, Ting; Du, Yi; Huang, Tao; Li, Xue
2016-02-01
Constrained by current hardware equipment and techniques, acquisition of geological data sometimes is difficult or even impossible. Stochastic simulation for geological data is helpful to address this issue, providing multiple possible results of geological data for resource prediction and risk evaluation. Multiple-point geostatistics (MPS) being one of the main branches of stochastic simulation can extract the intrinsic features of patterns from training images (TIs) that provide prior information to limit the under-determined simulated results, and then copy them to the simulated regions. Because the generated models from TIs are not always linear, some MPS methods using linear dimensionality reduction are not suitable to deal with nonlinear models of TIs. A new MPS method named ISOMAPSIM was proposed to resolve this issue, which reduces the dimensionality of patterns from TIs using isometric mapping (ISOMAP) and then classifies these low-dimensional patterns for simulation. Since conditional models including hard data and soft data influence the simulated results greatly, this paper further studies ISOMAPSIM using hard data and soft data to obtain more accurate simulations for geological modeling. Stochastic simulation of geological data is processed respectively under several conditions according to different situations of conditional models. The tests show that the proposed method can reproduce the structural characteristics of TIs under all conditions, but the condition using soft data and hard data together performs best in simulation quality; moreover, the proposed method shows its advantages over other MPS methods that use linear dimensionality reduction.
Regional flow duration curves: Geostatistical techniques versus multivariate regression
Pugliese, Alessio; Farmer, William H.; Castellarin, Attilio; Archfield, Stacey A.; Vogel, Richard M.
2016-10-01
A period-of-record flow duration curve (FDC) represents the relationship between the magnitude and frequency of daily streamflows. Prediction of FDCs is of great importance for locations characterized by sparse or missing streamflow observations. We present a detailed comparison of two methods which are capable of predicting an FDC at ungauged basins: (1) an adaptation of the geostatistical method, Top-kriging, employing a linear weighted average of dimensionless empirical FDCs, standardised with a reference streamflow value; and (2) regional multiple linear regression of streamflow quantiles, perhaps the most common method for the prediction of FDCs at ungauged sites. In particular, Top-kriging relies on a metric for expressing the similarity between catchments computed as the negative deviation of the FDC from a reference streamflow value, which we termed total negative deviation (TND). Comparisons of these two methods are made in 182 largely unregulated river catchments in the southeastern U.S. using a three-fold cross-validation algorithm. Our results reveal that the two methods perform similarly throughout flow-regimes, with average Nash-Sutcliffe Efficiencies 0.566 and 0.662, (0.883 and 0.829 on log-transformed quantiles) for the geostatistical and the linear regression models, respectively. The differences between the reproduction of FDC's occurred mostly for low flows with exceedance probability (i.e. duration) above 0.98.
Validating spatial structure in canopy water content using geostatistics
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.
Spatial prediction of soil penetration resistance using functional geostatistics
Directory of Open Access Journals (Sweden)
Diego Leonardo Cortés-D
Full Text Available ABSTRACT Knowledge of agricultural soils is a relevant factor for the sustainable development of farming activities. Studies on agricultural soils usually begin with the analysis of data obtained from sampling a finite number of sites in a particular region of interest. The variables measured at each site can be scalar (chemical properties or functional (infiltration water or penetration resistance. The use of functional geostatistics (FG allows to perform spatial curve interpolation to generate prediction curves (instead of single variables at sites that lack information. This study analyzed soil penetration resistance (PR data measured between 0 and 35 cm depth at 75 sites within a 37 ha plot dedicated to livestock. The data from each site were converted to curves using non-parametric smoothing techniques. In this study, a B-splines basis of 18 functions was used to estimate PR curves for each of the 75 sites. The applicability of FG as a spatial prediction tool for PR curves was then evaluated using cross-validation, and the results were compared with classical spatial prediction methods (univariate geostatistics that are generally used for studying this type of information. We concluded that FG is a reliable tool for analyzing PR because a high correlation was obtained between the observed and predicted curves (R2 = 94 %. In addition, the results from descriptive analyses calculated from field data and FG models were similar for the observed and predicted values.
Regional flow duration curves: Geostatistical techniques versus multivariate regression
Pugliese, Alessio; Farmer, William H.; Castellarin, Attilio; Archfield, Stacey A.; Vogel, Richard M.
2016-01-01
A period-of-record flow duration curve (FDC) represents the relationship between the magnitude and frequency of daily streamflows. Prediction of FDCs is of great importance for locations characterized by sparse or missing streamflow observations. We present a detailed comparison of two methods which are capable of predicting an FDC at ungauged basins: (1) an adaptation of the geostatistical method, Top-kriging, employing a linear weighted average of dimensionless empirical FDCs, standardised with a reference streamflow value; and (2) regional multiple linear regression of streamflow quantiles, perhaps the most common method for the prediction of FDCs at ungauged sites. In particular, Top-kriging relies on a metric for expressing the similarity between catchments computed as the negative deviation of the FDC from a reference streamflow value, which we termed total negative deviation (TND). Comparisons of these two methods are made in 182 largely unregulated river catchments in the southeastern U.S. using a three-fold cross-validation algorithm. Our results reveal that the two methods perform similarly throughout flow-regimes, with average Nash-Sutcliffe Efficiencies 0.566 and 0.662, (0.883 and 0.829 on log-transformed quantiles) for the geostatistical and the linear regression models, respectively. The differences between the reproduction of FDC's occurred mostly for low flows with exceedance probability (i.e. duration) above 0.98.
Malepaard, J.
2007-01-01
Balansschikkingen (of negatief gebonden of-constructies) zijn volgens de in dit artikel ontwikkelde hypothese inverse disjuncties (id's). Het zijn tweeledige zinnen waarvan het eerste lid een verplichte negatieve of minimaliserende constituent bevat en het tweede lid met of begint. Evenals
Application of Large-Scale Inversion Algorithms to Hydraulic Tomography in an Alluvial Aquifer.
Fischer, P; Jardani, A; Soueid Ahmed, A; Abbas, M; Wang, X; Jourde, H; Lecoq, N
2017-03-01
Large-scale inversion methods have been recently developed and permitted now to considerably reduce the computation time and memory needed for inversions of models with a large amount of parameters and data. In this work, we have applied a deterministic geostatistical inversion algorithm to a hydraulic tomography investigation conducted in an experimental field site situated within an alluvial aquifer in Southern France. This application aims to achieve a 2-D large-scale modeling of the spatial transmissivity distribution of the site. The inversion algorithm uses a quasi-Newton iterative process based on a Bayesian approach. We compared the results obtained by using three different methodologies for sensitivity analysis: an adjoint-state method, a finite-difference method, and a principal component geostatistical approach (PCGA). The PCGA is a large-scale adapted method which was developed for inversions with a large number of parameters by using an approximation of the covariance matrix, and by avoiding the calculation of the full Jacobian sensitivity matrix. We reconstructed high-resolution transmissivity fields (composed of up to 25,600 cells) which generated good correlations between the measured and computed hydraulic heads. In particular, we show that, by combining the PCGA inversion method and the hydraulic tomography method, we are able to substantially reduce the computation time of the inversions, while still producing high-quality inversion results as those obtained from the other sensitivity analysis methodologies.
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.
Directory of Open Access Journals (Sweden)
S. Ly
2011-07-01
Full Text Available Spatial interpolation of precipitation data is of great importance for hydrological modelling. Geostatistical methods (kriging are widely applied in spatial interpolation from point measurement to continuous surfaces. The first step in kriging computation is the semi-variogram modelling which usually used only one variogram model for all-moment data. The objective of this paper was to develop different algorithms of spatial interpolation for daily rainfall on 1 km^{2} regular grids in the catchment area and to compare the results of geostatistical and deterministic approaches. This study leaned on 30-yr daily rainfall data of 70 raingages in the hilly landscape of the Ourthe and Ambleve catchments in Belgium (2908 km^{2}. This area lies between 35 and 693 m in elevation and consists of river networks, which are tributaries of the Meuse River. For geostatistical algorithms, seven semi-variogram models (logarithmic, power, exponential, Gaussian, rational quadratic, spherical and penta-spherical were fitted to daily sample semi-variogram on a daily basis. These seven variogram models were also adopted to avoid negative interpolated rainfall. The elevation, extracted from a digital elevation model, was incorporated into multivariate geostatistics. Seven validation raingages and cross validation were used to compare the interpolation performance of these algorithms applied to different densities of raingages. We found that between the seven variogram models used, the Gaussian model was the most frequently best fit. Using seven variogram models can avoid negative daily rainfall in ordinary kriging. The negative estimates of kriging were observed for convective more than stratiform rain. The performance of the different methods varied slightly according to the density of raingages, particularly between 8 and 70 raingages but it was much different for interpolation using 4 raingages. Spatial interpolation with the geostatistical and
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...... is obtained by assuming that the a priori beliefs about the solution before having observed any data can be described by a prior distribution. The solution to the statistical inverse problem is then given by the posterior distribution obtained by Bayes' formula. Hence the solution of an ill-posed inverse...... 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...
A Geostatistical Approach to Indoor Surface Sampling Strategies
DEFF Research Database (Denmark)
Schneider, Thomas; Petersen, Ole Holm; Nielsen, Allan Aasbjerg
1990-01-01
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......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...... 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...
Geostatistical sampling optimization and waste characterization of contaminated premises
Energy Technology Data Exchange (ETDEWEB)
Desnoyers, Y.; Jeannee, N. [GEOVARIANCES, 49bis avenue Franklin Roosevelt, BP91, Avon, 77212 (France); Chiles, J.P. [Centre de geostatistique, Ecole des Mines de Paris (France); Dubot, D. [CEA DSV/FAR/USLT/SPRE/SAS (France); Lamadie, F. [CEA DEN/VRH/DTEC/SDTC/LTM (France)
2009-06-15
At the end of process equipment dismantling, the complete decontamination of nuclear facilities requires a radiological assessment of the building structure residual activity. From this point of view, the set up of an appropriate evaluation methodology is of crucial importance. 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) control of the emergent signal is commonly performed using in situ measurement methods such as surface controls combined with in situ gamma spectrometry. Finally, in order to assess the contamination depth, samples are collected at several locations within the premises and analyzed. Combined with historical information and emergent signal maps, such data allow the definition of a preliminary waste zoning. The exhaustive control of the emergent signal with surface measurements usually leads to inaccurate estimates, because of several factors: varying position of the measuring device, subtraction of an estimate of the background signal, etc. 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 initial activity usually presents a spatial continuity within the premises, with preferential contamination of specific areas or existence of activity gradients. Taking into account this spatial continuity is essential to avoid bias while setting up the sampling plan. In such a case, Geostatistics provides methods that integrate the contamination spatial structure. After the characterization of this spatial structure, most probable estimates of the surface activity at un-sampled locations can be derived using kriging techniques. Variants of these techniques also give access to estimates of the uncertainty associated to the spatial
A Geostatistical Approach to Indoor Surface Sampling Strategies
DEFF Research Database (Denmark)
Schneider, Thomas; Petersen, Ole Holm; Nielsen, Allan Aasbjerg
1990-01-01
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...... using the global information. Then methods for choosing a proper sampling area for a single sample of dust on a table are given. The global contamination of an object is determined by a maximum likelihood estimator. Finally, it is shown how specified experimental goals can be included to determine...... 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...
Bayesian geostatistics in health cartography: the perspective of malaria.
Patil, Anand P; Gething, Peter W; Piel, Frédéric B; Hay, Simon I
2011-06-01
Maps of parasite prevalences and other aspects of infectious diseases that vary in space are widely used in parasitology. However, spatial parasitological datasets rarely, if ever, have sufficient coverage to allow exact determination of such maps. Bayesian geostatistics (BG) is a method for finding a large sample of maps that can explain a dataset, in which maps that do a better job of explaining the data are more likely to be represented. This sample represents the knowledge that the analyst has gained from the data about the unknown true map. BG provides a conceptually simple way to convert these samples to predictions of features of the unknown map, for example regional averages. These predictions account for each map in the sample, yielding an appropriate level of predictive precision.
Medical Geography: a Promising Field of Application for Geostatistics.
Goovaerts, P
2009-01-01
The analysis of health data and putative covariates, such as environmental, socio-economic, behavioral or demographic factors, is a promising application for geostatistics. It presents, however, several methodological challenges that arise from the fact that data are typically aggregated over irregular spatial supports and consist of a numerator and a denominator (i.e. population size). This paper presents an overview of recent developments in the field of health geostatistics, with an emphasis on three main steps in the analysis of areal health data: estimation of the underlying disease risk, detection of areas with significantly higher risk, and analysis of relationships with putative risk factors. The analysis is illustrated using age-adjusted cervix cancer mortality rates recorded over the 1970-1994 period for 118 counties of four states in the Western USA. Poisson kriging allows the filtering of noisy mortality rates computed from small population sizes, enhancing the correlation with two putative explanatory variables: percentage of habitants living below the federally defined poverty line, and percentage of Hispanic females. Area-to-point kriging formulation creates continuous maps of mortality risk, reducing the visual bias associated with the interpretation of choropleth maps. Stochastic simulation is used to generate realizations of cancer mortality maps, which allows one to quantify numerically how the uncertainty about the spatial distribution of health outcomes translates into uncertainty about the location of clusters of high values or the correlation with covariates. Last, geographically-weighted regression highlights the non-stationarity in the explanatory power of covariates: the higher mortality values along the coast are better explained by the two covariates than the lower risk recorded in Utah.
Combining geostatistics with Moran's I analysis for mapping soil heavy metals in Beijing, China.
Huo, Xiao-Ni; Li, Hong; Sun, Dan-Feng; Zhou, Lian-Di; Li, Bao-Guo
2012-03-01
Production of high quality interpolation maps of heavy metals is important for risk assessment of environmental pollution. In this paper, the spatial correlation characteristics information obtained from Moran's I analysis was used to supplement the traditional geostatistics. According to Moran's I analysis, four characteristics distances were obtained and used as the active lag distance to calculate the semivariance. Validation of the optimality of semivariance demonstrated that using the two distances where the Moran's I and the standardized Moran's I, Z(I) reached a maximum as the active lag distance can improve the fitting accuracy of semivariance. Then, spatial interpolation was produced based on the two distances and their nested model. The comparative analysis of estimation accuracy and the measured and predicted pollution status showed that the method combining geostatistics with Moran's I analysis was better than traditional geostatistics. Thus, Moran's I analysis is a useful complement for geostatistics to improve the spatial interpolation accuracy of heavy metals.
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.
Energy Technology Data Exchange (ETDEWEB)
Dai, Heng [Pacific Northwest National Laboratory, Richland Washington USA; Chen, Xingyuan [Pacific Northwest National Laboratory, Richland Washington USA; Ye, Ming [Department of Scientific Computing, Florida State University, Tallahassee Florida USA; Song, Xuehang [Pacific Northwest National Laboratory, Richland Washington USA; Zachara, John M. [Pacific Northwest National Laboratory, Richland Washington USA
2017-05-01
Sensitivity analysis is an important tool for quantifying uncertainty in the outputs of mathematical models, especially for complex systems with a high dimension of spatially correlated parameters. Variance-based global sensitivity analysis has gained popularity because it can quantify the relative contribution of uncertainty from different sources. However, its computational cost increases dramatically with the complexity of the considered model and the dimension of model parameters. In this study we developed a hierarchical sensitivity analysis method that (1) constructs an uncertainty hierarchy by analyzing the input uncertainty sources, and (2) accounts for the spatial correlation among parameters at each level of the hierarchy using geostatistical tools. The contribution of uncertainty source at each hierarchy level is measured by sensitivity indices calculated using the variance decomposition method. Using this methodology, we identified the most important uncertainty source for a dynamic groundwater flow and solute transport in model at the Department of Energy (DOE) Hanford site. The results indicate that boundary conditions and permeability field contribute the most uncertainty to the simulated head field and tracer plume, respectively. The relative contribution from each source varied spatially and temporally as driven by the dynamic interaction between groundwater and river water at the site. By using a geostatistical approach to reduce the number of realizations needed for the sensitivity analysis, the computational cost of implementing the developed method was reduced to a practically manageable level. The developed sensitivity analysis method is generally applicable to a wide range of hydrologic and environmental problems that deal with high-dimensional spatially-distributed parameters.
Analysis of dengue fever risk using geostatistics model in bone regency
Amran, Stang, Mallongi, Anwar
2017-03-01
This research aim is to analysis of dengue fever risk based on Geostatistics model in Bone Regency. Risk levels of dengue fever are denoted by parameter of Binomial distribution. Effect of temperature, rainfalls, elevation, and larvae abundance are investigated through Geostatistics model. Bayesian hierarchical method is used in estimation process. Using dengue fever data in eleven locations this research shows that temperature and rainfall have significant effect of dengue fever risk in Bone regency.
Wingle, William L.; Poeter, Eileen P.; McKenna, Sean A.
1999-05-01
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.
Rhodes, Elena M; Liburd, Oscar E; Grunwald, Sabine
2011-08-01
Flower thrips (Frankliniella spp.) are one of the key pests of southern highbush blueberries (Vaccinium corymbosum L. x V. darrowii Camp), a high-value crop in Florida. Thrips' feeding and oviposition injury to flowers can result in fruit scarring that renders the fruit unmarketable. Flower thrips often form areas of high population, termed "hot spots", in blueberry plantings. The objective of this study was to model thrips spatial distribution patterns with geostatistical techniques. Semivariogram models were used to determine optimum trap spacing and two commonly used interpolation methods, inverse distance weighting (IDW) and ordinary kriging (OK), were compared for their ability to model thrips spatial patterns. The experimental design consisted of a grid of 100 white sticky traps spaced at 15.24-m and 7.61-m intervals in 2008 and 2009, respectively. Thirty additional traps were placed randomly throughout the sampling area to collect information on distances shorter than the grid spacing. The semivariogram analysis indicated that, in most cases, spacing traps at least 28.8 m apart would result in spatially independent samples. Also, the 7.61-m grid spacing captured more of the thrips spatial variability than the 15.24-m grid spacing. IDW and OK produced maps with similar accuracy in both years, which indicates that thrips spatial distribution patterns, including "hot spots," can be modeled using either interpolation method. Future studies can use this information to determine if the formation of "hot spots" can be predicted using flower density, temperature, and other environmental factors. If so, this development would allow growers to spot treat the "hot spots" rather than their entire field.
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...
Inverse imbalance reconstruction in rotordynamics
Energy Technology Data Exchange (ETDEWEB)
Ramlau, R. [Austrian Academy of Sciences, Linz (Austria). Johann Radon Inst. for Computational and Applied Mathematics; Dicken, V. [MeVis GmbH, Bremen (Germany); Maass, P. [Bremen Univ. (Germany). Zentrum fuer Technomathematik; Streller, C. [Rolls-Royce Germany GmbH, Dahlewitz (Germany); Rienaecker, A. [MTU Aero Engines GmbH, Muenchen (Germany)
2006-05-15
The goal of this work is to establish and compare algorithms for inverse imbalance reconstruction in aircraft turbines. Such algorithms are based on a validated whole engine model of a turbo engine under consideration. Base on the model, the impact of an imbalance distribution on the vibration behaviour of the turbine can be described as a matrix-vector multiplication Af = g, where f is the imbalance distribution and g the vibration response. It turns out that the matrix A is very ill-conditioned. As the measured data is highly affected with noise, we have to use regularization methods in order to stabilize the inversion. Our main interest was in the use of nonlinear regularization methods, in particular nonlinear filtered singular value decomposition and conjugate gradient regularization. (orig.)
Jensen, K. H.; He, X.; Sonnenborg, T. O.; Jørgensen, F.
2016-12-01
Multiple-point geostatistical simulation (MPS) of the geological structure has become popular in recent years in groundwater modeling. The method derives multi-point based structural information from a training image (TI) and as such is superior to the traditional two-point based geostatistical approach. Its application in 3D simulations has been constrained by the difficulty of constructing 3D TI. High resolution 3D electromagnetic data can be used for defining a TI but the data can also be used as secondary data for soft conditioning. An alternative approach for derived a TI is to use the object-based unconditional simulation program TiGenerator. In this study we present different MPS simulations of the geological structure for a site in Denmark based on different scenarios regarding TI and soft conditioning. The generated geostatistical realizations are used for developing groundwater models based on MODFLOW and each of these models is calibrated against hydraulic head measurements using the inversion code PEST. Based on the calibrated flow models the particle tracking code MODPATH is used to simulate probabilistic capture zones for abstraction wells. By comparing simulations of groundwater flow and probabilistic capture zone, comparable results are obtained based on TI directly derived from high resolution geophysical data and generated by theTiGenerator even for the probabilistic capture zones, which are highly sensitive to the geological structure. The study further suggests that soft conditioning in MPS is an effective way of integrating secondary data such as 3D airborne electromagnetic data (SkyTEM) leading to improved estimations of the geological structure as evidenced by the resulting hydraulic parameter values. However, care should be taken when the same data source is used for defining the TI and for soft conditioning as this may lead reduction in the uncertainty estimation.
A connectionist-geostatistical approach for classification of deformation types in ice surfaces
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.
The Geostatistical Framework for Spatial Prediction%空间预测的地统计学框架
Institute of Scientific and Technical Information of China (English)
张景雄; 姚娜
2008-01-01
Geostatistics provides a coherent framework for spatial prediction and uncertainty assessment, whereby spatial dependence, as quantified by variograms, is utilized for best linear unbiased estimation of a regionalized variable at unsampied locations. Geostatistics for prediction of continuous regionalized variables is reviewed, with key methods underlying the derivation of major variants of uni-variate Kriging described in an easy-to-follow manner. This paper will contribute to demystification and, hence, popularization of geostatistics in geoinformatics communities.
Geostatistical interpolation for modelling SPT data in northern Izmir
Indian Academy of Sciences (India)
Selim Altun; A Burak Göktepe; Alper Sezer
2013-12-01
In this study, it was aimed to map the corrected Standard Penetration Test(SPT) values in Karşıyaka city center by kriging approach. Six maps were prepared by this geostatistical approach at depths of 3, 6, 9, 13.5, 18 and 25.5m. Borehole test results obtained from 388 boreholes in central Karşıyaka were used to model the spatial variation of $(\\text{N}_1)_{\\text{60cs}}$ values in an area of 5.5 km2. Corrections were made for depth, hammer energy, rod length, sampler, borehole diameter and fines content, to the data in hand. At various depths, prepared variograms and the kriging method were used together to model the variation of corrected SPT data in the region, which enabled the estimation of missing data in the region. The results revealed that the estimation ability of the models were acceptable, which were validated by a number of parameters as well as the comparisons of the actual and estimated data. Outcomes of this study can be used in microzonation studies, site response analyses, calculation of bearing capacity of subsoils in the region and producing a number of parameters which are empirically related to corrected SPT number as well.
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.
A Classification for a Geostatistical Index of Spatial Dependence
Directory of Open Access Journals (Sweden)
Enio Júnior Seidel
Full Text Available ABSTRACT: In geostatistical studies, spatial dependence can generally be described by means of the semivariogram or, in complementary form, with a single index followed by its categorization to classify the degree of such dependence. The objective of this study was to construct a categorization for the spatial dependence index (SDI proposed by Seidel and Oliveira (2014 in order to classify spatial variability in terms of weak, moderate, and strong dependence. Theoretical values were constructed from different degrees of spatial dependence, which served as a basis for calculation of the SDI. In view of the form of distribution and SDI descriptive measures, we developed a categorization for posterior classification of spatial dependence, specific to each semivariogram model. The SDI categorization was based on its median and 3rd quartile, allowing us to classify spatial dependence as weak, moderate, or strong. We established that for the spherical semivariogram: SDISpherical (% ≤ 7 % (weak spatial dependence, 7 % 15 % (strong spatial dependence; for the exponential semivariogram: SDIExponential (% ≤ 6 % (weak spatial dependence, 6 % 13 % (strong spatial dependence; and for the Gaussian semivariogram: SDIGaussian (% ≤ 9 % (weak spatial dependence, 9 % 20 % (strong spatial dependence. The proposed categorization allows the user to transform the numerical values calculated for SDI into categories of variability of spatial dependence, with adequate power for explanation and comparison.
