#### Sample records for gravity inversion method

1. Gravity inversion code

Burkhard, N.R.

1979-01-01

The gravity inversion code applies stabilized linear inverse theory to determine the topography of a subsurface density anomaly from Bouguer gravity data. The gravity inversion program consists of four source codes: SEARCH, TREND, INVERT, and AVERAGE. TREND and INVERT are used iteratively to converge on a solution. SEARCH forms the input gravity data files for Nevada Test Site data. AVERAGE performs a covariance analysis on the solution. This document describes the necessary input files and the proper operation of the code. 2 figures, 2 tables

2. a method of gravity and seismic sequential inversion and its GPU implementation

Liu, G.; Meng, X.

2011-12-01

In this abstract, we introduce a gravity and seismic sequential inversion method to invert for density and velocity together. For the gravity inversion, we use an iterative method based on correlation imaging algorithm; for the seismic inversion, we use the full waveform inversion. The link between the density and velocity is an empirical formula called Gardner equation, for large volumes of data, we use the GPU to accelerate the computation. For the gravity inversion method , we introduce a method based on correlation imaging algorithm,it is also a interative method, first we calculate the correlation imaging of the observed gravity anomaly, it is some value between -1 and +1, then we multiply this value with a little density ,this value become the initial density model. We get a forward reuslt with this initial model and also calculate the correaltion imaging of the misfit of observed data and the forward data, also multiply the correaltion imaging result a little density and add it to the initial model, then do the same procedure above , at last ,we can get a inversion density model. For the seismic inveron method ,we use a mothod base on the linearity of acoustic wave equation written in the frequency domain,with a intial velociy model, we can get a good velocity result. In the sequential inversion of gravity and seismic , we need a link formula to convert between density and velocity ,in our method , we use the Gardner equation. Driven by the insatiable market demand for real time, high-definition 3D images, the programmable NVIDIA Graphic Processing Unit (GPU) as co-processor of CPU has been developed for high performance computing. Compute Unified Device Architecture (CUDA) is a parallel programming model and software environment provided by NVIDIA designed to overcome the challenge of using traditional general purpose GPU while maintaining a low learn curve for programmers familiar with standard programming languages such as C. In our inversion processing

3. Application of Cauchy-type integrals in developing effective methods for depth-to-basement inversion of gravity and gravity gradiometry data

Cai, Hongzhu; Zhdanov, Michael

2015-01-01

to be discretized for the calculation of gravity field. This was especially significant in the modeling and inversion of gravity data for determining the depth to the basement. Another important result was developing a novel method of inversion of gravity data to recover the depth to basement, based on the 3D...... Cauchy-type integral representation. Our numerical studies determined that the new method is much faster than conventional volume discretization method to compute the gravity response. Our synthetic model studies also showed that the developed inversion algorithm based on Cauchy-type integral is capable......One of the most important applications of gravity surveys in regional geophysical studies is determining the depth to basement. Conventional methods of solving this problem are based on the spectrum and/or Euler deconvolution analysis of the gravity field and on parameterization of the earth...

4. Inversion of Gravity Anomalies Using Primal-Dual Interior Point Methods

Aaron A. Velasco

2016-06-01

Full Text Available Structural inversion of gravity datasets based on the use of density anomalies to derive robust images of the subsurface (delineating lithologies and their boundaries constitutes a fundamental non-invasive tool for geological exploration. The use of experimental techniques in geophysics to estimate and interpret di erences in the substructure based on its density properties have proven e cient; however, the inherent non-uniqueness associated with most geophysical datasets make this the ideal scenario for the use of recently developed robust constrained optimization techniques. We present a constrained optimization approach for a least squares inversion problem aimed to characterize 2-Dimensional Earth density structure models based on Bouguer gravity anomalies. The proposed formulation is solved with a Primal-Dual Interior-Point method including equality and inequality physical and structural constraints. We validate our results using synthetic density crustal structure models with varying complexity and illustrate the behavior of the algorithm using di erent initial density structure models and increasing noise levels in the observations. Based on these implementations, we conclude that the algorithm using Primal-Dual Interior-Point methods is robust, and its results always honor the geophysical constraints. Some of the advantages of using this approach for structural inversion of gravity data are the incorporation of a priori information related to the model parameters (coming from actual physical properties of the subsurface and the reduction of the solution space contingent on these boundary conditions.

5. Comparison result of inversion of gravity data of a fault by particle swarm optimization and Levenberg-Marquardt methods.