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.
Ustaoglu, Beyza
2014-05-01
Rainfall is one of the most important climatic factor for environmental studies. Several methods (Thiessen polygon, Inverse Distance Weighting (IDW) and Kriging etc.) have been used by researchers for spatial interpolation of rainfall data. Kriging is a geostatistical method which is based on spatial correlation between neighbouring observations to predict attribute values at unsampled locations. The study area, Eastern Black Sea Basin is one of the highest rainfall accumulations in Turkey according to the measured station data (1942 - 2011). Eastern Black Sea Basin is the only basin in Turkey with an increase amount of winter (October, November, December) rainfall for 2013 in comparison to the long term mean and previous year winter rainfall. Regarding to the future projections (Ustaoglu, 2011), this basin has one of the strongest increasing trend according to the A2 scenario analysis obtained from RegCM3 regional climate model during the ten years periods (2011 - 2100). In this study, 2013 winter rainfall in the basin is highlighted and compared with the past and future rainfall conditions of the basin. Keywords: Geostatistical Analysis, Winter Rainfall, Eastern Black Sea Basin
多点地质统计学研究进展与展望%Progress and prospect of multiple-point geostatistics
Institute of Scientific and Technical Information of China (English)
尹艳树; 张昌民; 李玖勇; 石书缘
2011-01-01
在简要回顾多点地质统计学起源后,介绍了多点地质统计学的3种方法,并总结了多点地质统计学的研究进展.在应用领域,已经从河流相建模发展到扇环境建模,从储集层结构建模发展到储集层物性分布模拟,从宏观地质体预测发展到微观孔喉分布建模,从地质研究发展到地质统计反演.在整合信息建模方面,给出了3种综合地震属性的方法;在算法方面,提出了PRTT实时处理方法,完善了多点地质统计学建模,并开发了新的多点统计生长算法(Growthsim).对多点地质统计学未来发展进行了展望,指出在训练图像、数据综合以及建模方法耦合方面还需要进一步深入研究.%The paper summarizes the progress of multiple point geostatistics. First the origin of multiple point geostatistics is introduced and the theories of three main multiple-point geostatistic methods are analyzed. Then, the development status is concluded in three aspects. Firstly, in real reservoir modeling domain, the modeling environment is from fluvial to fan facies; the modeling content is from reservoir architecture to reservoir petrophysical property; the modeling scale is from large geologic deposits to micro pores and throats; the modeling region is from geological modeling to geological statistic inversion. Secondly, in integrating multi-disciplines modeling domain, there are three methods for integrating seismic data. Thirdly, in modeling methods domain, there are some improvements and new methods such as PRTT and the Growthsim. Based on the analysis of the development of multiple point geostatistics, the paper points out that the training image, data integration and modeling coupration are the main aims in further studies.
Allahdadi, M.; Partani, S.; Ahmadi, M.
2012-12-01
Taking discrete sampling from the water resource and measuring the parameters in quantity and quality and using the procedures of turning discrete points to integrated surface can lead the research process to surface variations consideration. There are different procedures for turning broken discrete points to integrated surface like procedure of Geostatistics which conclude Kriging procedure, Inverse Distance Weighting (IDW), Radial Basis Functions (RBF), Local Polynomial Interpolation, Global Polynomial Interpolation and Co-kriging. This research is going to explain any applications of Geostatistics for creating iso-maps such as underground water table contours, Iso-quality (for example EC and pH) contours, and place changes of too many other hydro-geological parameters. In this way, statistic signs such as Mean Absolute Error (MAE), Mean Absolute Relative Error (MARE), Root Mean Square Error (RMSE), MBE and Coefficient of Correlation, could be employed to select the best Geo-Statistic model in a GIS framework. Eventually, the power in IDW method has been optimized and also best Geo-Statistic method has been introduced for predicting the Electric Conductivity (EC) of underground water in Atrak plain. Finally any conclusions have been extracted. Table No. 1: Comparison of Statistical Indices for Best Estimator Selection G.S Method r RMSE MBE MAE Kriging 0.81 2200 485 1740 RBF 0.79 2263 427 1662 GPI 0.63 2981 347 2031 LPI 0.64 2942 349 2002 Power Optimized IDW 0.459 4816 -183 2845 The use of MAE shows the amount of absolute error, With regard to table No.1 kriging and RBF models have the best estimation which has the least absolute estimation error. As one of results figure No. 2 shows the Iso-Electric Conductivity Map which has been created by Kriging Method in a GIS Framework.; Figure No. 1: Power optimization in IDW method and the minimum of RMSE ; Figure No.2: Iso-Electric Conductivity Map which has been created by Kriging Method in a GIS Framework
INVERSE COEFFICIENT PROBLEMS FOR PARABOLIC HEMIVARIATIONAL INEQUALITIES
Institute of Scientific and Technical Information of China (English)
Liu Zhenhai; I.Szántó
2011-01-01
This paper is devoted to the class of inverse problems for a nonlinear parabolic hemivariational inequality.The unknown coefficient of the operator depends on the gradient of the solution and belongs to a set of admissible coefficients.It is proved that the convergence of solutions for the corresponding direct problems continuously depends on the coefficient convergence.Based on this result the existence of a quasisolution of the inverse problem is obtained.
Topological inverse semigroups
Institute of Scientific and Technical Information of China (English)
ZHU Yongwen
2004-01-01
That the projective limit of any projective system of compact inverse semigroups is also a compact inverse semigroup,the injective limit of any injective system of inverse semigroups is also an inverse semigroup, and that a compact inverse semigroup is topologically isomorphic to a strict projective limit of compact metric inverse semigroups are proved. It is also demonstrated that Horn (S,T) is a topological inverse semigroup provided that S or T is a topological inverse semigroup with some other conditions. Being proved by means of the combination of topological semigroup theory with inverse semigroup theory,all these results generalize the corresponding ones related to topological semigroups or topological groups.
The exact solutions for a nonisospectral nonlinear Schroedinger equation
Energy Technology Data Exchange (ETDEWEB)
Ning Tongke [Finance College, Shanghai Normal University, Shanghai 200234 (China)], E-mail: tkning@shnu.edu.cn; Zhang Weiguo; Jia Gao [Science College, University of Shanghai for Science and Technology, Shanghai 200093 (China)
2009-10-30
In this paper, lax pair for the nonisospectral nonlinear Schroedinger hierarchy is given, the time dependence of nonisospectral scattering data is derived and exact solutions for the nonisospectral nonlinear Schroedinger hierarchy are obtained through the inverse scattering transform.
Geostatistical Study of Precipitation on the Island of Crete
Agou, Vasiliki D.; Varouchakis, Emmanouil A.; Hristopulos, Dionissios T.
2015-04-01
precipitation which are fitted locally to a three-parameter probability distribution, based on which a normalized index is derived. We use the Spartan variogram function to model space-time correlations, because it is more flexible than classical models [3]. The performance of the variogram model is tested by means of leave-one-out cross validation. The variogram model is then used in connection with ordinary kriging to generate precipitation maps for the entire island. In the future, we will explore the joint spatiotemporal evolution of precipitation patterns on Crete. References [1] P. Goovaerts. Geostatistical approaches for incorporating elevation into the spatial interpolation of precipitation. Journal of Hydrology, 228(1):113-129, 2000. [2] N. B. Guttman. Accepting the standardized precipitation index: a calculation algorithm. American Water Resource Association, 35(2):311-322, 1999. [3] D. T Hristopulos. Spartan Gibbs random field models for geostatistical applications. SIAM Journal on Scientific Computing, 24(6):2125-2162, 2003. [4] A.G. Koutroulis, A.-E.K. Vrohidou, and I.K. Tsanis. Spatiotemporal characteristics of meteorological drought for the island of Crete. Journal of Hydrometeorology, 12(2):206-226, 2011. [5] T. B. McKee, N. J. Doesken, and J. Kleist. The relationship of drought frequency and duration to time scales. In Proceedings of the 8th Conference on Applied Climatology, page 179-184, Anaheim, California, 1993.
Institute of Scientific and Technical Information of China (English)
刘国海; 张懿; 魏海峰; 赵文祥
2012-01-01
针对神经网络逆控制存在的不足,对一类模型未知且某些状态量较难测得的多输入多输出（MIMO）非线性系统,在状态软测量函数存在的前提下,提出一种最小二乘支持向量机（LSSVM）广义逆辨识控制策略.通过广义逆将原被控系统转化为伪线性复合系统,并可使其极点任意配置,采用LSSVM代替神经网络拟合广义逆系统中的静态非线性映射.将系统的状态量辨识与LSSVM逆模型辨识结合,通过LSSVM训练拟合同时实现软测量功能.最后以双电机变频调速系统为对象,采用该控制策略进行仿真研究,结果验证了本文算法的有效性.%Considering the deficiency of neural network inverse control method,for a class of multi-input and multioutput（MIMO） nonlinear systems with unknown model,when soft-sensing functions for immeasurable states are available,we propose a new identification and control strategy based on the generalized inverse control of least squares support vector machines（LSSVM）.The generalized inverse converts the controlled nonlinear system into a pseudo linear system with expected pole placement.In place of the neural network,LSSVM is employed to fit the static nonlinear mapping of the generalized inverse system.The identification of state variables is combined with the identification of LSSVM inverse model.Meanwhile,the soft-sensing is implemented through LSSVM training and fitting.Simulation is performed on a two-motor variable-frequency speed-regulating system.Results show that the proposed control strategy is feasible and efficient.
Unsupervised classification of multivariate geostatistical data: Two algorithms
Romary, Thomas; Ors, Fabien; Rivoirard, Jacques; Deraisme, Jacques
2015-12-01
With the increasing development of remote sensing platforms and the evolution of sampling facilities in mining and oil industry, spatial datasets are becoming increasingly large, inform a growing number of variables and cover wider and wider areas. Therefore, it is often necessary to split the domain of study to account for radically different behaviors of the natural phenomenon over the domain and to simplify the subsequent modeling step. The definition of these areas can be seen as a problem of unsupervised classification, or clustering, where we try to divide the domain into homogeneous domains with respect to the values taken by the variables in hand. The application of classical clustering methods, designed for independent observations, does not ensure the spatial coherence of the resulting classes. Image segmentation methods, based on e.g. Markov random fields, are not adapted to irregularly sampled data. Other existing approaches, based on mixtures of Gaussian random functions estimated via the expectation-maximization algorithm, are limited to reasonable sample sizes and a small number of variables. In this work, we propose two algorithms based on adaptations of classical algorithms to multivariate geostatistical data. Both algorithms are model free and can handle large volumes of multivariate, irregularly spaced data. The first one proceeds by agglomerative hierarchical clustering. The spatial coherence is ensured by a proximity condition imposed for two clusters to merge. This proximity condition relies on a graph organizing the data in the coordinates space. The hierarchical algorithm can then be seen as a graph-partitioning algorithm. Following this interpretation, a spatial version of the spectral clustering algorithm is also proposed. The performances of both algorithms are assessed on toy examples and a mining dataset.
Patch-based iterative conditional geostatistical simulation using graph cuts
Li, Xue; Mariethoz, Gregoire; Lu, DeTang; Linde, Niklas
2016-08-01
Training image-based geostatistical methods are increasingly popular in groundwater hydrology even if existing algorithms present limitations that often make real-world applications difficult. These limitations include a computational cost that can be prohibitive for high-resolution 3-D applications, the presence of visual artifacts in the model realizations, and a low variability between model realizations due to the limited pool of patterns available in a finite-size training image. In this paper, we address these issues by proposing an iterative patch-based algorithm which adapts a graph cuts methodology that is widely used in computer graphics. Our adapted graph cuts method optimally cuts patches of pixel values borrowed from the training image and assembles them successively, each time accounting for the information of previously stitched patches. The initial simulation result might display artifacts, which are identified as regions of high cost. These artifacts are reduced by iteratively placing new patches in high-cost regions. In contrast to most patch-based algorithms, the proposed scheme can also efficiently address point conditioning. An advantage of the method is that the cut process results in the creation of new patterns that are not present in the training image, thereby increasing pattern variability. To quantify this effect, a new measure of variability is developed, the merging index, quantifies the pattern variability in the realizations with respect to the training image. A series of sensitivity analyses demonstrates the stability of the proposed graph cuts approach, which produces satisfying simulations for a wide range of parameters values. Applications to 2-D and 3-D cases are compared to state-of-the-art multiple-point methods. The results show that the proposed approach obtains significant speedups and increases variability between realizations. Connectivity functions applied to 2-D models transport simulations in 3-D models are used to
[Spatial distribution pattern of Chilo suppressalis analyzed by classical method and geostatistics].
Yuan, Zheming; Fu, Wei; Li, Fangyi
2004-04-01
Two original samples of Chilo suppressalis and their grid, random and sequence samples were analyzed by classical method and geostatistics to characterize the spatial distribution pattern of C. suppressalis. The limitations of spatial distribution analysis with classical method, especially influenced by the original position of grid, were summarized rather completely. On the contrary, geostatistics characterized well the spatial distribution pattern, congregation intensity and spatial heterogeneity of C. suppressalis. According to geostatistics, the population was up to Poisson distribution in low density. As for higher density population, its distribution was up to aggregative, and the aggregation intensity and dependence range were 0.1056 and 193 cm, respectively. Spatial heterogeneity was also found in the higher density population. Its spatial correlativity in line direction was more closely than that in row direction, and the dependence ranges in line and row direction were 115 and 264 cm, respectively.
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
for different soils. Here, variography is employed to analyse spatial variability of bioavailability factors (BFs) of metals at the global scale. First, published empirical regressions are employed to calculate BFs of metals for 7180 topsoil profiles. Next, geostatistical interpretation of calculated BFs...... 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...... at lags smaller than those in the data set. Geostatistical analyses indicate however, that BFs exhibit no signifficant spatial correlation at a range beyond 3200 km. Because BF is spatially correlated, its values at unsampled locations can be predicted, as demonstrated using ordinary kriggin method...
TiConverter: A training image converting tool for multiple-point geostatistics
Fadlelmula F., Mohamed M.; Killough, John; Fraim, Michael
2016-11-01
TiConverter is a tool developed to ease the application of multiple-point geostatistics whether by the open source Stanford Geostatistical Modeling Software (SGeMS) or other available commercial software. TiConverter has a user-friendly interface and it allows the conversion of 2D training images into numerical representations in four different file formats without the need for additional code writing. These are the ASCII (.txt), the geostatistical software library (GSLIB) (.txt), the Isatis (.dat), and the VTK formats. It performs the conversion based on the RGB color system. In addition, TiConverter offers several useful tools including image resizing, smoothing, and segmenting tools. The purpose of this study is to introduce the TiConverter, and to demonstrate its application and advantages with several examples from the literature.
Directory of Open Access Journals (Sweden)
Patrícia Alexandra Gregório Ramos
2013-07-01
Full Text Available Geostatistics has been successfully used to analyse and characterize the spatial variability of environmental properties. Besides providing estimated values at unsampled locations, geostatistics measures the accuracy of the estimate, which is a significant advantage over traditional methods used to assess pollution. This work uses universal block kriging to model and map the spatial distribution of salinity measurements gathered by an Autonomous Underwater Vehicle in a sea outfall monitoring campaign. The aim is to distinguish the effluent plume from the receiving waters, characterizing its spatial variability in the vicinity of the discharge and estimating dilution. The results demonstrate that geostatistical methodology can provide good estimates of the dispersion of effluents, which are valuable in assessing the environmental impact and managing sea outfalls. Moreover, since accurate measurements of the plume’s dilution are rare, these studies may be very helpful in the future to validate dispersion models.
DEFF Research Database (Denmark)
Troldborg, Mads; Nowak, Wolfgang; Lange, Ida Vedel
2012-01-01
. 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......-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...
DEFF Research Database (Denmark)
He, Xiulan
parameters and model structures, which are the primary focuses of this PhD research. Parameter uncertainty was analyzed using an optimization tool (PEST: Parameter ESTimation) in combination with a random sampling method (LHS: Latin Hypercube Sampling). Model structure, namely geological architecture...... was analyzed using both a traditional two-point based geostatistical approach and multiple-point geostatistics (MPS). Our results documented that model structure is as important as model parameter regarding groundwater modeling uncertainty. Under certain circumstances the inaccuracy on model structure can...
Energy Technology Data Exchange (ETDEWEB)
Vejbaek, O.V.
1998-12-31
The aim of this report was to demonstrate possible uses of seismic impedances as soft data for reservoir characterization. To illustrate the impact of the results and attempt to calculate oil in place was also carried out. It must, however, be emphasized that these results only apply to the Callovian portion of the Middle Jurassic West Lulu reservoir, and thus do not provide estimates of the entire Middle Jurassic West Lulu accumulation. It is important to realise that stochastic simulations does not provide exact predictions in areas outside the control of hard data. It is, however, offering possibilities to exploit every known or surmised property about the desired (target) data population. These properties include f.ex., mean, spread, spatial continuity (measured by variograms), horixontal and vertical trends, correlation to supporting soft data (e.g. seismic impedances) etc. Neither are predictions exact even through the term `narrowed solution space` is applied. This term merely implies that the error in prediction at any point may be less than the full range of the parameter. The quality of the predictions mainly depend on meticulous handling of data, avoiding errors like bad stratigraphic alignment of the data, obtaining good variograms, avoiding errors in the construction of the target populations and including every pertinent attribute about the data. The result is thus also depending on a full geological understanding of the problem (and moral of the modeller). The most important quality is the ability to provide a great number of equi-probable realisation that equally well satisfies any known or surmised property about the target data population. The goal of this study was to investigate the use of inversion derived seismic impedances for geostatistical reservoir characterisation in a complex clastic reservoir exemplified with the West Lulu reservoir of the Harald Field. The well database is rather modest, so substantial support has been gained from the
Institute of Scientific and Technical Information of China (English)
秦涛
2005-01-01
主流GIS软件ArcGIS 9的Geostatistics Analyst模块中所涉及的两大类空间内插方法:确定性内插方法和地统计内插方法.结合该软件对各种插值方法的应用和处理进行了介绍,应用示例比较各种内插方法的适用范围.
Underground water quality model inversion of genetic algorithm
Institute of Scientific and Technical Information of China (English)
MA Ruijie; LI Xin
2009-01-01
The underground water quality model with non-linear inversion problem is ill-posed, and boils down to solving the minimum of nonlinear function. Genetic algorithms are adopted in a number of individuals of groups by iterative search to find the optimal solution of the problem, the encoding strings as its operational objective, and achieving the iterative calculations by the genetic operators. It is an effective method of inverse problems of groundwater, with incomparable advantages and practical significances.
Abdu, Hiruy
Knowledge of the spatial distribution of soil textural properties at the watershed scale is important for understanding spatial patterns of water movement, and in determining soil moisture storage and soil hydraulic transport properties. Capturing the heterogeneous nature of the subsurface without exhaustive and costly sampling presents a significant challenge. Soil scientists and geologists have adapted geophysical methods that measure a surrogate property related to the vital underlying process. Apparent electrical conductivity (ECa) is such a proxy, providing a measure of charge mobility due to application of an electric field, and is highly correlated to the electrical conductivity of the soil solution, clay percentage, and water content. Electromagnetic induction (EMI) provides the possibility of obtaining high resolution images of ECa across a landscape to identify subtle changes in subsurface properties. The aim of this study was to better characterize subsurface textural properties using EMI mapping and geostatistical analysis techniques. The effect of variable temperature environments on EMI instrumental response, and EC a -- depth relationship were first determined. Then a procedure of repeated EMI mapping at varying soil water content was developed and integrated with temporal stability analysis to capture the time invariant properties of spatial soil texture on an agricultural field. In addition, an EMI imaging approach of densely sampling the subsurface of the Reynolds Mountain East watershed was presented using kriging to interpolate, and Sequential Gaussian Simulation to estimate the uncertainty in the maps. Due to the relative time-invariant characteristics of textural properties, it was possible to correlate clay samples collected over three seasons to ECa data of one mapping event. Kriging methods [ordinary kriging (OK), cokriging (CK), and regression kriging (RK)] were then used to integrate various levels of information (clay percentage, ECa
Abubakar, A.; Hu, W.; Habashy, T.M.; Van den Berg, P.M.
2009-01-01
We have applied the finite-difference contrast-source inversion (FDCSI) method to seismic full-waveform inversion problems. The FDCSI method is an iterative nonlinear inversion algorithm. However, unlike the nonlinear conjugate gradient method and the Gauss-Newton method, FDCSI does not solve any fu
Confronting uncertainty in model-based geostatistics using Markov Chain Monte Carlo simulation
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 distributi
The use of geostatistics in the study of floral phenology of Vulpia geniculata (L.) link.
León Ruiz, Eduardo J; García Mozo, Herminia; Domínguez Vilches, Eugenio; Galán, Carmen
2012-01-01
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 throughout 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 elaborate 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.
Adapting geostatistics to analyze spatial and temporal trends in weed populations
Geostatistics were originally developed in mining to estimate the location, abundance and quality of ore over large areas from soil samples to optimize future mining efforts. Here, some of these methods were adapted to weeds to account for a limited distribution area (i.e., inside a field), variatio...
Combining Geostatistics with Moran’s I Analysis for Mapping Soil Heavy Metals in Beijing, China
Directory of Open Access Journals (Sweden)
Bao-Guo Li
2012-03-01
Full Text Available Production of high quality interpolation maps of heavy metals is important for risk assessment of environmental pollution. In this paper, the spatial correlation characteristics information obtained from Moran’s I analysis was used to supplement the traditional geostatistics. According to Moran’s I analysis, four characteristics distances were obtained and used as the active lag distance to calculate the semivariance. Validation of the optimality of semivariance demonstrated that using the two distances where the Moran’s I and the standardized Moran’s I, Z(I reached a maximum as the active lag distance can improve the fitting accuracy of semivariance. Then, spatial interpolation was produced based on the two distances and their nested model. The comparative analysis of estimation accuracy and the measured and predicted pollution status showed that the method combining geostatistics with Moran’s I analysis was better than traditional geostatistics. Thus, Moran’s I analysis is a useful complement for geostatistics to improve the spatial interpolation accuracy of heavy metals.
Institute of Scientific and Technical Information of China (English)
ZENG ZhaoCheng; LEI LiPing; GUO LiJie; ZHANG Li; ZHANG Bing
2013-01-01
Observations of atmospheric carbon dioxide (CO2) from satellites offer new data sources to understand global carbon cycling.The correlation structure of satellite-observed CO2 can be analyzed and modeled by geostatistical methods,and CO2 values at unsampled locations can be predicted with a correlation model.Conventional geostatistical analysis only investigates the spatial correlation of CO2,and does not consider temporal variation in the satellite-observed CO2 data.In this paper,a spatiotemporal geostatistical method that incorporates temporal variability is implemented and assessed for analyzing the spatiotemporal correlation structure and prediction of monthly CO2 in China.The spatiotemporal correlation is estimated and modeled by a product-sum variogram model with a global nugget component.The variogram result indicates a significant degree of temporal correlation within satellite-observed CO2 data sets in China.Prediction of monthly CO2 using the spatiotemporal variogram model and spacetime kriging procedure is implemented.The prediction is compared with a spatial-only geostatistical prediction approach using a cross-validation technique.The spatiotemporal approach gives better results,with higher correlation coefficient (r2),and less mean absolute prediction error and root mean square error.Moreover,the monthly mapping result generated from the spatiotemporal approach has less prediction uncertainty and more detailed spatial variation of CO2 than those from the spatial-only approach.
DEFF Research Database (Denmark)
Kessler, Timo Christian; Klint, K.E.S.; Renard, P.;
2010-01-01
at a clay till outcrop in Denmark to characterise the shapes and the spatial variability. Further, geostatistics were applied to simulate the distribution and to develop a heterogeneity model that can be incorporated into an existing geological model of, for example, a contaminated site....
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.
Quantifying natural delta variability using a multiple-point geostatistics prior uncertainty model
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.
Energy Technology Data Exchange (ETDEWEB)
Fuente Martin, P.; Gonzalez Marroquin, V.M.; Fernandez de Castro Fernandez Sahw, F.; Saez Garcia, E. (HUNOSA, Oviedo (Spain))
1989-06-01
The aim of this project, which has been financed by Ocicarbon, is to develop both in theory and in practice, the use of geostatistics to predict the geological behaviour of coal seams, in virgin panels, using data from panels already worked. Examples of seams selected for full mechanisation are given. 3 figs., 3 tabs.
Introduction to This Special Issue on Geostatistics and Geospatial Techniques in Remote Sensing
Atkinson, Peter; Quattrochi, Dale A.; Goodman, H. Michael (Technical Monitor)
2000-01-01
The germination of this special Computers & Geosciences (C&G) issue began at the Royal Geographical Society (with the Institute of British Geographers) (RGS-IBG) annual meeting in January 1997 held at the University of Exeter, UK. The snow and cold of the English winter were tempered greatly by warm and cordial discussion of how to stimulate and enhance cooperation on geostatistical and geospatial research in remote sensing 'across the big pond' between UK and US researchers. It was decided that one way forward would be to hold parallel sessions in 1998 on geostatistical and geospatial research in remote sensing at appropriate venues in both the UK and the US. Selected papers given at these sessions would be published as special issues of C&G on the UK side and Photogrammetric Engineering and Remote Sensing (PE&RS) on the US side. These issues would highlight the commonality in research on geostatistical and geospatial research in remote sensing on both sides of the Atlantic Ocean. As a consequence, a session on "Geostatistics and Geospatial Techniques for Remote Sensing of Land Surface Processes" was held at the RGS-IBG annual meeting in Guildford, Surrey, UK in January 1998, organized by the Modeling and Advanced Techniques Special Interest Group (MAT SIG) of the Remote Sensing Society (RSS). A similar session was held at the Association of American Geographers (AAG) annual meeting in Boston, Massachusetts in March 1998, sponsored by the AAG's Remote Sensing Specialty Group (RSSG). The 10 papers that make up this issue of C&G, comprise 7 papers from the UK and 3 papers from the LIS. We are both co-editors of each of the journal special issues, with the lead editor of each journal issue being from their respective side of the Atlantic. The special issue of PE&RS (vol. 65) that constitutes the other half of this co-edited journal series was published in early 1999, comprising 6 papers by US authors. We are indebted to the International Association for Mathematical
Locally Inverse Semigroups with Inverse Transversals
Institute of Scientific and Technical Information of China (English)
SHAO Yong; ZHAO Xian Zhong
2009-01-01
Let S be a locally inverse semigroup with an inverse transversal S°. In this paper, we construct an amenable partial order on S by an R-cone. Conversely, every amenable partial order on S can be constructed in this way. We give some properties of a locally inverse semigroup with a Clifford transversal. In particular, if S is a locally inverse semigroup with a Clifford transversal, then there is an order-preserving bijection from the set of all amenable partial orders on S to the set of all R-cones of S.
Directory of Open Access Journals (Sweden)
Ali Akbar Moosavi
2017-02-01
diffusivity were week, whereas, the spatial correlation classes of the other studied soil hydraulic attributes were moderate. Results revealed that the Inverse Distance Weighting method was the most suitable approach for the prediction of all studied soil hydraulic attributes in the present study. Comparison of the calculated statistical evaluation measures (i.e. Determination coefficient, R2, Mean residual error, MRE, mean square error, MSE, Normalized mean square error, NRMSE and geometric mean error ratio, GMER and the final determined order of precision showed that the most and the least accurate predictions were obtained for Ks and Фm, respectively. Conclusion: It is suggested in the cases that we need to map the hydraulic attributes or need their quantities in a large number; geostatistical prediction be performed using the limited measurements to reduce the needed time and costs.
Workflows for Full Waveform Inversions
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.
Swarm intelligence optimization and its application in geophysical data inversion
Institute of Scientific and Technical Information of China (English)
Yuan Sanyi; Wang Shangxu; Tian Nan
2009-01-01
The inversions of complex geophysical data always solve multi-parameter, nonlinear, and multimodal optimization problems. Searching for the optimal inversion solutions is similar to the social behavior observed in swarms such as birds and ants when searching for food. In this article, first the particle swarm optimization algorithm was described in detail, and ant colony algorithm improved. Then the methods were applied to three different kinds of geophysical inversion problems: (1) a linear problem which is sensitive to noise, (2) a synchronous inversion of linear and nonlinear problems, and (3) a nonlinear problem. The results validate their feasibility and efficiency. Compared with the conventional genetic algorithm and simulated annealing, they have the advantages of higher convergence speed and accuracy. Compared with the quasi-Newton method and Levenberg-Marquardt method, they work better with the ability to overcome the locally optimal solutions.
HOMOTOPY SOLUTION OF THE INVERSE GENERALIZED EIGENVALUE PROBLEMS IN STRUCTURAL DYNAMICS
Institute of Scientific and Technical Information of China (English)
李书; 王波; 胡继忠
2004-01-01
The structural dynamics problems, such as structural design, parameter identification and model correction, are considered as a kind of the inverse generalized eigenvalue problems mathematically. The inverse eigenvalue problems are nonlinear. In general, they could be transformed into nonlinear equations to solve. The structural dynamics inverse problems were treated as quasi multiplicative inverse eigenalue problems which were solved by homotopy method for nonlinear equations. This method had no requirements for initial value essentially because of the homotopy path to solution. Numerical examples were presented to illustrate the homotopy method.
Energy Technology Data Exchange (ETDEWEB)
Edwards, Lloyd A. [Leading Solutions, LLC.; Paresol, Bernard [U.S. Department of Agriculture, Forest Service, Pacific Northwest Research Station, Portland, OR.
2014-09-01
This report of the geostatistical analysis results of the fire fuels response variables, custom reaction intensity and total dead fuels is but a part of an SRS 2010 vegetation inventory project. For detailed description of project, theory and background including sample design, methods, and results please refer to USDA Forest Service Savannah River Site internal report “SRS 2010 Vegetation Inventory GeoStatistical Mapping Report”, (Edwards & Parresol 2013).
Inverse anticipating chaos synchronization.
Shahverdiev, E M; Sivaprakasam, S; Shore, K A
2002-07-01
We derive conditions for achieving inverse anticipating synchronization where a driven time-delay chaotic system synchronizes to the inverse future state of the driver. The significance of inverse anticipating chaos in delineating synchronization regimes in time-delay systems is elucidated. The concept is extended to cascaded time-delay systems.
Locative Inversion in Cantonese.
Mok, Sui-Sang
This study investigates the phenomenon of "Locative Inversion" in Cantonese. The term "Locative Inversion" indicates that the locative phrase (LP) syntactic process in Cantonese and the appears at the sentence-initial position and its logical subject occurs postverbally. It is demonstrated that this Locative Inversion is a…
H, R. Baghshahi; M, K. Tavassoly; A, Behjat
2014-07-01
The interaction between a two-level atom and a single-mode field in the k-photon Jaynes—Cummings model (JCM) in the presence of the Stark shift and a Kerr medium is studied. All terms in the Hamiltonian, such as the single-mode field, its interaction with the atom, the contribution of the Stark shift and the Kerr medium effects are considered to be f-deformed. In particular, the effect of the initial state of the radiation field on the dynamical evolution of some physical properties such as atomic inversion and entropy squeezing are investigated by considering different initial field states (coherent, squeezed and thermal states).
Electromagnetic tomography (EMT): image reconstruction based on the inverse problem
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
Starting from Maxwell's equations for inhomogeneous media, nonlinear integral equations of the inverse problem of the electromagnetic tomography (EMT) are derived, whose kernel is the dyadic Green's function for the EMT sensor with a homogeneous medium in the object space. Then in terms of ill-posedness of the inverse problem, a Tikhonov-type regularization model is established based on a linearization-approximation of the nonlinear inverse problem. Finally, an iterative algorithm of image reconstruction based on the inverse problem and reconstruction images of some object flows for simplified sensor are given. Initial results of the image reconstruction show that the algorithm based on the inverse problem is superior to those based on the linear back-projection in the quality of image reconstruction.
Bloembergen, Nicolaas
1996-01-01
Nicolaas Bloembergen, recipient of the Nobel Prize for Physics (1981), wrote Nonlinear Optics in 1964, when the field of nonlinear optics was only three years old. The available literature has since grown by at least three orders of magnitude.The vitality of Nonlinear Optics is evident from the still-growing number of scientists and engineers engaged in the study of new nonlinear phenomena and in the development of new nonlinear devices in the field of opto-electronics. This monograph should be helpful in providing a historical introduction and a general background of basic ideas both for expe
Energy Technology Data Exchange (ETDEWEB)
Geniet, F; Leon, J [Physique Mathematique et Theorique, CNRS-UMR 5825, 34095 Montpellier (France)
2003-05-07
A nonlinear system possessing a natural forbidden band gap can transmit energy of a signal with a frequency in the gap, as recently shown for a nonlinear chain of coupled pendulums (Geniet and Leon 2002 Phys. Rev. Lett. 89 134102). This process of nonlinear supratransmission, occurring at a threshold that is exactly predictable in many cases, is shown to have a simple experimental realization with a mechanical chain of pendulums coupled by a coil spring. It is then analysed in more detail. First we go to different (nonintegrable) systems which do sustain nonlinear supratransmission. Then a Josephson transmission line (a one-dimensional array of short Josephson junctions coupled through superconducting wires) is shown to also sustain nonlinear supratransmission, though being related to a different class of boundary conditions, and despite the presence of damping, finiteness, and discreteness. Finally, the mechanism at the origin of nonlinear supratransmission is found to be a nonlinear instability, and this is briefly discussed here.
Weiland, E.F.; Connors, R.A.; Robinson, M.L.; Lindemann, J.W.; Meyer, W.T.
1982-01-01
A mineral assessment of the Arkansas Canyon Planning Unit was undertaken by Barringer Resources Inc., under the terms of contract YA-553-CTO-100 with the Bureau of Land Management, Colorado State Office. The study was based on a geochemical-geostatistical survey in which 700 stream sediment samples were collected and analyzed for 25 elements. Geochemical results were interpreted by statistical processing which included factor, discriminant, multiple regression and characteristic analysis. The major deposit types evaluated were massive sulfide-base metal, sedimentary and magmatic uranium, thorium vein, magmatic segregation, and carbonatite related deposits. Results of the single element data and multivariate geostatistical analysis indicate that limited potential exists for base metal mineralization near the Horseshoe, El Plomo, and Green Mountain Mines. Thirty areas are considered to be anomalous with regard to one or more of the geochemical parameters evaluated during this study. The evaluation of carbonatite related mineralization was restricted due to the lack of geochemical data specific to this environment.
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.
Geostatistical simulations for radon indoor with a nested model including the housing factor.
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.
Geostatistics for spatial genetic structures: study of wild populations of perennial ryegrass.
Monestiez, P; Goulard, M; Charmet, G
1994-04-01
Methods based on geostatistics were applied to quantitative traits of agricultural interest measured on a collection of 547 wild populations of perennial ryegrass in France. The mathematical background of these methods, which resembles spatial autocorrelation analysis, is briefly described. When a single variable is studied, the spatial structure analysis is similar to spatial autocorrelation analysis, and a spatial prediction method, called "kriging", gives a filtered map of the spatial pattern over all the sampled area. When complex interactions of agronomic traits with different evaluation sites define a multivariate structure for the spatial analysis, geostatistical methods allow the spatial variations to be broken down into two main spatial structures with ranges of 120 km and 300 km, respectively. The predicted maps that corresponded to each range were interpreted as a result of the isolation-by-distance model and as a consequence of selection by environmental factors. Practical collecting methodology for breeders may be derived from such spatial structures.
Geostatistical analysis and kriging of Hexachlorocyclohexane residues in topsoil from Tianjin, China
Energy Technology Data Exchange (ETDEWEB)
Li, B.G. [College of Environmental Sciences, MOE Laboratory for Earth Surface Processes, Peking University, Beijing 100871 (China); Cao, J. [College of Environmental Sciences, MOE Laboratory for Earth Surface Processes, Peking University, Beijing 100871 (China); Liu, W.X. [College of Environmental Sciences, MOE Laboratory for Earth Surface Processes, Peking University, Beijing 100871 (China); Shen, W.R. [Environmental Protection Bureau, Tianjin 300191 (China); Wang, X.J. [College of Environmental Sciences, MOE Laboratory for Earth Surface Processes, Peking University, Beijing 100871 (China); Tao, S. [College of Environmental Sciences, MOE Laboratory for Earth Surface Processes, Peking University, Beijing 100871 (China)]. E-mail: taos@urban.pku.edu.cn
2006-08-15
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.
Neural Network Inverse Adaptive Controller Based on Davidon Least Square
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
General neural network inverse adaptive controller haa two flaws: the first is the slow convergence speed; the second is the invalidation to the non-minimum phase system.These defects limit the scope in which the neural network inverse adaptive controller is used.We employ Davidon least squares in training the multi-layer feedforward neural network used in approximating the inverse model of plant to expedite the convergence,and then through constructing the pseudo-plant,a neural network inverse adaptive controller is put forward which is still effective to the nonlinear non-minimum phase system.The simulation results show the validity of this scheme.
Fischer, P.; Jardani, A.; Lecoq, N.
2017-03-01
Inverse problem permits to map the subsurface properties from a few observed data. The inverse problem can be physically constrained by a priori information on the property distribution in order to limit the nonuniqueness of the solution. The geostatistical information is often chosen as a priori information; however, when the field properties present a spatial locally distributed high variability, the geostatistical approach becomes inefficient. Therefore, we propose a new method adapted for fields presenting linear structures (such as a fractured field). The Cellular Automata-based Deterministic Inversion (CADI) method is, as far as we know when this paper is produced, the first inversion method which permits a deterministic inversion based on a Bayesian approach and using a dynamic optimization to generate different linear structures iteratively. The model is partitioned in cellular automaton subspaces, each one controlling a different zone of the model. A cellular automata subspace structures the properties of the model in two units ("structure" and "background") and control their dispensing direction and their values. The partitioning of the model in subspaces permits to monitor a large-scale structural model with only a few pilot-parameters and to generate linear structures with local direction changes. Thereby, the algorithm can easily handle with large-scale structures, and a sensitivity analysis is possible on these structural pilot-parameters, which permits to considerably accelerate the optimization process in order to find the best structural geometry. The algorithm has been successfully tested on simple, to more complex, theoretical models with different inversion techniques by using seismic and hydraulic data.
Messier, Kyle P.; Akita, Yasuyuki; Serre, Marc L.
2012-01-01
Geographic Information Systems (GIS) based techniques are cost-effective and efficient methods used by state agencies and epidemiology researchers for estimating concentration and exposure. However, budget limitations have made statewide assessments of contamination difficult, especially in groundwater media. Many studies have implemented address geocoding, land use regression, and geostatistics independently, but this is the first to examine the benefits of integrating these GIS techniques t...
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Shamloo, H.; Haghighi, A. [K.N. Toosi Univ. of Technology, Tehran (Iran, Islamic Republic of). Dept. of Civil Engineering
2009-07-01
The flow properties of pipes are affected by leaks. Leak detection methods based on hydraulic modelling and real data records aim to find a pipe's leak parameters including their number, location and size. Inverse Transient Analysis (ITA), generally in time domain, is a powerful approach to develop leak detection methods with considerable benefits. This paper introduced an ITA based leak detection method along with a numerical model developed for direct transient analysis of leaks in pipes using method of characteristics (MOC). Transient state flow was generated in pipe and the pressure fluctuations were sampled only at the end valve location. To minimize the effects of unsteadiness and uncertainties due to the numerical modeling and also practical problems caused by water hammer, the downstream end valve was considered to be closed gradually within a long enough time. Then, using the sampled data and a direct transient analysis model, a mixed integer nonlinear program was developed. A mixed genetic algorithm was used in which the binary chromosomes were decoded as mixed integer leak locations and real leak areas. In order to find unknown leak parameters in a pipe, an objective function was defined using the least squares criterion of differences between observed and calculated pressure heads at the valve location. The genetic algorithm was found to be a powerful and easy to use optimization tool to solve complicated mixed integer nonlinear program (MINLP) problems in leak detection. 24 refs., 1 tab., 7 figs.
Bayesian inversion for facies detection: An extensible level set framework
Cardiff, M.; Kitanidis, P. K.
2009-10-01
In many cases, it has been assumed that the variability in hydrologic parameters can be adequately described through a simple geostatistical model with a given variogram. In other cases, variability may be best described as a series of "jumps" in parameter behavior, e.g., those that occur at geologic facies contacts. When using indirect measurements such as pump tests to try to map such heterogeneity (during inverse modeling), the resulting images of the subsurface are always affected by the assumptions invoked. In this paper, we discuss inversion for parameter fields where prior information has suggested that major variability can be described by boundaries between geologic units or facies. In order to identify such parameter fields, we propose a Bayesian level set inversion protocol framework, which allows for flexible zones of any shape, size, and number. We review formulas for defining facies locations using the level set method and for moving the boundaries between zones using a gradient-based technique that improves fit through iterative deformation of the boundaries. We describe the optimization algorithm employed when multiple level set functions are used to represent a field with more than two facies. We extend these formulas to the investigation of the inverse problem in a Bayesian context in which prior information is taken into account and through which measures of uncertainty can be derived. We also demonstrate that the level set method is well suited for joint inversion problems and present a strategy for integrating different data types (such as hydrologic and geophysical) without assuming strict petrophysical relations. Our framework for joint inversion also contrasts with many previous methods in that all data sources (e.g., both hydrologic and geophysical) contribute to boundary delineation at once.
Nonlinear Dynamics Inversion Optimal Control for Hypersonic Vehicle%针对高超声速飞行器的非线性动态逆最优控制
Institute of Scientific and Technical Information of China (English)
谭毅伦; 闫杰
2011-01-01
高超声速飞行器具有高度非线性,并且输入输出之间存有耦合.传统控制方案中的线性化处理方法有严重的局限性.采用状态反馈线性化方法对高超声速飞行器纵向模型输入输出线性化,并结合最优控制理论设计控制系统,以求提供满意的非线性解耦控制能力,维持良好的纵向稳定性能.基于某常用的高超声速飞行器模型的仿真研究表明该方案能够使飞行器有效跟踪参考轨迹,满足系统需要.%Hypersonic aircrafts have a highly nonlinear dynamics and input/output coupling. Conventional control scheme of linearization method has serious limitations. In order to provide satisfactory nonlinear dacoupling ability and maintain good longitudinal stability, a kind of condition feedback linearization method is adopted in this paper to linearize the input and output of a hypersonic longitudinal vehicle model and optimal control theory is considered in the controller designing. Simulation based on an existing hypersonic vehicle model shows that the controller successfully tracks the reference trajectories and meets the system need.
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.
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.
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.
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.
Grisotto, Laura; Consonni, Dario; Cecconi, Lorenzo; Catelan, Dolores; Lagazio, Corrado; Bertazzi, Pier Alberto; Baccini, Michela; Biggeri, Annibale
2016-04-18
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.
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.
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.
Energy Technology Data Exchange (ETDEWEB)
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.
2010-08-01
Validation of the Geostatistical Temporal-Spatial Algorithm (GTS) for Optimization of Long-Term Monitoring (LTM) of Groundwater at Military and... Geostatistical Temporal-Spatial Algorithm (GTS) for Optimization of Long-Term Monitoring (LTM) of Groundwater at Military and Government Sites 5a. CONTRACT NUMBER...ABSTRACT The primary objective of this ESTCP project was to demonstrate and validate use of the Geostatistical Temporal-Spatial (GTS) groundwater
The Stewart-Lyth Inverse Problem
Ayón-Beato, E; Mansilla, R; Terrero-Escalante, C A; Ay\\'on-Beato, Eloy; Garc\\'{\\i}a, Alberto; Mansilla, Ricardo
2000-01-01
In this paper the Stewart-Lyth inverse problem is introduced. It consists of solving two non-linear differential equations for the first slow-roll parameter and finding the inflaton potential. The equations are derived from the Stewart-Lyth equations for the scalar and tensorial perturbations produced during the inflationary period. The geometry of the phase planes transverse to the trajectories is analyzed, and conclusions about the possible behaviour for general solutions are drawn.
Geostatistical and Statistical Classification of Sea-Ice Properties and Provinces from SAR Data
Directory of Open Access Journals (Sweden)
Ute C. Herzfeld
2016-07-01
Full Text Available Recent drastic reductions in the Arctic sea-ice cover have raised an interest in understanding the role of sea ice in the global system as well as pointed out a need to understand the physical processes that lead to such changes. Satellite remote-sensing data provide important information about remote ice areas, and Synthetic Aperture Radar (SAR data have the advantages of penetration of the omnipresent cloud cover and of high spatial resolution. A challenge addressed in this paper is how to extract information on sea-ice types and sea-ice processes from SAR data. We introduce, validate and apply geostatistical and statistical approaches to automated classification of sea ice from SAR data, to be used as individual tools for mapping sea-ice properties and provinces or in combination. A key concept of the geostatistical classification method is the analysis of spatial surface structures and their anisotropies, more generally, of spatial surface roughness, at variable, intermediate-sized scales. The geostatistical approach utilizes vario parameters extracted from directional vario functions, the parameters can be mapped or combined into feature vectors for classification. The method is flexible with respect to window sizes and parameter types and detects anisotropies. In two applications to RADARSAT and ERS-2 SAR data from the area near Point Barrow, Alaska, it is demonstrated that vario-parameter maps may be utilized to distinguish regions of different sea-ice characteristics in the Beaufort Sea, the Chukchi Sea and in Elson Lagoon. In a third and a fourth case study the analysis is taken further by utilizing multi-parameter feature vectors as inputs for unsupervised and supervised statistical classification. Field measurements and high-resolution aerial observations serve as basis for validation of the geostatistical-statistical classification methods. A combination of supervised classification and vario-parameter mapping yields best results
Hellies, Matteo; Deidda, Roberto; Langousis, Andreas
2016-04-01
We study the extreme rainfall regime of the Island of Sardinia in Italy, based on annual maxima of daily precipitation. The statistical analysis is conducted using 229 daily rainfall records with at least 50 complete years of observations, collected at different sites by the Hydrological Survey of the Sardinia Region. Preliminary analysis, and the L-skewness and L-kurtosis diagrams, show that the Generalized Extreme Value (GEV) distribution model performs best in describing daily rainfall extremes. The GEV distribution parameters are estimated using the method of Probability Weighted Moments (PWM). To obtain extreme rainfall estimates at ungauged sites, while minimizing uncertainties due to sampling variability, a regional and a geostatistical approach are compared. The regional approach merges information from different gauged sites, within homogeneous regions, to obtain GEV parameter estimates at ungauged locations. The geostatistical approach infers the parameters of the GEV distribution model at locations where measurements are available, and then spatially interpolates them over the study region. In both approaches we use local rainfall means as index-rainfall. In the regional approach we define homogeneous regions by applying a hierarchical cluster analysis based on Ward's method, with L-moment ratios (i.e. L-CV and L-Skewness) as metrics. The analysis results in four contiguous regions, which satisfy the Hosking and Wallis (1997) homogeneity tests. The latter have been conducted using a Monte-Carlo approach based on a 4-parameter Kappa distribution model, fitted to each station cluster. Note that the 4-parameter Kappa model includes the GEV distribution as a sub-case, when the fourth parameter h is set to 0. In the geostatistical approach we apply kriging for uncertain data (KUD), which accounts for the error variance in local parameter estimation and, therefore, may serve as a useful tool for spatial interpolation of metrics affected by high uncertainty. In
2016-07-01
Advanced Research Projects Agency (DARPA) Dynamics-Enabled Frequency Sources (DEFYS) program is focused on the convergence of nonlinear dynamics and...Early work in this program has shown that nonlinear dynamics can provide performance advantages. However, the pathway from initial results to...dependent nonlinear stiffness observed in these devices. This work is ongoing, and will continue through the final period of this program . Reference 9
Nayfeh, Ali Hasan
1995-01-01
Nonlinear Oscillations is a self-contained and thorough treatment of the vigorous research that has occurred in nonlinear mechanics since 1970. The book begins with fundamental concepts and techniques of analysis and progresses through recent developments and provides an overview that abstracts and introduces main nonlinear phenomena. It treats systems having a single degree of freedom, introducing basic concepts and analytical methods, and extends concepts and methods to systems having degrees of freedom. Most of this material cannot be found in any other text. Nonlinear Oscillations uses sim
Yoshida, Zensho
2010-01-01
This book gives a general, basic understanding of the mathematical structure "nonlinearity" that lies in the depths of complex systems. Analyzing the heterogeneity that the prefix "non" represents with respect to notions such as the linear space, integrability and scale hierarchy, "nonlinear science" is explained as a challenge of deconstruction of the modern sciences. This book is not a technical guide to teach mathematical tools of nonlinear analysis, nor a zoology of so-called nonlinear phenomena. By critically analyzing the structure of linear theories, and cl
Nanda, Sudarsan
2013-01-01
"Nonlinear analysis" presents recent developments in calculus in Banach space, convex sets, convex functions, best approximation, fixed point theorems, nonlinear operators, variational inequality, complementary problem and semi-inner-product spaces. Nonlinear Analysis has become important and useful in the present days because many real world problems are nonlinear, nonconvex and nonsmooth in nature. Although basic concepts have been presented here but many results presented have not appeared in any book till now. The book could be used as a text for graduate students and also it will be useful for researchers working in this field.