Toushmalani, Reza

2013-01-01

The purpose of this study was to compare the performance of two methods for gravity inversion of a fault. First method [Particle swarm optimization (PSO)] is a heuristic global optimization method and also an optimization algorithm, which is based on swarm intelligence. It comes from the research on the bird and fish flock movement behavior. Second method [The Levenberg-Marquardt algorithm (LM)] is an approximation to the Newton method used also for training ANNs. In this paper first we discussed the gravity field of a fault, then describes the algorithms of PSO and LM And presents application of Levenberg-Marquardt algorithm, and a particle swarm algorithm in solving inverse problem of a fault. Most importantly the parameters for the algorithms are given for the individual tests. Inverse solution reveals that fault model parameters are agree quite well with the known results. A more agreement has been found between the predicted model anomaly and the observed gravity anomaly in PSO method rather than LM method.

6. Toward Joint Inversion of Gravity and Dyanamics

Jacoby, W. R.

To better understand geodynamic processes as seafloor spreading, plumes, subduction, and isostatic adjustment, gravity is inverted with "a prioriinformation from topography/bathymetry, seismic structure and dynamic models. Examples are subduction of the Juan de Fuca plate below Vancouver Island, the passive Black Sea­Turkey margin and Iceland ridge-plume interaction. Gravity and other data are averaged 50 km wide strips. Mass balances are estimated (showing also that the free air anomaly is misleading for narrow structures). The mass balances represent plate forces and plate bending, affecting the gravity signals and the isostatic state of continental margins and ridge-plume effects, which are highly correlated in space and cannot be separated without a priori information from modelling. The examples from widely different tectonic situations demonstrate that the art of regional-scale gravity inversion requires extensive background knowledge and inclusion of dynamic processes. It is difficult to conceive any formal, globally applicable procedure taking care of this; it is even a question, what is data, what a priori information? They are not distinguishable if all are included as foreward routines. The "accuracy" of models cannot be perfectly determined, if the "real" mass distribution is not known ­ if known, gravity inversion would be unnecessary. In reality only guesses are possible on the basis of observations and physical laws governing geodynamics. A priori information and gravity data limit the resolution of gravity inversion. Different model types are indistinguishable because adjustments within their parameter uncertainties permit a good fit. But gravity excludes wrong models (Karl Popper: science evolves by falsification of wrong models), and precise gravity guides and defines aims, targets and strategies for new observations.

7. Constraining inverse curvature gravity with supernovae

Mena, Olga; Santiago, Jose; /Fermilab; Weller, Jochen; /University Coll., London /Fermilab

2005-10-01

We show that the current accelerated expansion of the Universe can be explained without resorting to dark energy. Models of generalized modified gravity, with inverse powers of the curvature can have late time accelerating attractors without conflicting with solar system experiments. We have solved the Friedman equations for the full dynamical range of the evolution of the Universe. This allows us to perform a detailed analysis of Supernovae data in the context of such models that results in an excellent fit. Hence, inverse curvature gravity models represent an example of phenomenologically viable models in which the current acceleration of the Universe is driven by curvature instead of dark energy. If we further include constraints on the current expansion rate of the Universe from the Hubble Space Telescope and on the age of the Universe from globular clusters, we obtain that the matter content of the Universe is 0.07 {le} {omega}{sub m} {le} 0.21 (95% Confidence). Hence the inverse curvature gravity models considered can not explain the dynamics of the Universe just with a baryonic matter component.

8. Automated gravity gradient tensor inversion for underwater object detection

Wu, Lin; Tian, Jinwen

2010-01-01

Underwater abnormal object detection is a current need for the navigation security of autonomous underwater vehicles (AUVs). In this paper, an automated gravity gradient tensor inversion algorithm is proposed for the purpose of passive underwater object detection. Full-tensor gravity gradient anomalies induced by an object in the partial area can be measured with the technique of gravity gradiometry on an AUV. Then the automated algorithm utilizes the anomalies, using the inverse method to estimate the mass and barycentre location of the arbitrary-shaped object. A few tests on simple synthetic models will be illustrated, in order to evaluate the feasibility and accuracy of the new algorithm. Moreover, the method is applied to a complicated model of an abnormal object with gradiometer and AUV noise, and interference from a neighbouring illusive smaller object. In all cases tested, the estimated mass and barycentre location parameters are found to be in good agreement with the actual values

9. Constraining inverse-curvature gravity with supernovae.

Mena, Olga; Santiago, José; Weller, Jochen

2006-02-03

We show that models of generalized modified gravity, with inverse powers of the curvature, can explain the current accelerated expansion of the Universe without resorting to dark energy and without conflicting with solar system experiments. We have solved the Friedmann equations for the full dynamical range of the evolution of the Universe and performed a detailed analysis of supernovae data in the context of such models that results in an excellent fit. If we further include constraints on the current expansion of the Universe and on its age, we obtain that the matter content of the Universe is 0.07baryonic matter component.