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.
Inversion of Stokes Profiles with Systematic Effects
Ramos, A Asensio; Gonzalez, M J Martinez; Yabar, A Pastor
2016-01-01
Quantitative thermodynamical, dynamical and magnetic properties of the solar and stellar plasmas are obtained by interpreting their emergent non-polarized and polarized spectrum. This inference requires the selection of a set of spectral lines particularly sensitive to the physical conditions in the plasma and a suitable parametric model of the solar/stellar atmosphere. Nonlinear inversion codes are then used to fit the model to the observations. However, the presence of systematic effects like nearby or blended spectral lines, telluric absorption or incorrect correction of the continuum, among others, can strongly affect the results. We present an extension to current inversion codes that can deal with these effects in a transparent way. The resulting algorithm is very simple and can be applied to any existing inversion code with the addition of a few lines of code as an extra step in each iteration.
Inverse Kinematics using Quaternions
DEFF Research Database (Denmark)
Henriksen, Knud; Erleben, Kenny; Engell-Nørregård, Morten
In this project I describe the status of inverse kinematics research, with the focus firmly on the methods that solve the core problem. An overview of the different methods are presented Three common methods used in inverse kinematics computation have been chosen as subject for closer inspection....... suite, developed in this project and in [4]. Source code developed for this project includes the CCD method , improvements on the BFGS method and Jacobian inverse originally developed in [4]....
Inverse periodic shadowing properties
Osipov, Alexey V
2011-01-01
We consider inverse periodic shadowing properties of discrete dynamical systems generated by diffeomorphisms of closed smooth manifolds. We show that the $C^1$-interior of the set of all diffeomorphisms having so-called inverse periodic shadowing property coincides with the set of $\\Omega$-stable diffeomorphisms. The equivalence of Lipschitz inverse periodic shadowing property and hyperbolicity of the closure of all periodic points is proved. Besides, we prove that the set of all diffeomorphisms that have Lipschitz inverse periodic shadowing property and whose periodic points are dense in the nonwandering set coincides with the set of Axiom A diffeomorphisms.
Simulation of non-linear ultrasound fields
DEFF Research Database (Denmark)
Jensen, Jørgen Arendt; Fox, Paul D.; Wilhjelm, Jens E.
2002-01-01
An approach for simulating non-linear ultrasound imaging using Field II has been implemented using the operator splitting approach, where diffraction, attenuation, and non-linear propagation can be handled individually. The method uses the Earnshaw/Poisson solution to Burgcrs' equation for the non......-linear ultrasound imaging in 3D using filters or pulse inversion for any kind of transducer, focusing, apodization, pulse emission and scattering phantom. This is done by first simulating the non-linear emitted field and assuming that the scattered field is weak and linear. The received signal is then the spatial...
An evolution equation modeling inversion of tulip flames
Energy Technology Data Exchange (ETDEWEB)
Dold, J.W. [Univ. of Bristol (United Kingdom). School of Mathematics; Joulin, G. [E.N.S.M.A., Poitiers (France). Lab. d`Energetique et de Detonique
1995-02-01
The authors attempt to reduce the number of physical ingredients needed to model the phenomenon of tulip-flame inversion to a bare minimum. This is achieved by synthesizing the nonlinear, first-order Michelson-Sivashinsky (MS) equation with the second order linear dispersion relation of Landau and Darrieus, which adds only one extra term to the MS equation without changing any of its stationary behavior and without changing its dynamics in the limit of small density change when the MS equation is asymptotically valid. However, as demonstrated by spectral numerical solutions, the resulting second-order nonlinear evolution equation is found to describe the inversion of tulip flames in good qualitative agreement with classical experiments on the phenomenon. This shows that the combined influences of front curvature, geometric nonlinearity and hydrodynamic instability (including its second-order, or inertial effects, which are an essential result of vorticity production at the flame front) are sufficient to reproduce the inversion process.
Timescape: a simple space-time interpolation geostatistical Algorithm
Ciolfi, Marco; Chiocchini, Francesca; Gravichkova, Olga; Pisanelli, Andrea; Portarena, Silvia; Scartazza, Andrea; Brugnoli, Enrico; Lauteri, Marco
2016-04-01
Environmental sciences include both time and space variability in their datasets. Some established tools exist for both spatial interpolation and time series analysis alone, but mixing space and time variability calls for compromise: Researchers are often forced to choose which is the main source of variation, neglecting the other. We propose a simple algorithm, which can be used in many fields of Earth and environmental sciences when both time and space variability must be considered on equal grounds. The algorithm has already been implemented in Java language and the software is currently available at https://sourceforge.net/projects/timescapeglobal/ (it is published under GNU-GPL v3.0 Free Software License). The published version of the software, Timescape Global, is focused on continent- to Earth-wide spatial domains, using global longitude-latitude coordinates for samples localization. The companion Timescape Local software is currently under development ad will be published with an open license as well; it will use projected coordinates for a local to regional space scale. The basic idea of the Timescape Algorithm consists in converting time into a sort of third spatial dimension, with the addition of some causal constraints, which drive the interpolation including or excluding observations according to some user-defined rules. The algorithm is applicable, as a matter of principle, to anything that can be represented with a continuous variable (a scalar field, technically speaking). The input dataset should contain position, time and observed value of all samples. Ancillary data can be included in the interpolation as well. After the time-space conversion, Timescape follows basically the old-fashioned IDW (Inverse Distance Weighted) interpolation Algorithm, although users have a wide choice of customization options that, at least partially, overcome some of the known issues of IDW. The three-dimensional model produced by the Timescape Algorithm can be
Gladwell, Graham ML
2011-01-01
The papers in this volume present an overview of the general aspects and practical applications of dynamic inverse methods, through the interaction of several topics, ranging from classical and advanced inverse problems in vibration, isospectral systems, dynamic methods for structural identification, active vibration control and damage detection, imaging shear stiffness in biological tissues, wave propagation, to computational and experimental aspects relevant for engineering problems.
Inverse Symmetric Inflationary Attractors
Odintsov, S D
2016-01-01
We present a class of inflationary potentials which are invariant under a special symmetry, which depends on the parameters of the models. As we show, in certain limiting cases, the inverse symmetric potentials are qualitatively similar to the $\\alpha$-attractors models, since the resulting observational indices are identical. However, there are some quantitative differences which we discuss in some detail. As we show, some inverse symmetric models always yield results compatible with observations, but this strongly depends on the asymptotic form of the potential at large $e$-folding numbers. In fact when the limiting functional form is identical to the one corresponding to the $\\alpha$-attractors models, the compatibility with the observations is guaranteed. Also we find the relation of the inverse symmetric models with the Starobinsky model and we highlight the differences. In addition, an alternative inverse symmetric model is studied and as we show, not all the inverse symmetric models are viable. Moreove...
0-Semidistributive Inverse Semigroups
Institute of Scientific and Technical Information of China (English)
田振际
2004-01-01
@@ For an inverse semigroup S, the set L(S) of all inverse subsemigroups (including the empty set) of S forms a lattice with respect to intersection denoted as usual by ∩ and union, where the union is the inverse subsemigroup generated by inverse subsemigroups A, B of S. The set LF(S) of all full inverse subsemigroups of S forms a complete sublattice of L(S), with Es as zero element (Es is the set of all idempotent of S)(see [3,5,6]). Note, that if S a group, then LF(S)=L(S), its lattice of all subgroups of S. If S = G0 is a group with adjoined zero, then clearly LF(S) ≌ L(G).
Institute of Scientific and Technical Information of China (English)
俞德孚; 陈庆东; 李文君
2003-01-01
Based on the theory and the practical experiences of linearity design of feasible design area and inverse solution of non-linear outer characteristic of suspension shock absorber, in accordance with non-linearity outer characteristic formed by open-up damping coefficient, full-open damping coefficient and smoothness to safety ratio of suspension shock absorber, a method and a research conclusion of the feasible design and inverse solution for the basic problems of designing and inverse solution of non-linear outer characteristic of suspension damping components are provided.
Elastic envelope inversion using multicomponent seismic data without low frequency
2014-01-01
Low frequency is a key issue to reduce the nonlinearity of elastic full waveform inversion. Hence, the lack of low frequency in recorded seismic data is one of the most challenging problems in elastic full waveform inversion. Theoretical derivations and numerical analysis are presented in this paper to show that envelope operator can retrieve strong low frequency modulation signal demodulated in multicomponent data, no matter what the frequency bands of the data is. With the be...
Conditioning geostatistical simulations of a bedrock fluvial aquifer using single well pumping tests
Niazi, A.; Bentley, L. R.; Hayashi, M.
2015-12-01
Geostatistical simulation is a powerful tool to explore the uncertainty associated with heterogeneity in groundwater and reservoir studies. Nonetheless, conditioning simulations merely with lithological information does not utilize all of the available information and so some workers additionally condition simulations with flow data. In this study, we introduce an approach to condition geostatistical simulations of the Paskapoo Formation, which is a paleo-fluvial system consisting of sandstone channels embedded in mudstone. The conditioning data consist of two-hour single well pumping tests extracted from the public water well database in Alberta, Canada. In this approach, lithologic models of an entire watershed are simulated and conditioned with hard lithological data using transition probability geostatistics (TPROGS). Then, a segment of the simulation around a pumping well was used to populate a flow model (FEFLOW) with either sand or mudstone. The values of the hydraulic conductivity and specific storage of sand and mudstone were then adjusted to minimize the difference between simulated and actual pumping test data using the parameter estimation program PEST. If the simulated data do not adequately match the measured data, the lithologic model is updated by locally deforming the lithology distribution using the probability perturbation method (PPM) and the model parameters are again updated with PEST. This procedure is repeated until the simulated and measured data agree within a pre-determined tolerance. The procedure is repeated for each pumping well that has pumping test data. The method constrains the lithological simulations and provides estimates of hydraulic conductivity and specific storage that are consistent with the pumping test data. Eventually, the simulations will be combined in watershed scale groundwater models.
Ishaq; Nur Heriawan, Mohamad; Saepuloh, Asep
2016-09-01
Mt. Wayang Windu is one of geothermal field located in West Java, Indonesia. The characterization of steam spots at surface manifestation zones based on the soil physical measurements of the area is presented in this study. The multivariate geostatistical methods incorporating the soil physical parameter data were used to characterize the zonation of geothermal surface manifestations. The purpose of this study is to evaluate the performance of spatial estimation method of multivariate geostatistics using Ordinary Cokriging (COK) to characterize the physical properties of geothermal surface manifestations at Mt. Wayang Windu. The COK method was selected because this method is favorable when the secondary variables has more number than the primary variables. There are four soil physical parameters used as the basis of COK method, i.e. Electrical Conductivity, Susceptibility, pH, and Temperature. The parameters were measured directly at and around geothermal surface manifestations including hot springs, fumaroles, and craters. Each location of surface manifestations was measured about 30 points with 30 x 30 m grids. The measurement results were analyzed by descriptive statistics to identify at the nature of data. The correlation among variables was analyzed using linear regression. When the correlation coefficient among variables is higher, the estimation results is expected to have better Linear Coregionalization Model (LCM). LCM was used to analyze the spatial correlation of each variable based on their variogram and cross-variogram model. In oder to evaluate the performance of multivariate geostatistical using COK method, a Root Mean Square Error (RMSE) was performed. Estimation result using COK method is well applicable for characterizing the surface physics parameters of radar images data.
Can Geostatistical Models Represent Nature's Variability? An Analysis Using Flume Experiments
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
Directory of Open Access Journals (Sweden)
Cristiano Cigagna
2015-12-01
Full Text Available Abstract Aim: This study aimed to map the concentrations of limnological variables in a reservoir employing semivariogram geostatistical techniques and Kriging estimates for unsampled locations, as well as the uncertainty calculation associated with the estimates. Methods: We established twenty-seven points distributed in a regular mesh for sampling. Then it was determined the concentrations of chlorophyll-a, total nitrogen and total phosphorus. Subsequently, a spatial variability analysis was performed and the semivariogram function was modeled for all variables and the variographic mathematical models were established. The main geostatistical estimation technique was the ordinary Kriging. The work was developed with the estimate of a heavy grid points for each variables that formed the basis of the interpolated maps. Results: Through the semivariogram analysis was possible to identify the random component as not significant for the estimation process of chlorophyll-a, and as significant for total nitrogen and total phosphorus. Geostatistical maps were produced from the Kriging for each variable and the respective standard deviations of the estimates calculated. These measurements allowed us to map the concentrations of limnological variables throughout the reservoir. The calculation of standard deviations provided the quality of the estimates and, consequently, the reliability of the final product. Conclusions: The use of the Kriging statistical technique to estimate heavy mesh points associated with the error dispersion (standard deviation of the estimate, made it possible to make quality and reliable maps of the estimated variables. Concentrations of limnological variables in general were higher in the lacustrine zone and decreased towards the riverine zone. The chlorophyll-a and total nitrogen correlated comparing the grid generated by Kriging. Although the use of Kriging is more laborious compared to other interpolation methods, this
A geostatistical approach to estimate mining efficiency indicators with flexible meshes
Freixas, Genis; Garriga, David; Fernàndez-Garcia, Daniel; Sanchez-Vila, Xavier
2014-05-01
Geostatistics is a branch of statistics developed originally to predict probability distributions of ore grades for mining operations by considering the attributes of a geological formation at unknown locations as a set of correlated random variables. Mining exploitations typically aim to maintain acceptable mineral laws to produce commercial products based upon demand. In this context, we present a new geostatistical methodology to estimate strategic efficiency maps that incorporate hydraulic test data, the evolution of concentrations with time obtained from chemical analysis (packer tests and production wells) as well as hydraulic head variations. The methodology is applied to a salt basin in South America. The exploitation is based on the extraction of brines through vertical and horizontal wells. Thereafter, brines are precipitated in evaporation ponds to obtain target potassium and magnesium salts of economic interest. Lithium carbonate is obtained as a byproduct of the production of potassium chloride. Aside from providing an assemble of traditional geostatistical methods, the strength of this study falls with the new methodology developed, which focus on finding the best sites to exploit the brines while maintaining efficiency criteria. Thus, some strategic indicator efficiency maps have been developed under the specific criteria imposed by exploitation standards to incorporate new extraction wells in new areas that would allow maintain or improve production. Results show that the uncertainty quantification of the efficiency plays a dominant role and that the use flexible meshes, which properly describe the curvilinear features associated with vertical stratification, provides a more consistent estimation of the geological processes. Moreover, we demonstrate that the vertical correlation structure at the given salt basin is essentially linked to variations in the formation thickness, which calls for flexible meshes and non-stationarity stochastic processes.
DEFF Research Database (Denmark)
Kessler, Timo Christian; Nilsson, Bertel; Klint, Knud Erik;
2010-01-01
the geology of e.g. a contaminated site, it is not always possible to gather enough information to build a representative geological model. Mapping in analogue geological settings and applying geostatistical tools to simulate spatial variability of heterogeneities can improve ordinary geological models...... that are predicated only on vertical borehole information. This study documents methods to map geological heterogeneity in clay till and ways to calibrate geostatistical models with field observations. A well-exposed cross-section in an excavation pit was used to measure and illustrate the occurrence and distribution...... of sand-lenses in clay till. Sand-lenses mainly account for horizontal transport and are prioritised in this study. Based on field observations, the distribution has been modeled using two different geostatistical approaches. One method uses a Markov chain model calculating the transition probabilities...
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
Zhu, Hong-Ming; Pen, Ue-Li; Chen, Xuelei; Yu, Hao-Ran
2016-01-01
We present a direct approach to non-parametrically reconstruct the linear density field from an observed non-linear map. We solve for the unique displacement potential consistent with the non-linear density and positive definite coordinate transformation using a multigrid algorithm. We show that we recover the linear initial conditions up to $k\\sim 1\\ h/\\mathrm{Mpc}$ with minimal computational cost. This reconstruction approach generalizes the linear displacement theory to fully non-linear fields, potentially substantially expanding the BAO and RSD information content of dense large scale structure surveys, including for example SDSS main sample and 21cm intensity mapping.
Boyd, Robert W
2013-01-01
Nonlinear Optics is an advanced textbook for courses dealing with nonlinear optics, quantum electronics, laser physics, contemporary and quantum optics, and electrooptics. Its pedagogical emphasis is on fundamentals rather than particular, transitory applications. As a result, this textbook will have lasting appeal to a wide audience of electrical engineering, physics, and optics students, as well as those in related fields such as materials science and chemistry.Key Features* The origin of optical nonlinearities, including dependence on the polarization of light* A detailed treatment of the q
Unwrapped phase inversion with an exponential damping
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.
Fluidized bed control system based on inverse system method
Institute of Scientific and Technical Information of China (English)
SONG Fu-hua; LI Ping
2005-01-01
The invertible of the Large Air Dense Medium Fluidized Bed (ADMFB) were studied by introducing the concept of the inverse system theory of nonlinear systems.Then the ADMFB, which was a multivariable, nonlinear and coupled strongly system,was decoupled into independent SISO pseudo-linear subsystems. Linear controllers were designed for each of subsystems based on linear systems theory. The practice output proves that this method improves the stability of the ADMFB obviously.
An inverse model for magnetorheological dampers based on a restructured phenomenological model
Qian, Li-Jun; Liu, Bo; Chen, Peng; Bai, Xian-Xu
2016-04-01
Magnetorheological dampers (MRDs), a semi-active actuator based on MR effect, have great potential in vibration/shock control systems. However, it is difficult to establish its inverse model due to its intrinsic strong nonlinear hysteresis behaviors, and sequentially the precise, fast and effective control could not be realized effectively. This paper presents an inverse model for MRDs based on a restructured phenomenological model with incorporation of the "normalization" concept. The proposed inverse model of MRDs is validated by the simulation of the force tracking. The research results indicate that the inverse model could be applied for the damping force control with consideration of the strong nonlinear hysteresis behaviors of the MRDs.
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
Image smoothing of multispectral imagery based on the HNN and geo-statistics
Institute of Scientific and Technical Information of China (English)
Nguyen Quang Minh
2011-01-01
A new method for image down-scaling using geostatistical interpolation or smoothing based on the Hopfield Neural Network (HNN) and zero semivariance value is introduced.The method utilises the smoothing effect of the semivariogram matching process to produce the smoothened sub-pixel multispectral (MS) image with smaller RMSEs in comparison with the bilinear interpolation.In fact,the zero semivariograms increase the spatial correlation between the adjacent sub-pixels of the superresolution image.Containing higher spatial correlation,the resulting super-resolution MS image has smaller RMSEs compared with the original coarse image.
Geostatistical analysis of soil properties at field scale using standardized data
Millan, H.; Tarquis, A. M.; Pérez, L. D.; Matos, J.; González-Posada, M.
2012-04-01
Indentifying areas with physical degradation is a crucial step to ameliorate the effects in soil erosion. The quantification and interpretation of spatial variability is a key issue for site-specific soil management. Geostatistics has been the main methodological tool for implementing precision agriculture using field data collected at different spatial resolutions. Even though many works have made significant contributions to the body of knowledge on spatial statistics and its applications, some other key points need to be addressed for conducting precise comparisons between soil properties using geostatistical parameters. The objectives of the present work were (i) to quantify the spatial structure of different physical properties collected from a Vertisol, (ii) to search for potential correlations between different spatial patterns and (iii) to identify relevant components through multivariate spatial analysis. The study was conducted on a Vertisol (Typic Hapludert) dedicated to sugarcane (Saccharum officinarum L.) production during the last sixty years. We used six soil properties collected from a squared grid (225 points) (penetrometer resistance (PR), total porosity, fragmentation dimension (Df), vertical electrical conductivity (ECv), horizontal electrical conductivity (ECh) and soil water content (WC)). All the original data sets were z-transformed before geostatistical analysis. Three different types of semivariogram models were necessary for fitting individual experimental semivariograms. This suggests the different natures of spatial variability patterns. Soil water content rendered the largest nugget effect (C0 = 0.933) while soil total porosity showed the largest range of spatial correlation (A = 43.92 m). The bivariate geostatistical analysis also rendered significant cross-semivariance between different paired soil properties. However, four different semivariogram models were required in that case. This indicates an underlying co
Herzfeld, Ute Christina; Mayer, Helmut; Higginson, Chris A.; Matassa, Michael
1996-01-01
Geostatistical methods for interpolation and extrapolation techniques are used in glaciological data analysis. The results of a program involving the mapping of the Antarctica from satellite radar altimeter data are discussed. A combination of high and low resolution techniques was applied in the analysis of the Bering Glacier (Alaska). The global positioning system (GPS) located video data collected from small aircraft and the ERS-1 synthetic aperture radar (SAR) images were used. From the perspective of SAR data analysis, the Bering Glacier surge was the opportunity to characterize the surface of fast flowing ice and the rapid changes in the surface roughness.
Ruszczynski, Andrzej
2011-01-01
Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects, Nonlinear Optimization is the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates t
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
Inversion as an iterative puzzle: A probabilistic formulation with graph cuts
Linde, Niklas; Pirot, Guillaume; Mariethoz, Grégoire; Zahner, Tobias
2016-04-01
Geophysical inversion results should ideally feature realistic connectivity patterns when considering applications of relevance for subsurface mass transfer. We argue that persistent resolution limitations of geophysical data are most likely to prohibit such a goal if the inversion framework does not incorporate geological considerations. Geological concepts can be included through multiple-point statistics tools that produce multiple subsurface realizations that are in agreement with a training image that defines the underlying conceptual geological model. A recent patch-based geostatistical resimulation algorithm that uses a graph cuts strategy allows for model realizations of similar quality as state-of-the-art multiple point statistics simulation codes, but at a fraction of their computational cost. This enables considerable speed-ups in sequential geostatistical resimulation algorithms that use Markov chain Monte Carlo to sample the posterior probability density function. Our algorithm works very well when considering continuous and discontinuous property fields for cases of noise-contaminated synthetic data and a training image that is consistent with the higher-order statistics of the test model. Applications to field data are more challenging due to inevitable discrepancies between the actual subsurface structure and the assumptions made in deriving the training image. We argue that the degradation of the inversion results obtained by using an inappropriate training image can be seen as a strength of the method as it forces the user to reconsider the conceptual geological model and petrophysical relationships until sufficient and appropriate details are included to obtain meaningful results. Possible pitfalls and working strategies for field data will be presented together with an outlook towards joint inversion of multiple geophysical and hydrogeological data types.
Forward and inverse modelling of post-seismic deformation
Crawford, Ophelia; Al-Attar, David; Tromp, Jeroen; Mitrovica, Jerry X.
2016-11-01
We consider a new approach to both the forward and inverse problems in post-seismic deformation. We present a method for forward modelling post-seismic deformation in a self-gravitating, heterogeneous and compressible earth with a variety of linear and non-linear rheologies. We further demonstrate how the adjoint method can be applied to the inverse problem both to invert for rheological structure and to calculate the sensitivity of a given surface measurement to changes in rheology or time-dependence of the source. Both the forward and inverse aspects are illustrated with several numerical examples implemented in a spherically symmetric earth model.
Forward and inverse modelling of post-seismic deformation
Crawford, Ophelia; Al-Attar, David; Tromp, Jeroen; Mitrovica, Jerry X.
2017-02-01
We consider a new approach to both the forward and inverse problems in post-seismic deformation. We present a method for forward modelling post-seismic deformation in a self-gravitating, heterogeneous and compressible earth with a variety of linear and nonlinear rheologies. We further demonstrate how the adjoint method can be applied to the inverse problem both to invert for rheological structure and to calculate the sensitivity of a given surface measurement to changes in rheology or time-dependence of the source. Both the forward and inverse aspects are illustrated with several numerical examples implemented in a spherically symmetric earth model.
Fast Linear Algebra Applications in Stochastic Inversion and Data Assimilation
Kitanidis, P. K.; Ambikasaran, S.; Saibaba, A.; Li, J. Y.; Darve, E. F.
2012-12-01
Inverse problems and data assimilation problems arise frequently in earth-science applications, such as hydraulic tomography, cross-well seismic travel-time tomography, electrical resistivity tomography, contaminant source identification, assimilation of weather data, etc. A common feature amongst inverse problems is that the parameters we are interested in estimating are hard to measure directly, and a crucial component of inverse modeling is using sparse data to evaluate many model parameters. To quantify uncertainty, stochastic methods such as the geostatistical approach to inverse problems and Kalman filtering are often used. The algorithms for the implementation of these methods were originally developed for small-size problems and their cost of implementation increases quickly with the size of the problem, which is usually defined by the number of observations and the number of unknowns. From a practical standpoint, it is critical to develop computational algorithms in linear algebra for which the computational effort, both in terms of storage and computational time, increases roughly linearly with the size of the problem. This is in contrast, for example, with matrix-vector products (resp. LU factorization) that scale quadratically (resp. cubically). This objective is achieved by tailoring methods to the structure of problems. We present an overview of the challenges and general approaches available for reducing computational cost and then present applications focusing on algorithms that use the hierarchical matrix approach. The hierarchical method reduces matrix vector products involving the dense covariance matrix from O(m2) to O(m log m), where m is the number of unknowns. We illustrate the performance of our algorithm on a few applications, such as monitoring CO2 concentrations using crosswell seismic tomography.
Directory of Open Access Journals (Sweden)
Saeid Gharechelou
2016-03-01
Full Text Available Soil moisture (SM plays a key role in many environmental processes and has a high spatial and temporal variability. Collecting sample SM data through field surveys (e.g., for validation of remote sensing-derived products can be very expensive and time consuming if a study area is large, and producing accurate SM maps from the sample point data is a difficult task as well. In this study, geospatial processing techniques are used to combine several geo-environmental layers relevant to SM (soil, geology, rainfall, land cover, etc. into a land unit area (LUA map, which delineates regions with relatively homogeneous geological/geomorphological, land use/land cover, and climate characteristics. This LUA map is used to guide the collection of sample SM data in the field, and the field data is finally spatially interpolated to create a wall-to-wall map of SM in the study area (Garmsar, Iran. The main goal of this research is to create a SM map in an arid area, using a land unit area (LUA approach to obtain the most appropriate sample locations for collecting SM field data. Several environmental GIS layers, which have an impact on SM, were combined to generate a LUA map, and then field surveying was done in each class of the LUA map. A SM map was produced based on LUA, remote sensing data indexes, and spatial interpolation of the field survey sample data. The several interpolation methods (inverse distance weighting, kriging, and co-kriging were evaluated for generating SM maps from the sample data. The produced maps were compared to each other and validated using ground truth data. The results show that the LUA approach is a reasonable method to create the homogenous field to introduce a representative sample for field soil surveying. The geostatistical SM map achieved adequate accuracy; however, trend analysis and distribution of the soil sample point locations within the LUA types should be further investigated to achieve even better results. Co
Tsunami waveform inversion by adjoint methods
Pires, Carlos; Miranda, Pedro M. A.
2001-09-01
An adjoint method for tsunami waveform inversion is proposed, as an alternative to the technique based on Green's functions of the linear long wave model. The method has the advantage of being able to use the nonlinear shallow water equations, or other appropriate equation sets, and to optimize an initial state given as a linear or nonlinear function of any set of free parameters. This last facility is used to perform explicit optimization of the focal fault parameters, characterizing the initial sea surface displacement of tsunamigenic earthquakes. The proposed methodology is validated with experiments using synthetic data, showing the possibility of recovering all relevant details of a tsunami source from tide gauge observations, providing that the adjoint method is constrained in an appropriate manner. It is found, as in other methods, that the inversion skill of tsunami sources increases with the azimuthal and temporal coverage of assimilated tide gauge stations; furthermore, it is shown that the eigenvalue analysis of the Hessian matrix of the cost function provides a consistent and useful methodology to choose the subset of independent parameters that can be inverted with a given dataset of observations and to evaluate the error of the inversion process. The method is also applied to real tide gauge series, from the tsunami of the February 28, 1969, Gorringe Bank earthquake, suggesting some reasonable changes to the assumed focal parameters of that event. It is suggested that the method proposed may be able to deal with transient tsunami sources such as those generated by submarine landslides.
On Generalized Inverse Transversals
Institute of Scientific and Technical Information of China (English)
Rong Hua ZHANG; Shou Feng WANG
2008-01-01
Let S be a regular semigroup,S° an inverse subsemigroup of S.S° is called a generalized inverse transversal of S,if V(x) ∩N S°≠φ.In this paper,some properties of this kind of semigroups are discussed.In particular,a construction theorem is obtained which contains some recent results in the literature as its special cases.
3D Geostatistical Modeling and Uncertainty Analysis in a Carbonate Reservoir, SW Iran
Directory of Open Access Journals (Sweden)
Mohammad Reza Kamali
2013-01-01
Full Text Available The aim of geostatistical reservoir characterization is to utilize wide variety of data, in different scales and accuracies, to construct reservoir models which are able to represent geological heterogeneities and also quantifying uncertainties by producing numbers of equiprobable models. Since all geostatistical methods used in estimation of reservoir parameters are inaccurate, modeling of “estimation error” in form of uncertainty analysis is very important. In this paper, the definition of Sequential Gaussian Simulation has been reviewed and construction of stochastic models based on it has been discussed. Subsequently ranking and uncertainty quantification of those stochastically populated equiprobable models and sensitivity study of modeled properties have been presented. Consequently, the application of sensitivity analysis on stochastic models of reservoir horizons, petrophysical properties, and stochastic oil-water contacts, also their effect on reserve, clearly shows any alteration in the reservoir geometry has significant effect on the oil in place. The studied reservoir is located at carbonate sequences of Sarvak Formation, Zagros, Iran; it comprises three layers. The first one which is located beneath the cap rock contains the largest portion of the reserve and other layers just hold little oil. Simulations show that average porosity and water saturation of the reservoir is about 20% and 52%, respectively.
Long, Y. Q.; Cui, T. T.; Li, W.; Yang, Z. P.; Gai, Y. W.
2017-08-01
The geostatistical approach has been studied for many year to identify the pollution source re-lease history in groundwater. We focus on the influence of observation error and hydraulic parameters on the groundwater pollution identification (PSI) result in the paper. Numerical experiment and sensitivity analysis are carried out to find the influence of observation point configuration, error and hydraulic parameters on the PSI result in a 1D homogeneous aquifer. It has been found out that if concentration observation data could accurately describe the characteristics of the real concentration plume at the observed time point, a nice identification of the pollution release process could be obtained. If the calculated pollution discharge process has good similarity with the real discharge process, the order of the observation error fell within 10-6 and 10-3.5, the dispersion coefficient varies fells within -10% and 5%, and the actual mean velocity fell within ±2%. The actual mean velocity is the most sensitive parameter of the geostatistical approach in this case.
de Carvalho Alves, Marcelo; de Carvalho, Luiz Gonsaga; Vianello, Rubens Leite; Sediyama, Gilberto C.; de Oliveira, Marcelo Silva; de Sá Junior, Arionaldo
2013-07-01
The objective of the present study was to use the simple cokriging methodology to characterize the spatial variability of Penman-Monteith reference evapotranspiration and Thornthwaite potential evapotranspiration methods based on Moderate Resolution Imaging Spetroradiometer (MODIS) global evapotranspiration products and high-resolution surfaces of WordClim temperature and precipitation data. The climatic element data referred to 39 National Institute of Meteorology climatic stations located in Minas Gerais state, Brazil and surrounding states. The use of geostatistics and simple cokriging technique enabled the characterization of the spatial variability of the evapotranspiration providing uncertainty information on the spatial prediction pattern. Evapotranspiration and precipitation surfaces were implemented for the climatic classification in Minas Gerais. Multivariate geostatistical determined improvements of evapotranspiration spatial information. The regions in the south of Minas Gerais derived from the moisture index estimated with the MODIS evapotranspiration (2000-2010), presented divergence of humid conditions when compared to the moisture index derived from the simple kriged and cokriged evapotranspiration (1961-1990), indicating climate change in this region. There was stronger pattern of crossed covariance between evapotranspiration and precipitation rather than temperature, indicating that trends in precipitation could be one of the main external drivers of the evapotranspiration in Minas Gerais state, Brazil.
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.
DEFF Research Database (Denmark)
Schur, Nadine; Hürlimann, Eveline; Stensgaard, Anna-Sofie
2013-01-01
Schistosomiasis remains one of the most prevalent parasitic diseases in the tropics and subtropics, but current statistics are outdated due to demographic and ecological transformations and ongoing control efforts. Reliable risk estimates are important to plan and evaluate interventions in a spat......Schistosomiasis remains one of the most prevalent parasitic diseases in the tropics and subtropics, but current statistics are outdated due to demographic and ecological transformations and ongoing control efforts. Reliable risk estimates are important to plan and evaluate interventions...... in a spatially explicit and cost-effective manner. We analysed a large ensemble of georeferenced survey data derived from an open-access neglected tropical diseases database to create smooth empirical prevalence maps for Schistosoma mansoni and Schistosoma haematobium for a total of 13 countries of eastern...... Africa. Bayesian geostatistical models based on climatic and other environmental data were used to account for potential spatial clustering in spatially structured exposures. Geostatistical variable selection was employed to reduce the set of covariates. Alignment factors were implemented to combine...
geoCount: An R Package for the Analysis of Geostatistical Count Data
Directory of Open Access Journals (Sweden)
Liang Jing
2015-02-01
Full Text Available We describe the R package geoCount for the analysis of geostatistical count data. The package performs Bayesian analysis for the Poisson-lognormal and binomial-logitnormal spatial models, which are subclasses of the class of generalized linear spatial models proposed by Diggle, Tawn, and Moyeed (1998. The package implements the computational intensive tasks in C++ using an R/C++ interface, and has parallel computation capabilities to speed up the computations. geoCount also implements group updating, Langevin- Hastings algorithms and a data-based parameterization, algorithmic approaches proposed by Christensen, Roberts, and Sko ?ld (2006 to improve the efficiency of the Markov chain Monte Carlo algorithms. In addition, the package includes functions for simulation and visualization, as well as three geostatistical count datasets taken from the literature. One of those is used to illustrate the package capabilities. Finally, we provide a side-by-side comparison between geoCount and the R packages geoRglm and INLA.
Directory of Open Access Journals (Sweden)
Waldir de Carvalho Junior
2014-06-01
Full Text Available Soil properties have an enormous impact on economic and environmental aspects of agricultural production. Quantitative relationships between soil properties and the factors that influence their variability are the basis of digital soil mapping. The predictive models of soil properties evaluated in this work are statistical (multiple linear regression-MLR and geostatistical (ordinary kriging and co-kriging. The study was conducted in the municipality of Bom Jardim, RJ, using a soil database with 208 sampling points. Predictive models were evaluated for sand, silt and clay fractions, pH in water and organic carbon at six depths according to the specifications of the consortium of digital soil mapping at the global level (GlobalSoilMap. Continuous covariates and categorical predictors were used and their contributions to the model assessed. Only the environmental covariates elevation, aspect, stream power index (SPI, soil wetness index (SWI, normalized difference vegetation index (NDVI, and b3/b2 band ratio were significantly correlated with soil properties. The predictive models had a mean coefficient of determination of 0.21. Best results were obtained with the geostatistical predictive models, where the highest coefficient of determination 0.43 was associated with sand properties between 60 to 100 cm deep. The use of a sparse data set of soil properties for digital mapping can explain only part of the spatial variation of these properties. The results may be related to the sampling density and the quantity and quality of the environmental covariates and predictive models used.
Geostatistics: a common link between medical geography, mathematical geology, and medical geology.
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.
Geostatistical Analysis on the Temporal Patterns of the Yellow Rice Borer, Tryporyza incertulas
Institute of Scientific and Technical Information of China (English)
YUAN Zhe-ming; WANG Zhi; HU Xiang-yue
2005-01-01
In order to comprehend temporal pattern of the larvae population of the yellow rice borer, Tryporyza incertulas, and provide valuable information for its forecast model, the data series of the population for each generation and the over-wintered larvae from 1960 to 1990 in Dingcheng District, Changde City, Hunan Province, were analyzed with geostatistics. The data series of total number,the 1 st generation, the 3rd generation and the over-wintered larvae year to year displayed rather better autocorrelation and prediction.The data series of generation to generation, the 2nd generation and the 4th generation year to year, however, demonstrated poor autocorrelation, especially for the 4th generation, whose autocorrelation degree was zero. The population dynamics of the yellow rice borer was obviously intermittent. A remarkable cycle of four generations, one year, was observed in the population of generation to generation. Omitting the certain generation or interposing the over-wintered larvae only resulted in a less or slight change of autocorrelation of the whole data series generation to generation. Crop system, food, climate and natural enemies, therefore, played more important roles in regulating the population dynamics than base number of the larvae. The basic techniques of geostatistics applied in analyzing temporal population dynamics were outlined.
Geostatistical borehole image-based mapping of karst-carbonate aquifer pores
Michael Sukop,; Cunningham, Kevin J.
2016-01-01
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.
Peredo, Oscar; Ortiz, Julián M.; Herrero, José R.
2015-12-01
The Geostatistical Software Library (GSLIB) has been used in the geostatistical community for more than thirty years. It was designed as a bundle of sequential Fortran codes, and today it is still in use by many practitioners and researchers. Despite its widespread use, few attempts have been reported in order to bring this package to the multi-core era. Using all CPU resources, GSLIB algorithms can handle large datasets and grids, where tasks are compute- and memory-intensive applications. In this work, a methodology is presented to accelerate GSLIB applications using code optimization and hybrid parallel processing, specifically for compute-intensive applications. Minimal code modifications are added decreasing as much as possible the elapsed time of execution of the studied routines. If multi-core processing is available, the user can activate OpenMP directives to speed up the execution using all resources of the CPU. If multi-node processing is available, the execution is enhanced using MPI messages between the compute nodes.Four case studies are presented: experimental variogram calculation, kriging estimation, sequential gaussian and indicator simulation. For each application, three scenarios (small, large and extra large) are tested using a desktop environment with 4 CPU-cores and a multi-node server with 128 CPU-nodes. Elapsed times, speedup and efficiency results are shown.
Geostatistical analysis of soil moisture distribution in a part of Solani River catchment
Kumar, Kamal; Arora, M. K.; Hariprasad, K. S.
2016-03-01
The aim of this paper is to estimate soil moisture at spatial level by applying geostatistical techniques on the point observations of soil moisture in parts of Solani River catchment in Haridwar district of India. Undisturbed soil samples were collected at 69 locations with soil core sampler at a depth of 0-10 cm from the soil surface. Out of these, discrete soil moisture observations at 49 locations were used to generate a spatial soil moisture distribution map of the region. Two geostatistical techniques, namely, moving average and kriging, were adopted. Root mean square error (RMSE) between observed and estimated soil moisture at remaining 20 locations was determined to assess the accuracy of the estimated soil moisture. Both techniques resulted in low RMSE at small limiting distance, which increased with the increase in the limiting distance. The root mean square error varied from 7.42 to 9.77 in moving average method, while in case of kriging it varied from 7.33 to 9.99 indicating similar performance of the two techniques.
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.
Selective remediation of contaminated sites using a two-level multiphase strategy and geostatistics.
Saito, Hirotaka; Goovaerts, Pierre
2003-05-01
Selective soil remediation aims to reduce costs by cleaning only the fraction of an exposure unit (EU) necessary to lower the average concentration below the regulatory threshold. This approach requires a prior stratification of each EU into smaller remediation units (RU) which are then selected according to various criteria. This paper presents a geostatistical framework to account for uncertainties attached to both RU and EU average concentrations in selective remediation. The selection of RUs is based on their impact on the postremediation probability for the EU average concentration to exceed the regulatory threshold, which is assessed using geostatistical stochastic simulation. Application of the technique to a set of 600 dioxin concentrations collected at Piazza Road EPA Superfund site in Missouri shows a substantial decrease in the number of RU remediated compared with single phase remediation. The lower remediation costs achieved by the new strategy are obtained to the detriment of a higher risk of false negatives, yet for this data set this risk remains below the 5% rate set by EPA region 7.
Source Apportionment of Heavy Metals in Soils Using Multivariate Statistics and Geostatistics
Institute of Scientific and Technical Information of China (English)
QU Ming-Kai; LI Wei-Dong; ZHANG Chuan-Rong; WANG Shan-Qin; YANG Yong; HE Li-Yuan
2013-01-01
The main objectives of this study were to introduce an integrated method for effectively identifying soil heavy metal pollution sources and apportioning their contributions,and apply it to a case study.The method combines the principal component analysis/absolute principal component scores (PCA/APCS) receptor model and geostatistics.The case study was conducted in an area of 31 km2 in the urban-rural transition zone of Wuhan,a metropolis of central China.124 topsoil samples were collected for measuring the concentrations of eight heavy metal elements (Mn,Cu,Zn,Pb,Cd,Cr,Ni and Co).PCA results revealed that three major factors were responsible for soil heavy metal pollution,which were initially identified as "steel production","agronomic input" and "coal consumption".The APCS technique,combined with multiple linear regression analysis,was then applied for source apportionment.Steel production appeared to be the main source for Ni,Co,Cd,Zn and Mn,agronomic input for Cu,and coal consumption for Pb and Cr.Geostatistical interpolation using ordinary kriging was finally used to map the spatial distributions of the contributions of pollution sources and further confirm the result interpretations.The introduced method appears to be an effective tool in soil pollution source apportionment and identification,and might provide valuable reference information for pollution control and environmental management.
Jha, Sanjeev Kumar
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.
Directory of Open Access Journals (Sweden)
Juliano de Bastos Pazini
2015-06-01
Full Text Available Tibraca limbativentris (rice stem bug is an insect highly injurious to the rice crop in Brazil. The aim of this research was to define the spatial distribution of the T. limbativentris and improve the sampling process by means of geostatistical application techniques and construction of prediction maps in a flooded rice field located in the "Planalto da Campanha" Region, Rio Grande do Sul (RS, Brazil. The experiments were conducted in rice crop in the municipality of Itaqui - RS, in the crop years of 2009/10, 2010/11 and 2011/12, counting fortnightly the number of nymphs and adults in a georeferenced grid with points spaced at 50m in the first year and in 10m in the another years. It was performed a geostatistical analysis by means adjusting semivariogram and interpolation of numeric data by kriging to verify the spatial dependence and the subsequent mapping population. The results obtained indicated that the rice stem bug, T. limbativentris, has a strong spatial dependence. The prediction maps allow estimating population density of the pest and visualization of the spatial distribution in flooded rice fields, enabling the improvement of the traditional method of sampling for rice stem bug
Directory of Open Access Journals (Sweden)
Ricardo Ríos
2017-04-01
Full Text Available This contribution describes the creation of a landslide hazard assessment model for San Salvador, a department in El Salvador. The analysis started with an aerial photointerpretation from Ministry of Environment and Natural Resources of El Salvador (MARN Spanish acronym, where 4792 landslides were identified and georeferenced along with 7 conditioning factors including: geomorphology, geology, rainfall intensity, peak ground acceleration, slope angle, distance to road, and distance to geological fault. Artificial Neural Networks (ANN were utilized to assess the susceptibility to landslides, achieving results where more than 80% of landslide were properly classified using in-sample and out of sample criteria. Logistic regression was used as base of comparison. Logistic regression obtained a lower performance. To complete the analysis we have performed interpolation of the points using the kriging method from geostatistical approach. Finally, the results show that is possible to derive a landslide hazard map, making use of a combination of ANNs and geostatistical techniques, thus the present study can help landslide mitigation in El Salvador.
The inverse electroencephalography pipeline
Weinstein, David Michael
The inverse electroencephalography (EEG) problem is defined as determining which regions of the brain are active based on remote measurements recorded with scalp EEG electrodes. An accurate solution to this problem would benefit both fundamental neuroscience research and clinical neuroscience applications. However, constructing accurate patient-specific inverse EEG solutions requires complex modeling, simulation, and visualization algorithms, and to date only a few systems have been developed that provide such capabilities. In this dissertation, a computational system for generating and investigating patient-specific inverse EEG solutions is introduced, and the requirements for each stage of this Inverse EEG Pipeline are defined and discussed. While the requirements of many of the stages are satisfied with existing algorithms, others have motivated research into novel modeling and simulation methods. The principal technical results of this work include novel surface-based volume modeling techniques, an efficient construction for the EEG lead field, and the Open Source release of the Inverse EEG Pipeline software for use by the bioelectric field research community. In this work, the Inverse EEG Pipeline is applied to three research problems in neurology: comparing focal and distributed source imaging algorithms; separating measurements into independent activation components for multifocal epilepsy; and localizing the cortical activity that produces the P300 effect in schizophrenia.
Generalized emissivity inverse problem.
Ming, DengMing; Wen, Tao; Dai, XianXi; Dai, JiXin; Evenson, William E
2002-04-01
Inverse problems have recently drawn considerable attention from the physics community due to of potential widespread applications [K. Chadan and P. C. Sabatier, Inverse Problems in Quantum Scattering Theory, 2nd ed. (Springer Verlag, Berlin, 1989)]. An inverse emissivity problem that determines the emissivity g(nu) from measurements of only the total radiated power J(T) has recently been studied [Tao Wen, DengMing Ming, Xianxi Dai, Jixin Dai, and William E. Evenson, Phys. Rev. E 63, 045601(R) (2001)]. In this paper, a new type of generalized emissivity and transmissivity inverse (GETI) problem is proposed. The present problem differs from our previous work on inverse problems by allowing the unknown (emissivity) function g(nu) to be temperature dependent as well as frequency dependent. Based on published experimental information, we have developed an exact solution formula for this GETI problem. A universal function set suggested for numerical calculation is shown to be robust, making this inversion method practical and convenient for realistic calculations.
A hybrid inverse method for hydraulic tomography in fractured and karstic media
Wang, Xiaoguang; Jardani, Abderrahim; Jourde, Hervé
2017-08-01
We apply a stochastic Newton (SN) approach to solve a high-dimensional hydraulic inverse problem in highly heterogeneous geological media. By recognizing the connection between the cost function of deterministic optimizations and the posterior probability density of stochastic inversions, the Markov chain Monte Carlo (MCMC) sampler of SN is constructed by two parts: a deterministic part, which corresponds to a Newton step of deterministic optimization, and a stochastic part, which is a Gaussian distribution with the inverse of the local Hessian as the covariance matrix. The hybrid inverse method exploits the efficient tools for fast solution of deterministic inversions to improve the efficiency of the MCMC sampler. To address the ill-posedness of the inverse problem, a priori models, generated by a transition-probability geostatistical method, and conditioned to inter-well connection data, are used as regularization constraints. The effectiveness of the stochastic Newton method is first demonstrated by a synthetic test. The transmissivity field of the synthetic model is highly heterogeneous, and includes sharp variations. The inverse approach was then applied to a field hydraulic tomography investigation in a fractured and karstified aquifer to reconstruct its transmissivity field from a collection of real hydraulic head measurements. From the inversions, a series of transmissivity fields that produce good correlations between the inverted and the measured hydraulic heads were obtained. The inverse approach produced slightly different a posteriori transmissivity patterns for different a priori structure models of transmissivity; however, the trend and location of the high-transmissivity channels are consistent among various realizations. In addition, the uncertainty associated with each realization of the inverted transmissivity fields was quantified.
In, Visarath; Longhini, Patrick; Kho, Andy; Neff, Joseph D.; Leung, Daniel; Liu, Norman; Meadows, Brian K.; Gordon, Frank; Bulsara, Adi R.; Palacios, Antonio
2012-12-01
The nonlinear channelizer is an integrated circuit made up of large parallel arrays of analog nonlinear oscillators, which, collectively, serve as a broad-spectrum analyzer with the ability to receive complex signals containing multiple frequencies and instantaneously lock-on or respond to a received signal in a few oscillation cycles. The concept is based on the generation of internal oscillations in coupled nonlinear systems that do not normally oscillate in the absence of coupling. In particular, the system consists of unidirectionally coupled bistable nonlinear elements, where the frequency and other dynamical characteristics of the emergent oscillations depend on the system's internal parameters and the received signal. These properties and characteristics are being employed to develop a system capable of locking onto any arbitrary input radio frequency signal. The system is efficient by eliminating the need for high-speed, high-accuracy analog-to-digital converters, and compact by making use of nonlinear coupled systems to act as a channelizer (frequency binning and channeling), a low noise amplifier, and a frequency down-converter in a single step which, in turn, will reduce the size, weight, power, and cost of the entire communication system. This paper covers the theory, numerical simulations, and some engineering details that validate the concept at the frequency band of 1-4 GHz.
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.
Energy Technology Data Exchange (ETDEWEB)
Turchetti, G. (Bologna Univ. (Italy). Dipt. di Fisica)
1989-01-01
Research in nonlinear dynamics is rapidly expanding and its range of applications is extending beyond the traditional areas of science where it was first developed. Indeed while linear analysis and modelling, which has been very successful in mathematical physics and engineering, has become a mature science, many elementary phenomena of intrinsic nonlinear nature were recently experimentally detected and investigated, suggesting new theoretical work. Complex systems, as turbulent fluids, were known to be governed by intrinsically nonlinear laws since a long time ago, but received purely phenomenological descriptions. The pioneering works of Boltzmann and Poincare, probably because of their intrinsic difficulty, did not have a revolutionary impact at their time; it is only very recently that their message is reaching a significant number of mathematicians and physicists. Certainly the development of computers and computer graphics played an important role in developing geometric intuition of complex phenomena through simple numerical experiments, while a new mathematical framework to understand them was being developed.
Energy Technology Data Exchange (ETDEWEB)
NONE
1996-12-01
The geostatistical model represents a section of the Dan field in the Danish part of the North See. The Dan-field is a low permeability medium porosity oil reservoir. The section is placed on the southern flank of the Dan field. Using Annealing cosimulation technique (ACS) permeability and porosity distribution was derived from core samples of 15 wells (as hard data) and seismic impedances as secondary (soft) data. In this report 2 different 3D-sections of the geostatistical model are upscaled according to the principles of Stiles. A horizontal model consisting of the 3 top layers in the geostatistical model and a 3-D vertical segment was chosen. A single porosity BlackOil reservoir model is used as simulation model (i.e. gas soluted in the oil phase but no oil soluted in the gas phase). The following fluid- well- and initial state reservoir-data are used as input for the simulation of the geostatistical models: Oil formation volume factor; Oil compressibility; Oil viscosity. For the upscaled models the well data are adjusted to account for the upscaled grid size. Furthermore the relative permeabilities, the absolute permeabilities and the porosity are changed, according to the Stiles upscaling procedure. (EG)
Razack, Moumtaz; Lasm, Théophile
2006-06-01
This work is aimed at estimating the transmissivity of highly fractured hard rock aquifers using a geostatistical approach. The studied aquifer is formed by the crystalline and metamorphic rocks of the Western Ivory Coast (West Africa), in the Man Danané area. The study area covers 7290 km 2 (90 km×81 km). The fracturing network is dense and well connected, without a marked fracture direction. A data base comprising 118 transmissivity ( T) values and 154 specific capacity ( Q/ s) values was compiled. A significant empirical relationship between T and Q/ s was found, which enabled the transmissivity data to be supplemented. The variographic analysis of the two variables showed that the variograms of T and Q/ s (which are lognormal variables) are much more structured than those of log T and log Q/ s (which are normal variables). This result is contrary to what was previously published and raises the question whether normality is necessary in geostatistical analysis. Several input and geostatistical estimations of the transmissivity were tested using the cross validation procedure: measured transmissivity data; supplemented transmissivity data; kriging; cokriging. The cross validation results showed that the best estimation is provided using the kriging procedure, the transmissivity field represented by the whole data sample (measured+estimated using specific capacity) and the structural model evaluated solely on the measured transmissivity. The geostatistical approach provided in fine a reliable estimation of the transmissivity of the Man Danané aquifer, which will be used as an input in forthcoming modelling.
Solving probabilistic inverse problems rapidly with prior samples
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
Solving probabilistic inverse problems rapidly with prior samples
Käufl, Paul; Valentine, Andrew P.|info:eu-repo/dai/nl/364418680; de Wit, Ralph W.|info:eu-repo/dai/nl/344668908; Trampert, Jeannot|info:eu-repo/dai/nl/304829250
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 practic
Dimensionality Reduction and Uncertainty Quantification for Inverse Problems
van Leeuwen, Tristan
2015-01-01
Many inverse problems in science and engineering involve multi-experiment data and thus require a large number of forward simulations. Dimensionality reduction techniques aim at reducing the number of forward solves by (randomly) subsampling the data. In the special case of non-linear least-squares
Inverse Kinematics of Concentric Tube Steerable Needles
Sears, Patrick; Dupont, Pierre E.
2013-01-01
Prior papers have introduced steerable needles composed of precurved concentric tubes. The curvature and extent of these needles can be controlled by the relative rotation and translation of the individual tubes. Under certain assumptions on the geometry and design of these needles, the forward kinematics problem can be solved in closed form by means of algebraic equations. The inverse kinematics problem, however, is not as straightforward owing to the nonlinear map between relative tube displacements and needle tip configuration as well as to the multiplicity of solutions as the number of tubes increases. This paper presents a general approach to solving the inverse kinematics problem using a pseudoinverse solution together with gradients of nullspace potential functions to enforce geometric and mechanical constraints. PMID:23685532
Analog fault diagnosis by inverse problem technique
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.
Studies of GRACE Gravity Field Inversion Techniques
Wang, L.; Shum, C.; Duan, J.; Schmidt, M.; Yuan, D.; Watkins, M. M.
2008-12-01
The geophysical inverse problem using satellite observations, such as GRACE, to estimate gravity change and mass variations at the Earth's surface is a well-known ill-posed problem. Different methods using different basis function (representing the gravity field) for different purposes (global or regional inversion) have been employed to obtain a stable solution, such as Bayesian estimation with prior information, the repro-BIQUUE of variance components and iterative least-squares estimation with simultaneous updating of a prior covariance, and to achieve enhanced spatial resolutions. The gravity field representation methods include spherical harmonics, regional gridded data (including mascons), and various wavelet representations (Poisson wavelets, Blackman band-limited regional wavelets with global representation). Finally, the use of data types (KBR range, range-rate, range-rate-rate) and data-generation methods (e.g., nonlinear orbit determination and geophysical inverse approach, energy conservation principle, etc) could also reflect relative inversion accuracy and the content of signal spectra in the resulting solution. In this contribution, we present results of a simulation experiment, which used various solution techniques and data types to attempt to quantify the relative advantage and disadvantage of each of the techniques.
The inverse problem for Schwinger pair production
Energy Technology Data Exchange (ETDEWEB)
Hebenstreit, F., E-mail: hebenstreit@itp.unibe.ch
2016-02-10
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.
An inverse problem for Schwinger pair production
Hebenstreit, Florian
2016-01-01
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.
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.
Hevesi, Joseph A.; Flint, Alan L.; Istok, Jonathan D.
1992-01-01
Values of average annual precipitation (AAP) may be important for hydrologic characterization of a potential high-level nuclear-waste repository site at Yucca Mountain, Nevada. Reliable measurements of AAP are sparse in the vicinity of Yucca Mountain, and estimates of AAP were needed for an isohyetal mapping over a 2600-square-mile watershed containing Yucca Mountain. Estimates were obtained with a multivariate geostatistical model developed using AAP and elevation data from a network of 42 precipitation stations in southern Nevada and southeastern California. An additional 1531 elevations were obtained to improve estimation accuracy. Isohyets representing estimates obtained using univariate geostatistics (kriging) defined a smooth and continuous surface. Isohyets representing estimates obtained using multivariate geostatistics (cokriging) defined an irregular surface that more accurately represented expected local orographic influences on AAP. Cokriging results included a maximum estimate within the study area of 335 mm at an elevation of 7400 ft, an average estimate of 157 mm for the study area, and an average estimate of 172 mm at eight locations in the vicinity of the potential repository site. Kriging estimates tended to be lower in comparison because the increased AAP expected for remote mountainous topography was not adequately represented by the available sample. Regression results between cokriging estimates and elevation were similar to regression results between measured AAP and elevation. The position of the cokriging 250-mm isohyet relative to the boundaries of pinyon pine and juniper woodlands provided indirect evidence of improved estimation accuracy because the cokriging result agreed well with investigations by others concerning the relationship between elevation, vegetation, and climate in the Great Basin. Calculated estimation variances were also mapped and compared to evaluate improvements in estimation accuracy. Cokriging estimation variances
Introduction to this Special Issue on Geostatistics and Scaling of Remote Sensing
Quattrochi, Dale A.
1999-01-01
The germination of this special PE&RS issue began at the Royal Geographical Society (with the Institute of British Geographers)(RCS-IBC) annual meeting in January, 1997 held at the University of Exeter in Exeter, England. The cold and snow of an England winter were greatly tempered by the friendly and cordial discussions that ensued at the meeting on possible ways to foster both dialog and research across "the Big Pond" between geographers in the US and the UK on the use of geostatistics and geospatial techniques for remote sensing of land surface processes. It was decided that one way to stimulate and enhance cooperation on the application of geostatistics and geospatial methods in remote sensing was to hold parallel sessions on these topics at appropriate meeting venues in 1998 in both the US and the UK Selected papers given at these sessions would be published as a special issue of PE&RS on the US side, and as a special issue of Computers and Geosciences (C&G) on the UK side, to highlight the commonality in research on geostatistics and geospatial methods in remote sensing and spatial data analysis on both sides of the Atlantic Ocean. As a consequence, a session on "Ceostatistics and Geospatial Techniques for Remote Sensing of Land Surface Processes" was held at the Association of American Geographers (AAG) annual meeting in Boston, Massachusetts in March, 1998, sponsored by the AAG's Remote Sensing Specialty Group (RSSG). A similar session was held at the RGS-IBG annual meeting in Guildford, Surrey, England in January 1998, organized by the Modeling and Advanced Techniques Special Interest Group (MAT SIG) of the Remote Sensing Society (RSS). The six papers that in part, comprise this issue of PE&RS, are the US complement to such a dual journal publication effort. Both of us are co-editors of each of the journal special issues, with the lead editor of each journal being from their respective side of the Atlantic where the journals are published. The special
Directory of Open Access Journals (Sweden)
Goovaerts Pierre
2005-12-01
Full Text Available Abstract Background Cancer mortality maps are used by public health officials to identify areas of excess and to guide surveillance and control activities. Quality of decision-making thus relies on an accurate quantification of risks from observed rates which can be very unreliable when computed from sparsely populated geographical units or recorded for minority populations. This paper presents a geostatistical methodology that accounts for spatially varying population sizes and spatial patterns in the processing of cancer mortality data. Simulation studies are conducted to compare the performances of Poisson kriging to a few simple smoothers (i.e. population-weighted estimators and empirical Bayes smoothers under different scenarios for the disease frequency, the population size, and the spatial pattern of risk. A public-domain executable with example datasets is provided. Results The analysis of age-adjusted mortality rates for breast and cervix cancers illustrated some key features of commonly used smoothing techniques. Because of the small weight assigned to the rate observed over the entity being smoothed (kernel weight, the population-weighted average leads to risk maps that show little variability. Other techniques assign larger and similar kernel weights but they use a different piece of auxiliary information in the prediction: global or local means for global or local empirical Bayes smoothers, and spatial combination of surrounding rates for the geostatistical estimator. Simulation studies indicated that Poisson kriging outperforms other approaches for most scenarios, with a clear benefit when the risk values are spatially correlated. Global empirical Bayes smoothers provide more accurate predictions under the least frequent scenario of spatially random risk. Conclusion The approach presented in this paper enables researchers to incorporate the pattern of spatial dependence of mortality rates into the mapping of risk values and the
Geostatistical Evaluation of Spring Water Quality in an Urbanizing Carbonate Aquifer
McGinty, A.; Welty, C.
2003-04-01
As part of an investigation of the impacts of urbanization on the hydrology and ecology of Valley Creek watershed near Philadelphia, Pennsylvania, we have analyzed the chemical composition of 110 springs to assess the relative influence of geology and anthropogenic activities on water quality. The 60 km^2 watershed is underlain by productive fractured rock aquifers composed of Cambrian and Ordovician carbonate rocks in the central valley and Cambrian crystalline and siliciclastic rocks (quartzite and phyllite) in the north and south hills that border the valley. All tributaries of the surface water system originate in the crystalline and siliciclastic hills. The watershed is covered by 17% impervious area and contains 6 major hazardous waste sites, one active quarrying operation and one golf course; 25% of the area utilizes septic systems for sewage disposal. We identified 172 springs, 110 of which had measurable flow rates ranging from 0.002 to 5 l/s. The mapped surficial geology appears as an anisotropic pattern, with long bands of rock formations paralleling the geographic orientation of the valley. Mapped development appears as a more isotropic pattern, characterized by isolated patches of land use that are not coincident with the evident geologic pattern. Superimposed upon these characteristics is a dense array of depressions and shallow sinkholes in the carbonate rocks, and a system of major faults at several formation contacts. We used indicator geostatistics to quantitatively characterize the spatial extent of the major geologic formations and patterns of land use. Maximum correlation scales for the rock types corresponded with strike direction and ranged from 1000 to 3000 m. Anisotropy ratios ranged from 2 to 4. Land-use correlation scales were generally smaller (200 to 500 m) with anisotropy ratios of around 1.2, i.e., nearly isotropic as predicted. Geostatistical analysis of spring water quality parameters related to geology (pH, specific conductance
Sharp spatially constrained inversion
DEFF Research Database (Denmark)
Vignoli, Giulio G.; Fiandaca, Gianluca G.; Christiansen, Anders Vest C A.V.C.;
2013-01-01
We present sharp reconstruction of multi-layer models using a spatially constrained inversion with minimum gradient support regularization. In particular, its application to airborne electromagnetic data is discussed. Airborne surveys produce extremely large datasets, traditionally inverted...... by using smoothly varying 1D models. Smoothness is a result of the regularization constraints applied to address the inversion ill-posedness. The standard Occam-type regularized multi-layer inversion produces results where boundaries between layers are smeared. The sharp regularization overcomes......, the results are compatible with the data and, at the same time, favor sharp transitions. The focusing strategy can also be used to constrain the 1D solutions laterally, guaranteeing that lateral sharp transitions are retrieved without losing resolution. By means of real and synthetic datasets, sharp...
Nonlinear and fault-tolerant flight control using multivariate splines
Tol, H.J.; De Visser, C.C.; Van Kampen, E.J.; Chu, Q.P.
2015-01-01
This paper presents a study on fault tolerant flight control of a high performance aircraft using multivariate splines. The controller is implemented by making use of spline model based adaptive nonlinear dynamic inversion (NDI). This method, indicated as SANDI, combines NDI control with nonlinear
Nonlinear and fault-tolerant flight control using multivariate splines
Tol, H.J.; De Visser, C.C.; Van Kampen, E.J.; Chu, Q.P.
2015-01-01
This paper presents a study on fault tolerant flight control of a high performance aircraft using multivariate splines. The controller is implemented by making use of spline model based adaptive nonlinear dynamic inversion (NDI). This method, indicated as SANDI, combines NDI control with nonlinear c
Seider, Warren D.; Ungar, Lyle H.
1987-01-01
Describes a course in nonlinear mathematics courses offered at the University of Pennsylvania which provides an opportunity for students to examine the complex solution spaces that chemical engineers encounter. Topics include modeling many chemical processes, especially those involving reaction and diffusion, auto catalytic reactions, phase…
'Inverse' temporomandibular joint dislocation.
Alemán Navas, R M; Martínez Mendoza, M G
2011-08-01
Temporomandibular joint (TMJ) dislocation can be classified into four groups (anterior, posterior, lateral, and superior) depending on the direction of displacement and the location of the condylar head. All the groups are rare except for anterior dislocation. 'Inverse' TMJ dislocation is a bilateral anterior and superior dislocation with impaction of the mandible over the maxilla; to the authors' knowledge only two cases have previously been reported in the literature. Inverse TMJ dislocation has unique clinical and radiographic findings, which are described for this case. Copyright © 2011 International Association of Oral and Maxillofacial Surgeons. Published by Elsevier Ltd. All rights reserved.
Application of Seismic Inversion Using Logging Data as Constraints in Coalfield
Institute of Scientific and Technical Information of China (English)
许永忠; 潘冬明; 张宝水; 崔若飞
2004-01-01
Seismic inversion and basic theory are briefly presented and the main idea of this method is introduced. Both non-linear wave equation inversion technique and Complete Utilization of Samples Information (CUSI) neural network analysis are used in lithological interpretation in Jibei coal field. The prediction results indicate that this method can provide reliable data for thin coal exploitation and promising area evaluation.
Approximating parameters in nonlinear reaction diffusion equations
Directory of Open Access Journals (Sweden)
Robert R. Ferdinand
2001-07-01
Full Text Available We present a model describing population dynamics in an environment. The model is a nonlinear, nonlocal, reaction diffusion equation with Neumann boundary conditions. An inverse method, involving minimization of a least-squares cost functional, is developed to identify unknown model parameters. Finally, numerical results are presented which display estimates of these parameters using computationally generated data.
Inverse problems and uncertainty quantification
Litvinenko, Alexander
2013-12-18
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. This is especially the case as 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 is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisa- tion 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 quadratic Bayesian update on the small but taxing example of the chaotic Lorenz 84 model, where we experiment with the influence of different observation or measurement operators on the update.
Inverse Problems and Uncertainty Quantification
Litvinenko, Alexander
2014-01-06
In a Bayesian setting, inverse problems and uncertainty quantification (UQ) - the propagation of uncertainty through a computational (forward) modelare strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. This is especially the case as 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 is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisa- tion 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 quadratic Bayesian update on the small but taxing example of the chaotic Lorenz 84 model, where we experiment with the influence of different observation or measurement operators on the update.
Prandtl-Ishlinskii hysteresis models for complex time dependent hysteresis nonlinearities
Al Janaideh, M.; Krejčí, P
2012-01-01
We introduce a new class of time dependent hysteresis models by combining the time dependent Prandtl–Ishlinskii model with functional nonlinearities. This combination improves the capability of the time dependent Prandtl–Ishlinskii model to characterize a class of complex time dependent hysteresis nonlinearities in smart actuators. The analytical inversion for the proposed time dependent hysteresis model is also presented in order to extend the inversion algorithm of the inverse time dependen...
Ibrahim, Elsy; Adam, Stefanie; De Wever, Aaike; Govaerts, Annelies; Vervoort, Andre; Monbaliu, Jaak
2014-08-01
To investigate bio-chemical processes of intertidal sediments, variations in sediment properties such as moisture content, mud content, and chlorophyll a content need to be understood. Remote sensing has been an efficient alternative to traditional data collection methods for such properties. Yet, with the availability of various types of useful sensors, choosing a suitable spatial resolution is challenging, especially that each type has its own cost, availability, and data specifications. This paper investigates the losses in spatial information of sediment properties on the Molenplaat, an intertidal flat on the Western-Scheldt estuary, upon the use of various resolutions. This was carried out using a synergy between remote sensing and geostatistics. The results showed that for the Molenplaat, chlorophyll a content can be well represented by low to medium resolutions. Yet, for moisture and mud content, spatial structures would be lost upon any decrease of resolution from a 4 m×4 m pixel size.
Erdin, R.; Frei, C.; Sideris, I.; Kuensch, H.-R.
2010-09-01
There is an increasing demand for accurate mapping of precipitation at a spatial resolution of kilometers. Radar and rain gauges - the two main precipitation measurement systems - exhibit complementary strengths and weaknesses. Radar offers high spatial and temporal resolution but lacks accuracy of absolute values, whereas rain gauges provide accurate values at their specific point location but suffer from poor spatial representativeness. Methods of geostatistical mapping have been proposed to combine radar and rain gauge data for quantitative precipitation estimation (QPE). The aim is to combine the respective strengths and compensate for the respective weaknesses of the two observation platforms. Several studies have demonstrated the potential of these methods over topography of moderate complexity, but their performance remains unclear for high-mountain regions where rainfall patterns are complex, the representativeness of rain gauge measurements is limited and radar observations are obstructed. In this study we examine the potential and limitations of two frequently used geostatistical mapping methods for the territory of Switzerland, where the mountain chain of the Alps poses particular challenges to QPE. The two geostatistical methods explored are kriging with external drift (KED) using radar as drift variable and ordinary kriging of radar errors (OKRE). The radar data is a composite from three C-band radars using a constant Z-R relationship, advanced correction processings for visibility, ground clutter and beam shielding and a climatological bias adjustment. The rain gauge data originates from an automatic network with a typical inter-station distance of 25 km. Both combination methods are applied to a set of case examples representing typical rainfall situations in the Alps with their inherent challenges at daily and hourly time resolution. The quality of precipitation estimates is assessed by several skill scores calculated from cross validation errors at
An assessment of gas emanation hazard using a geographic information system and geostatistics.
Astorri, F; Beaubien, S E; Ciotoli, G; Lombardi, S
2002-03-01
This paper describes the use of geostatistical analysis and GIS techniques to assess gas emanation hazards. The Mt. Vulsini volcanic district was selected for this study because of the wide range of natural phenomena locally present that affect gas migration in the near surface. In addition, soil gas samples that were collected in this area should allow for a calibration between the generated risk/hazard models and the measured distribution of toxic gas species at surface. The approach used during this study consisted of three general stages. First data were digitally organized into thematic layers, then software functions in the GIS program "ArcView" were used to compare and correlate these various layers, and then finally the produced "potential-risk" map was compared with radon soil gas data in order to validate the model and/or to select zones for further, more-detailed soil gas investigations.
Geostatistics as a validation tool for setting ozone standards for durum wheat.
De Marco, Alessandra; Screpanti, Augusto; Paoletti, Elena
2010-02-01
Which is the best standard for protecting plants from ozone? To answer this question, we must validate the standards by testing biological responses vs. ambient data in the field. A validation is missing for European and USA standards, because the networks for ozone, meteorology and plant responses are spatially independent. We proposed geostatistics as validation tool, and used durum wheat in central Italy as a test. The standards summarized ozone impact on yield better than hourly averages. Although USA criteria explained ozone-induced yield losses better than European criteria, USA legal level (75 ppb) protected only 39% of sites. European exposure-based standards protected > or =90%. Reducing the USA level to the Canadian 65 ppb or using W126 protected 91% and 97%, respectively. For a no-threshold accumulated stomatal flux, 22 mmol m(-2) was suggested to protect 97% of sites. In a multiple regression, precipitation explained 22% and ozone explained <0.9% of yield variability.
Zhang, Rong; Leng, Yun-fa; Zhu, Meng-meng; Wang, Fang
2007-11-01
Based on geographic information system and geostatistics, the spatial structure of Therioaphis trifolii population of different periods in Yuanzhou district of Guyuan City, the southern Ningxia Province, was analyzed. The spatial distribution of Therioaphis trifolii population was also simulated by ordinary Kriging interpretation. The results showed that Therioaphis trifolii population of different periods was correlated spatially in the study area. The semivariograms of Therioaphis trifolii could be described by exponential model, indicating an aggregated spatial arrangement. The spatial variance varied from 34.13%-48.77%, and the range varied from 8.751-12.049 km. The degree and direction of aggregation showed that the trend was increased gradually from southwest to northeast. The dynamic change of Therioaphis trifolii population in different periods could be analyzed intuitively on the simulated maps of the spatial distribution from the two aspects of time and space, The occurrence position and degree of Therioaphis trifolii to a state of certain time could be determined easily.
Komnitsas, Kostas; Modis, Kostas
2006-12-01
The present paper aims to map As and Zn contamination and assess the risk for agricultural soils in a wider disposal site containing wastes derived from coal beneficiation. Geochemical data related to environmental studies show that the waste characteristics favor solubilisation and mobilization of inorganic contaminants and in some cases the generation of acidic leachates. 135 soil samples were collected from a 34 km(2) area and analysed by using geostatistics under the maximum entropy principle in order to produce risk assessment maps and estimate the probability of soil contamination. In addition, the present paper discusses the main issues related to risk assessment in wider mining and waste disposal sites in order to assist decision makers in selecting feasible rehabilitation schemes.
Xie, Zheng-miao; Li, Jing; Wang, Bi-ling; Chen, Jian-jun
2006-10-01
Contents of heavy metals (Pb, Zn, Cd, Cu) in soils and vegetables from Dongguan town in Shangyu city, China were studied using geostatistical analysis and GIS technique to evaluate environmental quality. Based on the evaluation criteria, the distribution of the spatial variability of heavy metals in soil-vegetable system was mapped and analyzed. The results showed that the distribution of soil heavy metals in a large number of soil samples in Dongguan town was asymmetric. The contents of Zn and Cu were lower than those of Cd and Pb. The concentrations distribution of Pb, Zn, Cd and Cu in soils and vegetables were different in spatial variability. There was a close relationship between total and available contents of heavy metals in soil. The contents of Pb and Cd in green vegetables were higher than those of Zn and Cu and exceeded the national sanitation standards for vegetables.
Supervised restoration of degraded medical images using multiple-point geostatistics.
Pham, Tuan D
2012-06-01
Reducing noise in medical images has been an important issue of research and development for medical diagnosis, patient treatment, and validation of biomedical hypotheses. Noise inherently exists in medical and biological images due to the acquisition and transmission in any imaging devices. Being different from image enhancement, the purpose of image restoration is the process of removing noise from a degraded image in order to recover as much as possible its original version. This paper presents a statistically supervised approach for medical image restoration using the concept of multiple-point geostatistics. Experimental results have shown the effectiveness of the proposed technique which has potential as a new methodology for medical and biological image processing.
The Importance of the Range Parameter for Estimation and Prediction in Geostatistics
Kaufman, Cari
2011-01-01
Two canonical problems in geostatistics are estimating the parameters in a specified family of stochastic process models and predicting the process at new locations. A number of asymptotic results for these problems over a fixed spatial domain indicate that, for a Gaussian process with Mat\\'ern covariance function, one can fix the range parameter controlling the rate of decay of the process and obtain results that are asymptotically equivalent to the case that the range parameter is known. We discuss why these results do not always provide the appropriate intuition for finite samples. Moreover, we prove that a number of these asymptotic results may be extended to the case that the variance and range parameters are jointly estimated via maximum likelihood or maximum tapered likelihood. Our simulation results show that performance on a variety of metrics is improved and asymptotic approximations are applicable for smaller sample sizes when the range parameter is estimated. These effects are particularly apparen...
Hanks, Ephraim M.; Schliep, Erin M.; Hooten, Mevin B.; Hoeting, Jennifer A.
2015-01-01
In spatial generalized linear mixed models (SGLMMs), covariates that are spatially smooth are often collinear with spatially smooth random effects. This phenomenon is known as spatial confounding and has been studied primarily in the case where the spatial support of the process being studied is discrete (e.g., areal spatial data). In this case, the most common approach suggested is restricted spatial regression (RSR) in which the spatial random effects are constrained to be orthogonal to the fixed effects. We consider spatial confounding and RSR in the geostatistical (continuous spatial support) setting. We show that RSR provides computational benefits relative to the confounded SGLMM, but that Bayesian credible intervals under RSR can be inappropriately narrow under model misspecification. We propose a posterior predictive approach to alleviating this potential problem and discuss the appropriateness of RSR in a variety of situations. We illustrate RSR and SGLMM approaches through simulation studies and an analysis of malaria frequencies in The Gambia, Africa.
Xia, Peng-Liang; Wang, Rui; Tan, Jun
2014-03-01
Tobacco budworm (Helicoverpa assulta) larvae feed on tobacco leaves (Nicotiana sp.), resulting in significant loss in tobacco production. Geostatistical method was used to analyze H. assulta spatial patterns and dynamics in this paper. The results showed that, H. assulta larvae appeared 40 days after the tobacco plants transplanting, and reached its peak at the early-mature period. The nested spherical and exponential model was the major model for tobacco budworm larva in the field, suggesting its aggregated distribution. The spatial variability C/(C0 + C) was larger than 0.75, which indicated H. assulta larva had wider structural variation and narrower random variation. There was a massive migration of tobacco budworm larva in the fast-growing stage of tobacco. Its quantity became stable after that, especially at the mature stage of tobacco.
Geostatistical stability analysis of co-depositional sand-thickened tailings embankments
Energy Technology Data Exchange (ETDEWEB)
Elkateb, T. [Thurber Engineering Ltd., Edmonton, AB (Canada); Chalaturnyk, R.; Robertson, P.K. [Alberta Univ., Edmonton, AB (Canada). Dept. of Civil and Environmental Engineering
2003-07-01
Co-deposition is a novel technique for the disposal of thickened tailings pockets. In co-deposition, tailings are randomly distributed within a bigger mass of sand. The oil sands industry of Alberta is currently considering using this technique. This paper describes the attempt that was made to assess the engineering behaviour of this tailing disposal system in a probabilistic analysis framework. Several realizations of co-depositional embankments were generated using geostatistical theories. In turn, the stability of the disposal system expressed in terms of factors of safety against shear failure and the associated vertical deformations was assessed using these realizations and FLAC software. A sensitivity to embankment characteristics was revealed by failure probabilities and vertical displacements, such as embankment height and side slopes, and undrained shear strength of thickened tailings. The authors proposed an allowable failure probability of 17 per cent for these embankments to avoid irreparable excessive deformations. 11 refs., 1 tab., 8 figs.
Szatmári, Gábor; Laborczi, Annamária; Takács, Katalin; Pásztor, László
2017-04-01
The knowledge about soil organic carbon (SOC) baselines and changes, and the detection of vulnerable hot spots for SOC losses and gains under climate change and changed land management is still fairly limited. Thus Global Soil Partnership (GSP) has been requested to develop a global SOC mapping campaign by 2017. GSPs concept builds on official national data sets, therefore, a bottom-up (country-driven) approach is pursued. The elaborated Hungarian methodology suits the general specifications of GSOC17 provided by GSP. The input data for GSOC17@HU mapping approach has involved legacy soil data bases, as well as proper environmental covariates related to the main soil forming factors, such as climate, organisms, relief and parent material. Nowadays, digital soil mapping (DSM) highly relies on the assumption that soil properties of interest can be modelled as a sum of a deterministic and stochastic component, which can be treated and modelled separately. We also adopted this assumption in our methodology. In practice, multiple regression techniques are commonly used to model the deterministic part. However, this global (and usually linear) models commonly oversimplify the often complex and non-linear relationship, which has a crucial effect on the resulted soil maps. Thus, we integrated machine learning algorithms (namely random forest and quantile regression forest) in the elaborated methodology, supposing then to be more suitable for the problem in hand. This approach has enable us to model the GSOC17 soil properties in that complex and non-linear forms as the soil itself. Furthermore, it has enable us to model and assess the uncertainty of the results, which is highly relevant in decision making. The applied methodology has used geostatistical approach to model the stochastic part of the spatial variability of the soil properties of interest. We created GSOC17@HU map with 1 km grid resolution according to the GSPs specifications. The map contributes to the GSPs
Generalized Variational Principle for Long Water-Wave Equation by He's Semi-Inverse Method
Directory of Open Access Journals (Sweden)
Weimin Zhang
2009-01-01
Full Text Available Variational principles for nonlinear partial differential equations have come to play an important role in mathematics and physics. However, it is well known that not every nonlinear partial differential equation admits a variational formula. In this paper, He's semi-inverse method is used to construct a family of variational principles for the long water-wave problem.
Han, Xujun; Li, Xin; Rigon, Riccardo; Jin, Rui; Endrizzi, Stefano
2015-01-01
The observation could be used to reduce the model uncertainties with data assimilation. If the observation cannot cover the whole model area due to spatial availability or instrument ability, how to do data assimilation at locations not covered by observation? Two commonly used strategies were firstly described: One is covariance localization (CL); the other is observation localization (OL). Compared with CL, OL is easy to parallelize and more efficient for large-scale analysis. This paper evaluated OL in soil moisture profile characterizations, in which the geostatistical semivariogram was used to fit the spatial correlated characteristics of synthetic L-Band microwave brightness temperature measurement. The fitted semivariogram model and the local ensemble transform Kalman filter algorithm are combined together to weight and assimilate the observations within a local region surrounding the grid cell of land surface model to be analyzed. Six scenarios were compared: 1_Obs with one nearest observation assimilated, 5_Obs with no more than five nearest local observations assimilated, and 9_Obs with no more than nine nearest local observations assimilated. The scenarios with no more than 16, 25, and 36 local observations were also compared. From the results we can conclude that more local observations involved in assimilation will improve estimations with an upper bound of 9 observations in this case. This study demonstrates the potentials of geostatistical correlation representation in OL to improve data assimilation of catchment scale soil moisture using synthetic L-band microwave brightness temperature, which cannot cover the study area fully in space due to vegetation effects.
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.
Geostatistical regionalization of low-flow indices: PSBI and Top-Kriging
Directory of Open Access Journals (Sweden)
S. Castiglioni
2010-09-01
Full Text Available Recent studies highlight that geostatistical interpolation, which has been originally developed for the spatial interpolation of point data, can be effectively applied to the problem of regionalization of hydrometric information. This study compares two innovative geostatistical approaches for the prediction of low-flows in ungauged basins. The first one, named Physiographic-Space Based Interpolation (PSBI, performs the spatial interpolation of the desired streamflow index (e.g., annual streamflow, low-flow index, flood quantile, etc. in the space of catchment descriptors. The second technique, named Topological kriging or Top-Kriging, predicts the variable of interest along river networks taking both the area and nested nature of catchments into account. PSBI and Top-Kriging are applied for the regionalization of Q_{355} (i.e., the streamflow that is equalled or exceeded 355 days in a year, on average over a broad geographical region in central Italy, which contains 51 gauged catchments. Both techniques are cross-validated through a leave-one-out procedure at all available gauges and applied to a subregion to produce a continuous estimation of Q_{355} along the river network extracted from a 90 m DEM. The results of the study show that Top-Kriging and PSBI present complementary features and have comparable performances (Nash-Sutcliffe efficiencies in cross-validation of 0.89 and 0.83, respectively. Both techniques provide plausible and accurate predictions of Q_{355} in ungauged basins and represent promising opportunities for regionalization of low-flows.
Geostatistical three-dimensional modeling of oolite shoals, St. Louis Limestone, southwest Kansas
Qi, L.; Carr, T.R.; Goldstein, R.H.
2007-01-01
In the Hugoton embayment of southwestern Kansas, reservoirs composed of relatively thin (oil. The geometry and distribution of oolitic deposits control the heterogeneity of the reservoirs, resulting in exploration challenges and relatively low recovery. Geostatistical three-dimensional (3-D) models were constructed to quantify the geometry and spatial distribution of oolitic reservoirs, and the continuity of flow units within Big Bow and Sand Arroyo Creek fields. Lithofacies in uncored wells were predicted from digital logs using a neural network. The tilting effect from the Laramide orogeny was removed to construct restored structural surfaces at the time of deposition. Well data and structural maps were integrated to build 3-D models of oolitic reservoirs using stochastic simulations with geometry data. Three-dimensional models provide insights into the distribution, the external and internal geometry of oolitic deposits, and the sedimentologic processes that generated reservoir intervals. The structural highs and general structural trend had a significant impact on the distribution and orientation of the oolitic complexes. The depositional pattern and connectivity analysis suggest an overall aggradation of shallow-marine deposits during pulses of relative sea level rise followed by deepening near the top of the St. Louis Limestone. Cemented oolitic deposits were modeled as barriers and baffles and tend to concentrate at the edge of oolitic complexes. Spatial distribution of porous oolitic deposits controls the internal geometry of rock properties. Integrated geostatistical modeling methods can be applicable to other complex carbonate or siliciclastic reservoirs in shallow-marine settings. Copyright ?? 2007. The American Association of Petroleum Geologists. All rights reserved.
Geostatistical prediction of flow-duration curves in an index-flow framework
Pugliese, A.; Castellarin, A.; Brath, A.
2014-09-01
An empirical period-of-record flow-duration curve (FDC) describes the percentage of time (duration) in which a given streamflow was equaled or exceeded over an historical period of time. In many practical applications one has to construct FDCs in basins that are ungauged or where very few observations are available. We present an application strategy of top-kriging, which makes the geostatistical procedure capable of predicting FDCs in ungauged catchments. Previous applications of top-kriging mainly focused on the prediction of point streamflow indices (e.g. flood quantiles, low-flow indices, etc.); here the procedure is used to predict the entire curve in ungauged sites as a weighted average of standardised empirical FDCs through the traditional linear-weighting scheme of kriging methods. In particular, we propose to standardise empirical FDCs by a reference index-flow value (i.e. mean annual flow, or mean annual precipitation × the drainage area) and to compute the overall negative deviation of the curves from this reference value. We then propose to use these values, which we term total negative deviation (TND), for expressing the hydrological similarity between catchments and for deriving the geostatistical weights. We focus on the prediction of FDCs for 18 unregulated catchments located in central Italy, and we quantify the accuracy of the proposed technique under various operational conditions through an extensive cross-validation and sensitivity analysis. The cross-validation points out that top-kriging is a reliable approach for predicting FDCs with Nash-Sutcliffe efficiency measures ranging from 0.85 to 0.96 (depending on the model settings) very low biases over the entire duration range, and an enhanced representation of the low-flow regime relative to other regionalisation models that were recently developed for the same study region.
Broekhuis, H.
2005-01-01
This article aims at reformulating in more current terms Hoekstra and Mulder’s (1990) analysis of the Locative Inversion (LI) construction. The new proposal is crucially based on the assumption that Small Clause (SC) predicates agree with their external argument in phi-features, which may be morphol
Bayesian seismic AVO inversion
Energy Technology Data Exchange (ETDEWEB)
Buland, Arild
2002-07-01
A new linearized AVO inversion technique is developed in a Bayesian framework. The objective is to obtain posterior distributions for P-wave velocity, S-wave velocity and density. Distributions for other elastic parameters can also be assessed, for example acoustic impedance, shear impedance and P-wave to S-wave velocity ratio. The inversion algorithm is based on the convolutional model and a linearized weak contrast approximation of the Zoeppritz equation. The solution is represented by a Gaussian posterior distribution with explicit expressions for the posterior expectation and covariance, hence exact prediction intervals for the inverted parameters can be computed under the specified model. The explicit analytical form of the posterior distribution provides a computationally fast inversion method. Tests on synthetic data show that all inverted parameters were almost perfectly retrieved when the noise approached zero. With realistic noise levels, acoustic impedance was the best determined parameter, while the inversion provided practically no information about the density. The inversion algorithm has also been tested on a real 3-D dataset from the Sleipner Field. The results show good agreement with well logs but the uncertainty is high. The stochastic model includes uncertainties of both the elastic parameters, the wavelet and the seismic and well log data. The posterior distribution is explored by Markov chain Monte Carlo simulation using the Gibbs sampler algorithm. The inversion algorithm has been tested on a seismic line from the Heidrun Field with two wells located on the line. The uncertainty of the estimated wavelet is low. In the Heidrun examples the effect of including uncertainty of the wavelet and the noise level was marginal with respect to the AVO inversion results. We have developed a 3-D linearized AVO inversion method with spatially coupled model parameters where the objective is to obtain posterior distributions for P-wave velocity, S
Calculation of the inverse data space via sparse inversion
Saragiotis, Christos
2011-01-01
The inverse data space provides a natural separation of primaries and surface-related multiples, as the surface multiples map onto the area around the origin while the primaries map elsewhere. However, the calculation of the inverse data is far from trivial as theory requires infinite time and offset recording. Furthermore regularization issues arise during inversion. We perform the inversion by minimizing the least-squares norm of the misfit function by constraining the $ell_1$ norm of the solution, being the inverse data space. In this way a sparse inversion approach is obtained. We show results on field data with an application to surface multiple removal.
Directory of Open Access Journals (Sweden)
M. Fischer
2011-07-01
Full Text Available Robust estimates of regional-scale terrestrial CO2 exchange are needed to support carbon management policies and to improve the predictive ability of models representing carbon-climate feedbacks. Large discrepancies remain, however, both among and between CO2 flux estimates from atmospheric inverse models and terrestrial biosphere models. Improved atmospheric inverse models that provide robust estimates at sufficiently fine spatial scales could prove especially useful for monitoring efforts, while also serving as a validation tool for process-based assumptions in terrestrial biosphere models. A growing network of continental sites collecting continuous CO2 measurements provides the information needed to drive such models. This study presents results from a regional geostatistical inversion over North America for 2004, taking advantage of continuous data from the nine sites operational in that year, as well as available flask and aircraft observations. The approach does not require explicit prior flux estimates, resolves fluxes at finer spatiotemporal scales than previous North American inversion studies, and uses a Lagrangian transport model coupled with high-resolution winds (i.e. WRF-STILT to resolve near-field influences around measurement locations. The estimated fluxes are used in an inter-comparison with other inversion studies and a suite of terrestrial biosphere model estimates collected through the North American Carbon Program Regional and Continental Interim Synthesis. Differences among inversions are found to be smallest in areas of the continent best-constrained by the atmospheric data, pointing to the value of an expanded measurement network. Aggregation errors in previous coarser-scale inversion studies are likely to explain a portion of the remaining spread. The spatial patterns from a geostatistical inversion that includes auxiliary environmental variables from the North American Regional Reanalysis were similar to those from
Nonlinear System Control Using Neural Networks
Directory of Open Access Journals (Sweden)
Jaroslava Žilková
2006-10-01
Full Text Available The paper is focused especially on presenting possibilities of applying off-linetrained artificial neural networks at creating the system inverse models that are used atdesigning control algorithm for non-linear dynamic system. The ability of cascadefeedforward neural networks to model arbitrary non-linear functions and their inverses isexploited. This paper presents a quasi-inverse neural model, which works as a speedcontroller of an induction motor. The neural speed controller consists of two cascadefeedforward neural networks subsystems. The first subsystem provides desired statorcurrent components for control algorithm and the second subsystem providescorresponding voltage components for PWM converter. The availability of the proposedcontroller is verified through the MATLAB simulation. The effectiveness of the controller isdemonstrated for different operating conditions of the drive system.
Energy Technology Data Exchange (ETDEWEB)
Shin, Chang Soo; Park, Keun Pil [Korea Inst. of Geology Mining and Materials, Taejon (Korea, Republic of); Suh, Jung Hee; Hyun, Byung Koo; Shin, Sung Ryul [Seoul National University, Seoul (Korea, Republic of)
1995-12-01
The seismic reflection exploration technique which is one of the geophysical methods for oil exploration became effectively to image the subsurface structure with rapid development of computer. However, the imagining of subsurface based on the conventional data processing is almost impossible to obtain the information on physical properties of the subsurface such as velocity and density. Since seismic data are implicitly function of velocities of subsurface, it is necessary to develop the inversion method that can delineate the velocity structure using seismic topography and waveform inversion. As a tool to perform seismic inversion, seismic forward modeling program using ray tracing should be developed. In this study, we have developed the algorithm that calculate the travel time of the complex geologic structure using shooting ray tracing by subdividing the geologic model into blocky structure having the constant velocity. With the travel time calculation, the partial derivatives of travel time can be calculated efficiently without difficulties. Since the current ray tracing technique has a limitation to calculate the travel times for extremely complex geologic model, our aim in the future is to develop the powerful ray tracer using the finite element technique. After applying the pseudo waveform inversion to the seismic data of Korea offshore, we can obtain the subsurface velocity model and use the result in bring up the quality of the seismic data processing. If conventional seismic data processing and seismic interpretation are linked with this inversion technique, the high quality of seismic data processing can be expected to image the structure of the subsurface. Future research area is to develop the powerful ray tracer of ray tracing which can calculate the travel times for the extremely complex geologic model. (author). 39 refs., 32 figs., 2 tabs.
2015-01-01
From the Back Cover: The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications re...
Preconditioning Strategies in Elastic Full Waveform Inversion.
Matharu, G.; Sacchi, M. D.
2016-12-01
Elastic full waveform inversion (FWI) is inherently more non-linear than its acoustic counterpart, a property that stems from the increased model space of the problem. Whereas acoustic media can be parametrized by density and P-wave velocity, visco-elastic media are parametrized by density, attenuation and 21 independent coefficients of the elastic tensor. Imposing assumptions of isotropy and perfect elasticity to simplify the physics, reduces the number of independent parameters required to characterize a medium. Isotropic, elastic media can be parametrized in terms of density and the Lamé parameters. The different parameters can exhibit trade-off that manifest as attributes in the data. In the context of FWI, this means that certain parameters cannot be uniquely resolved. An ideal model update in full waveform inversion is equivalent to a Newton step. Explicit computation of the Hessian and its inverse is not computationally feasible in elastic FWI. The inverse Hessian scales the gradients to account for trade-off between parameters as well as compensating for inadequate illumination related to source-receiver coverage. Gradient preconditioners can be applied to mimic the action of the inverse Hessian and partially correct for inaccuracies in the gradient. In this study, we investigate the effects of model reparametrization by recasting a regularized form of the least-squares waveform misfit into a preconditioned formulation. New model parameters are obtained by applying invertible weighting matrices to the model vector. The weighting matrices are related to estimates of the prior model covariance matrix and incorporate information about spatially variant correlations of model parameters as well as correlations between independent parameters. We compare the convergence of conventional FWI to FWI after model reparametrization.
Geostatistics and Its Application in Geological Engineering%地质统计学及其在地质工程中的应用分析
Institute of Scientific and Technical Information of China (English)
常维
2011-01-01
随着科技日益发展,地质统计学在地质工程中也发挥着重要的作用,这就对地质统计提出了更高的要求.本文从地质统计方法入手,简要阐述了地质统计学发展的现状,并分析了统计方法在地质工程中的重要作用及其应用.%With the development of science and technology, geostatistics plays an important role in geological engineering, which puts forward higher demand for geostatistics. Starting from geostatistics, this article illustrates the status quo of geostatistics development, and analyzes the important role of statistical methods and its applications in the geological engineering.
Interpolation of steady-state concentration data by inverse modeling.
Schwede, Ronnie L; Cirpka, Olaf A
2010-01-01
In most groundwater applications, measurements of concentration are limited in number and sparsely distributed within the domain of interest. Therefore, interpolation techniques are needed to obtain most likely values of concentration at locations where no measurements are available. For further processing, for example, in environmental risk analysis, interpolated values should be given with uncertainty bounds, so that a geostatistical framework is preferable. Linear interpolation of steady-state concentration measurements is problematic because the dependence of concentration on the primary uncertain material property, the hydraulic conductivity field, is highly nonlinear, suggesting that the statistical interrelationship between concentration values at different points is also nonlinear. We suggest interpolating steady-state concentration measurements by conditioning an ensemble of the underlying log-conductivity field on the available hydrological data in a conditional Monte Carlo approach. Flow and transport simulations for each conditional conductivity field must meet the measurements within their given uncertainty. The ensemble of transport simulations based on the conditional log-conductivity fields yields conditional statistical distributions of concentration at points between observation points. This method implicitly meets physical bounds of concentration values and non-Gaussianity of their statistical distributions and obeys the nonlinearity of the underlying processes. We validate our method by artificial test cases and compare the results to kriging estimates assuming different conditional statistical distributions of concentration. Assuming a beta distribution in kriging leads to estimates of concentration with zero probability of concentrations below zero or above the maximal possible value; however, the concentrations are not forced to meet the advection-dispersion equation.
Dynamic data integration and stochastic inversion of a confined aquifer
Wang, D.; Zhang, Y.; Irsa, J.; Huang, H.; Wang, L.
2013-12-01
Much work has been done in developing and applying inverse methods to aquifer modeling. The scope of this paper is to investigate the applicability of a new direct method for large inversion problems and to incorporate uncertainty measures in the inversion outcomes (Wang et al., 2013). The problem considered is a two-dimensional inverse model (50×50 grid) of steady-state flow for a heterogeneous ground truth model (500×500 grid) with two hydrofacies. From the ground truth model, decreasing number of wells (12, 6, 3) were sampled for facies types, based on which experimental indicator histograms and directional variograms were computed. These parameters and models were used by Sequential Indicator Simulation to generate 100 realizations of hydrofacies patterns in a 100×100 (geostatistical) grid, which were conditioned to the facies measurements at wells. These realizations were smoothed with Simulated Annealing, coarsened to the 50×50 inverse grid, before they were conditioned with the direct method to the dynamic data, i.e., observed heads and groundwater fluxes at the same sampled wells. A set of realizations of estimated hydraulic conductivities (Ks), flow fields, and boundary conditions were created, which centered on the 'true' solutions from solving the ground truth model. Both hydrofacies conductivities were computed with an estimation accuracy of ×10% (12 wells), ×20% (6 wells), ×35% (3 wells) of the true values. For boundary condition estimation, the accuracy was within × 15% (12 wells), 30% (6 wells), and 50% (3 wells) of the true values. The inversion system of equations was solved with LSQR (Paige et al, 1982), for which coordinate transform and matrix scaling preprocessor were used to improve the condition number (CN) of the coefficient matrix. However, when the inverse grid was refined to 100×100, Gaussian Noise Perturbation was used to limit the growth of the CN before the matrix solve. To scale the inverse problem up (i.e., without smoothing
Wave-equation reflection traveltime inversion
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.
Review of the Study of Nonlinear Atmospheric Dynamics in China (1999-2002)
Institute of Scientific and Technical Information of China (English)
刁一娜; 封国林; 刘式达; 刘式适; 罗德海; 黄思训; 陆维松; 丑纪范
2004-01-01
Researches on nonlinear atmospheric dynamics in China (1999-2002) are briefly surveyed. This review includes the major achievements in the following branches of nonlinear dynamics: nonlinear stability theory,nonlinear blocking dynamics, 3D spiral structure in the atmosphere, traveling wave solution of the nonlinear evolution equation, numerical predictability in a chaotic system, and global analysis of climate dynamics.Some applications of nonlinear methods such as hierarchy structure of climate and scaling invariance, the spatial-temporal series predictive method, the nonlinear inverse problem, and a new difference scheme with multi-time levels are also introduced.
Himpe, Christian; Ohlberger, Mario
2014-01-01
Bayesian inversion of models with large state and parameter spaces proves to be computationally complex. A combined state and parameter reduction can significantly decrease the computational time and cost required for the parameter estimation. The presented technique is based on the well-known balanced truncation approach. Classically, the balancing of the controllability and observability gramians allows a truncation of discardable states. Here the underlying model, being a linear or nonline...
Martinez-Camara, Marta; Dokmanic, Ivan; Ranieri, Juri; Scheibler, Robin; Vetterli, Martin; STOHL Andreas
2013-01-01
Knowing what amount of radioactive material was released from Fukushima in March 2011 and at what time instants is crucial to assess the risk, the pollution, and to understand the scope of the consequences. Moreover, it could be used in forward simulations to obtain accurate maps of deposition. But these data are often not publicly available. We propose to estimate the emission waveforms by solving an inverse problem. Previous approaches have relied on a detailed expert guess of how the relea...
DEFF Research Database (Denmark)
Fakhreddine, Sarah; Lee, Jonghyun; Kitanidis, Peter K.
2016-01-01
-bearing reactive minerals as aquifer contaminants. We use synthetic applications to demonstrate the ability of inverse modeling techniques combined with mechanistic reactive transport models to image reactive mineral lenses in the subsurface and quantify estimation error using indirect, commonly measured...... such as managed aquifer recharge and recovery operations. The modeling investigation is carried out at various scales and considers different flow-through domains including (i) a ID lab-scale column (SO cm), (ii) a 2D lab-scale setup (60 cm x 30 cm) and (iii) a 2D field scale domain (20 nix 4 m). In these setups......, synthetic dissolved oxygen data and forward reactive transport simulations are used to image the spatial distribution of As-bearing pyrite using the Principal Component Geostatistical Approach (PCGA) for inverse modeling. (C) 2015 Elsevier Ltd. All rights reserved....
[Total inversion of the uterus].
Novachkov, V; Baltadzhieva, B; Ilieva, A; Rachev, E
2008-01-01
Non puerperal inversion of the uterus is very uncommon. Patients may present with pelvic pain, vaginal bleeding or hemodynamic shock. We report a fifty five old woman with uterus inversion second stage.
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.
Institute of Scientific and Technical Information of China (English)
ZHANG Jingxiong; LI Deren
2005-01-01
This paper seeks a synthesis of Bayesian and geostatistical approaches to combining categorical data in the context of remote sensing classification.By experiment with aerial photographs and Landsat TM data, accuracy of spectral, spatial, and combined classification results was evaluated.It was confirmed that the incorporation of spatial information in spectral classification increases accuracy significantly.Secondly, through test with a 5-class and a 3-class classification schemes, it was revealed that setting a proper semantic framework for classification is fundamental to any endeavors of categorical mapping and the most important factor affecting accuracy.Lastly, this paper promotes non-parametric methods for both definition of class membership profiling based on band-specific histograms of image intensities and derivation of spatial probability via indicator kriging, a non-parametric geostatistical technique.
Carter, Gail P; Miskewitz, Robert J; Isukapalli, Sastry; Mun, Yuri; Vyas, Vikram; Yoon, Sungwon; Georgeopoulos, Panos; Uchrin, Christopher G
2011-01-01
Groundwater is a major water source in New Jersey; hence, accurate hydrogeologic data are extremely important. However, most measured data have inadequate spatial density and their locations are often clustered. Our study focuses on implementing geostatistical methods to generate the spatial distribution of specific capacity over the Newark Basin in New Jersey. Two geostatistical methods, ordinary kriging and cokriging, were employed and compared. Ordinary kriging was employed to estimate the spatial distribution of specific capacity by using measured values. Cokriging incorporated the spatial variability of fracture density into the estimation with the spatial variability of specific capacity, as groundwater flow in fractured rock aquifers depends on the fracture characteristics in the Newark Basin. Results indicate that cokriging manifested substantial improvements over ordinary kriging including a larger areal coverage, a more detailed variation of specific capacity, and reduction in the variance of its estimates.
Frequency-domain waveform inversion using the unwrapped phase
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.
Hansen, P. J.; Lonngren, K. E.
1993-01-01
A heuristic estimate for the soliton production rate by a pulse is verified for the Korteweg - de Vries equation using inverse scattering. An observation from this result, which is shown to hold for some other nonlinear equations and for the case of the 'forced' nonlinear Schroedinger equation, is that production is determined by quantities that are invariant under rescaling of the original nonlinear equations. We speculate that this result may be useful to the development of an inverse scattering theory for 'forced' nonlinear systems.
Diaz-Lacava, A. N.; Walier, M; D. Holler; Steffens, M; Gieger, C; C. Furlanello; Lamina, C; Wichmann, H E; Becker, T
2015-01-01
Aiming to investigate fine-scale patterns of genetic heterogeneity in modern humans from a geographic perspective, a genetic geostatistical approach framed within a geographic information system is presented. A sample collected for prospective studies in a small area of southern Germany was analyzed. None indication of genetic heterogeneity was detected in previous analysis. Socio-demographic and genotypic data of German citizens were analyzed (212 SNPs; n = 728). Genetic heterogeneity was ev...
[Application of inverse distance weighted interpolation method in contaminated site assessment].
Yang, Wen-Rui; Wang, Ru-Song; Huang, Jin-Lou; Chen, Zhan; Li, Feng
2007-09-01
There are many difficulties in ascertaining the area that needs to be remedied in contaminated site. This paper integrated the experts' judgments with grids as the sampling strategy in an abandoned pesticide plant in northern China, and applied a geostatistical method, inverse distance weighted interpolation (IDW), to simulate the pollutants- and risk spatial distribution. Based on soil environmental benchmark, two scenarios were designed for ascertaining the polluted area. The results showed that the area needed to be remedied and determined by IDW was somewhat larger, according to the national environmental 2nd standard for agricultural soils, but the area and cost needed for remedy were smaller and more economic and reasonable, based on the health risk threshold level and IDW method. A combination of IDW and health risk assessment in ascertaining polluted area would be a new way for site assessment and soil remediation in the future.
Joint Inversion of Hydrological and Geophysical Data for Enhanced Reservoir Characterization
Commer, M.; Finsterle, S.; Zhang, Y.; Hoversten, G. M.
2015-12-01
We present two hydrogeophysical joint inver sion studies that target the enhanced prediction of fluid saturations in CO2-induced enhanced oil recovery (EOR) operations as well as sequestration. Considered are two geophysical data types. The first study involves the combination of production data with time-domain electromagnetic (TEM) data. The second combines production with seismic amplitude-versus-angle (AVA) data. The pilot point method combined with geostatistical simulation is used to generate a spatially correlated, heterogeneous permeability field that is flexibly adjustable during the joint inversion process. Both geophysical data types promise an improved prediction of the CO2-saturation, indicating potential benefits in both EOR as well as CO2-sequestration monitoring operations.
Inverse Problems in Geosciences: Modelling the Rock Properties of an Oil Reservoir
DEFF Research Database (Denmark)
Lange, Katrine
the probability that a model adhere to prior knowledge by having specific multiple-point statistics, for instance, learned from a training image. Existing methods efficiently sample an a priori probability density function to create a set of acceptable models; but they cannot evaluate the probability of a model......Even the most optimistic forecasts predict that Danish oil production will decrease by 80% in the period between 2006 and 2040, and only a strong innovative technological effort can change that. Due to the geological structures of the subsurface in the Danish part of the North Sea, Denmark...... 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...
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.
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...
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; Caroline Looms, Majken
2013-01-01
for solving such probabilistically formulated inverse problems by sampling the a posteriori probability density function. In order to describe the a priori probability density function, we consider both simple Gaussian models and more complex (and realistic) a priori models based on higher order statistics....... These a priori models can be used with both linear and non-linear inverse problems. For linear inverse Gaussian problems we make use of least-squares and kriging-based methods to describe the a posteriori probability density function directly. For general non-linear (i.e. non-Gaussian) inverse problems, we make...... use of the extended Metropolis algorithm to sample the a posteriori probability density function. Together with the extended Metropolis algorithm, we use sequential Gibbs sampling that allow computationally efficient sampling of complex a priori models. The toolbox can be applied to any inverse...
Kisaka, M. Oscar; Mucheru-Muna, M.; Ngetich, F. K.; Mugwe, J.; Mugendi, D.; Mairura, F.; Shisanya, C.; Makokha, G. L.
2016-04-01
Drier parts of Kenya's Central Highlands endure persistent crop failure and declining agricultural productivity. These have, in part, attributed to high temperatures, prolonged dry spells and erratic rainfall. Understanding spatial-temporal variability of climatic indices such as rainfall at seasonal level is critical for optimal rain-fed agricultural productivity and natural resource management in the study area. However, the predominant setbacks in analysing hydro-meteorological events are occasioned by either lack, inadequate, or inconsistent meteorological data. Like in most other places, the sole sources of climatic data in the study region are scarce and only limited to single stations, yet with persistent missing/unrecorded data making their utilization a challenge. This study examined seasonal anomalies and variability in rainfall, drought occurrence and the efficacy of interpolation techniques in the drier regions of eastern Kenyan. Rainfall data from five stations (Machang'a, Kiritiri, Kiambere and Kindaruma and Embu) were sourced from both the Kenya Meteorology Department and on-site primary recording. Owing to some experimental work ongoing, automated recording for primary dailies in Machang'a have been ongoing since the year 2000 to date; thus, Machang'a was treated as reference (for period of record) station for selection of other stations in the region. The other stations had data sets of over 15 years with missing data of less than 10 % as required by the world meteorological organization whose quality check is subject to the Centre for Climate Systems Modeling (C2SM) through MeteoSwiss and EMPA bodies. The dailies were also subjected to homogeneity testing to evaluate whether they came from the same population. Rainfall anomaly index, coefficients of variance and probability were utilized in the analyses of rainfall variability. Spline, kriging and inverse distance weighting interpolation techniques were assessed using daily rainfall data and
Inverse Kinematic Analysis of Human Hand Thumb Model
Toth-Tascau, Mirela; Pater, Flavius; Stoia, Dan Ioan; Menyhardt, Karoly; Rosu, Serban; Rusu, Lucian; Vigaru, Cosmina
2011-09-01
This paper deals with a kinematic model of the thumb of the human hand. The proposed model has 3 degrees of freedom being able to model the movements of the thumb tip with respect to the wrist joint centre. The kinematic equations are derived based on Denavit-Hartenberg Convention and solved in both direct and inverse way. Inverse kinematic analysis of human hand thumb model reveals multiple and connected solutions which are characteristic to nonlinear systems when the number of equations is greater than number of unknowns and correspond to natural movements of the finger.
Enhanced Kerr electro-optic nonlinearity through cascaded Pockels effects
Li, Guang-Zhen; Jiang, Hao-Wei; Chen, Xian-Feng
2015-01-01
We demonstrated a large enhancement of Kerr electro-optic nonlinearity through cascaded Pockels effects in a domain inversion ferroelectric crystal. We designed a structure that can implement the cascaded Pockels effects and second-harmonic generation simultaneously. The energy coupling between the fundamental lights of different polarizations led to a large nonlinear phase shift, and thus an effective electro-optic nonlinear refractive index. The effective nonlinearity can be either positive or negative, causing the second-harmonic spectra to move towards the coupling center, which in turn, offered us a way to measure the effective electro-optic nonlinear refractive index. The corresponding enhanced Kerr electro-optic nonlinearity is more than three orders of magnitude higher than the intrinsic value. These results open a door to manipulate the nonlinear phase by applying external electric field instead of light intensity in noncentrosymmetric crystals.
Energy Technology Data Exchange (ETDEWEB)
Chen, DI-WEN
2001-11-21
Airborne hazardous plumes inadvertently released during nuclear/chemical/biological incidents are mostly of unknown composition and concentration until measurements are taken of post-accident ground concentrations from plume-ground deposition of constituents. Unfortunately, measurements often are days post-incident and rely on hazardous manned air-vehicle measurements. Before this happens, computational plume migration models are the only source of information on the plume characteristics, constituents, concentrations, directions of travel, ground deposition, etc. A mobile ''lighter than air'' (LTA) system is being developed at Oak Ridge National Laboratory that will be part of the first response in emergency conditions. These interactive and remote unmanned air vehicles will carry light-weight detectors and weather instrumentation to measure the conditions during and after plume release. This requires a cooperative computationally organized, GPS-controlled set of LTA's that self-coordinate around the objectives in an emergency situation in restricted time frames. A critical step before an optimum and cost-effective field sampling and monitoring program proceeds is the collection of data that provides statistically significant information, collected in a reliable and expeditious manner. Efficient aerial arrangements of the detectors taking the data (for active airborne release conditions) are necessary for plume identification, computational 3-dimensional reconstruction, and source distribution functions. This report describes the application of stochastic or geostatistical simulations to delineate the plume for guiding subsequent sampling and monitoring designs. A case study is presented of building digital plume images, based on existing ''hard'' experimental data and ''soft'' preliminary transport modeling results of Prairie Grass Trials Site. Markov Bayes Simulation, a coupled Bayesian/geostatistical
Ahmed, Zia U; Panaullah, Golam M; DeGloria, Stephen D; Duxbury, John M
2011-12-15
Knowledge of the spatial correlation of soil arsenic (As) concentrations with environmental variables is needed to assess the nature and extent of the risk of As contamination from irrigation water in Bangladesh. We analyzed 263 paired groundwater and paddy soil samples covering highland (HL) and medium highland-1 (MHL-1) land types for geostatistical mapping of soil As and delineation of As contaminated areas in Tala Upazilla, Satkhira district. We also collected 74 non-rice soil samples to assess the baseline concentration of soil As for this area. The mean soil As concentrations (mg/kg) for different land types under rice and non-rice crops were: rice-MHL-1 (21.2)>rice-HL (14.1)>non-rice-MHL-1 (11.9)>non-rice-HL (7.2). Multiple regression analyses showed that irrigation water As, Fe, land elevation and years of tubewell operation are the important factors affecting the concentrations of As in HL paddy soils. Only years of tubewell operation affected As concentration in the MHL-1 paddy soils. Quantitatively similar increases in soil As above the estimated baseline-As concentration were observed for rice soils on HL and MHL-1 after 6-8 years of groundwater irrigation, implying strong retention of As added in irrigation water in both land types. Application of single geostatistical methods with secondary variables such as regression kriging (RK) and ordinary co-kriging (OCK) gave little improvement in prediction of soil As over ordinary kriging (OK). Comparing single prediction methods, kriging within strata (KWS), the combination of RK for HL and OCK for MHL-1, gave more accurate soil As predictions and showed the lowest misclassification of declaring a location "contaminated" with respect to 14.8 mg As/kg, the highest value obtained for the baseline soil As concentration. Prediction of soil As buildup over time indicated that 75% or the soils cropped to rice would contain at least 30 mg/L As by the year 2020. Copyright © 2011 Elsevier B.V. All rights reserved.
Warnery, E; Ielsch, G; Lajaunie, C; Cale, E; Wackernagel, H; Debayle, C; Guillevic, J
2015-01-01
Terrestrial gamma dose rates show important spatial variations in France. Previous studies resulted in maps of arithmetic means of indoor terrestrial gamma dose rates by "departement" (French district). However, numerous areas could not be characterized due to the lack of data. The aim of our work was to obtain more precise estimates of the spatial variability of indoor terrestrial gamma dose rates in France by using a more recent and complete data base and geostatistics. The study was based on the exploitation of 97,595 measurements results distributed in 17,404 locations covering all of France. Measurements were done by the Institute for Radioprotection and Nuclear Safety (IRSN) using RPL (Radio Photo Luminescent) dosimeters, exposed during several months between years 2011 and 2012 in French dentist surgeries and veterinary clinics. The data used came from dosimeters which were not exposed to anthropic sources. After removing the cosmic rays contribution in order to study only the telluric gamma radiation, it was decided to work with the arithmetic means of the time-series measurements, weighted by the time-exposure of the dosimeters, for each location. The values varied between 13 and 349 nSv/h, with an arithmetic mean of 76 nSv/h. The observed statistical distribution of the gamma dose rates was skewed to the right. Firstly, ordinary kriging was performed in order to predict the gamma dose rate on cells of 1*1 km(2), all over the domain. The second step of the study was to use an auxiliary variable in estimates. The IRSN achieved in 2010 a classification of the French geological formations, characterizing their uranium potential on the bases of geology and local measurement results of rocks uranium content. This information is georeferenced in a map at the scale 1:1,000,000. The geological uranium potential (GUP) was classified in 5 qualitative categories. As telluric gamma rays mostly come from the progenies of the (238)Uranium series present in rocks, this
SPARSE ELECTROMAGNETIC IMAGING USING NONLINEAR LANDWEBER ITERATIONS
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.
Nonlinear model predictive control theory and algorithms
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...
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...
Inversion assuming weak scattering
DEFF Research Database (Denmark)
Xenaki, Angeliki; Gerstoft, Peter; Mosegaard, Klaus
2013-01-01
The study of weak scattering from inhomogeneous media or interface roughness has long been of interest in sonar applications. In an acoustic backscattering model of a stationary field of volume inhomogeneities, a stochastic description of the field is more useful than a deterministic description...... due to the complex nature of the field. A method based on linear inversion is employed to infer information about the statistical properties of the scattering field from the obtained cross-spectral matrix. A synthetic example based on an active high-frequency sonar demonstrates that the proposed...
Inverse Degree and Connectivity
Institute of Scientific and Technical Information of China (English)
MA Xiao-ling; TIAN Ying-zhi
2013-01-01
Let G be a connected graph with vertex set V(G),order n =丨V(G)丨,minimum degree δ(G) and connectivity κ(G).The graph G is called maximally connected if κ(G) =δ(G).Define the inverse degree of G with no isolated vertices as R(G) =Σv∈V(G)1/d(v),where d(v) denotes the degree of the vertex v.We show that G is maximally connected if R(G) ＜ 1 + 2/δ + n-2δ+1/(n-1)(n-3).
Geoacoustic inversion using the vector field
Crocker, Steven E.
The main goal of this project was to study the use of the acoustic vector field, separately or in combination with the scalar field, to estimate the depth dependent geoacoustic properties of the seafloor via non-linear inversion. The study was performed in the context of the Sediment Acoustics Experiment 2004 (SAX04) conducted in the Northern Gulf of Mexico (GOM) where a small number of acoustic vector sensors were deployed in close proximity to the seafloor. A variety of acoustic waveforms were transmitted into the seafloor at normal incidence. The acoustic vector sensors were located both above and beneath the seafloor interface where they measured the acoustic pressure and the acoustic particle acceleration. Motion data provided by the buried vector sensors were affected by a suspension response that was sensitive to the mass properties of the sensor, the sediment density and sediment elasticity (e.g., shear wave speed). The suspension response for the buried vector sensors included a resonance within the analysis band of 0.4 to 2.0 kHz. The suspension resonance represented an unknown complex transfer function between the acoustic vector field in the seabed and data representing that field. Therefore, inverse methods developed for this study were required to 1) estimate dynamic properties of the sensor suspension resonance and 2) account for the associated corruption of vector field data. A method to account for the vector sensor suspense response function was integrated directly into the inversion methods such that vector channel data corruption was reduced and an estimate of the shear wave speed in the sediment was returned. Inversions of real and synthetic data sets indicated that information about sediment shear wave speed was carried by the suspension response of the buried sensors, as opposed to being contained inherently within the acoustic vector field.
Inverse spatial principal component analysis for geophysical survey data interpolation
Li, Qingmou; Dehler, Sonya A.
2015-04-01
The starting point for data processing, visualization, and overlay with other data sources in geological applications often involves building a regular grid by interpolation of geophysical measurements. Typically, the sampling interval along survey lines is much higher than the spacing between survey lines because the geophysical recording system is able to operate with a high sampling rate, while the costs and slower speeds associated with operational platforms limit line spacing. However, currently available interpolating methods often smooth data observed with higher sampling rate along a survey line to accommodate the lower spacing across lines, and much of the higher resolution information is not captured in the interpolation process. In this approach, a method termed as the inverse spatial principal component analysis (isPCA) is developed to address this problem. In the isPCA method, a whole profile observation as well as its line position is handled as an entity and a survey collection of line entities is analyzed for interpolation. To test its performance, the developed isPCA method is used to process a simulated airborne magnetic survey from an existing magnetic grid offshore the Atlantic coast of Canada. The interpolation results using the isPCA method and other methods are compared with the original survey grid. It is demonstrated that the isPCA method outperforms the Inverse Distance Weighting (IDW), Kriging (Geostatistical), and MINimum Curvature (MINC) interpolation methods in retaining detailed anomaly structures and restoring original values. In a second test, a high resolution magnetic survey offshore Cape Breton, Nova Scotia, Canada, was processed and the results are compared with other geological information. This example demonstrates the effective performance of the isPCA method in basin structure identification.