10. Pareto joint inversion of 2D magnetotelluric and gravity data

2015-04-01

In this contribution, the first results of the "Innovative technology of petrophysical parameters estimation of geological media using joint inversion algorithms" project were described. At this stage of the development, Pareto joint inversion scheme for 2D MT and gravity data was used. Additionally, seismic data were provided to set some constrains for the inversion. Sharp Boundary Interface(SBI) approach and description model with set of polygons were used to limit the dimensionality of the solution space. The main engine was based on modified Particle Swarm Optimization(PSO). This algorithm was properly adapted to handle two or more target function at once. Additional algorithm was used to eliminate non- realistic solution proposals. Because PSO is a method of stochastic global optimization, it requires a lot of proposals to be evaluated to find a single Pareto solution and then compose a Pareto front. To optimize this stage parallel computing was used for both inversion engine and 2D MT forward solver. There are many advantages of proposed solution of joint inversion problems. First of all, Pareto scheme eliminates cumbersome rescaling of the target functions, that can highly affect the final solution. Secondly, the whole set of solution is created in one optimization run, providing a choice of the final solution. This choice can be based off qualitative data, that are usually very hard to be incorporated into the regular inversion schema. SBI parameterisation not only limits the problem of dimensionality, but also makes constraining of the solution easier. At this stage of work, decision to test the approach using MT and gravity data was made, because this combination is often used in practice. It is important to mention, that the general solution is not limited to this two methods and it is flexible enough to be used with more than two sources of data. Presented results were obtained for synthetic models, imitating real geological conditions, where

11. Joint Inversion of Gravity and Gravity Tensor Data Using the Structural Index as Weighting Function Rate Decay

Ialongo, S.; Cella, F.; Fedi, M.; Florio, G.

2011-12-01

Most geophysical inversion problems are characterized by a number of data considerably higher than the number of the unknown parameters. This corresponds to solve highly underdetermined systems. To get a unique solution, a priori information must be therefore introduced. We here analyze the inversion of the gravity gradient tensor (GGT). Previous approaches to invert jointly or independently more gradient components are by Li (2001) proposing an algorithm using a depth weighting function and Zhdanov et alii (2004), providing a well focused inversion of gradient data. Both the methods give a much-improved solution compared with the minimum length solution, which is invariably shallow and not representative of the true source distribution. For very undetermined problems, this feature is due to the role of the depth weighting matrices used by both the methods. Recently, Cella and Fedi (2011) showed however that for magnetic and gravity data the depth weighting function has to be defined carefully, under a preliminary application of Euler Deconvolution or Depth from Extreme Point methods, yielding the appropriate structural index and then using it as the rate decay of the weighting function. We therefore propose to extend this last approach to invert jointly or independently the GGT tensor using the structural index as weighting function rate decay. In case of a joint inversion, gravity data can be added as well. This multicomponent case is also relevant because the simultaneous use of several components and gravity increase the number of data and reduce the algebraic ambiguity compared to the inversion of a single component. The reduction of such ambiguity was shown in Fedi et al, (2005) decisive to get an improved depth resolution in inverse problems, independently from any form of depth weighting function. The method is demonstrated to synthetic cases and applied to real cases, such as the Vredefort impact area (South Africa), characterized by a complex density

12. Superconducting gravity gradiometer and a test of inverse square law

Moody, M.V.; Paik, H.J.

1989-01-01

The equivalence principle prohibits the distinction of gravity from acceleration by a local measurement. However, by making a differential measurement of acceleration over a baseline, platform accelerations can be cancelled and gravity gradients detected. In an in-line superconducting gravity gradiometer, this differencing is accomplished with two spring-mass accelerometers in which the proof masses are confined to motion in a single degree of freedom and are coupled together by superconducting circuits. Platform motions appear as common mode accelerations and are cancelled by adjusting the ratio of two persistent currents in the sensing circuit. The sensing circuit is connected to a commercial SQUID amplifier to sense changes in the persistent currents generated by differential accelerations, i.e., gravity gradients. A three-axis gravity gradiometer is formed by mounting six accelerometers on the faces of a precision cube, with the accelerometers on opposite faces of the cube forming one of three in-line gradiometers. A dedicated satellite mission for mapping the earth's gravity field is an important one. Additional scientific goals are a test of the inverse square law to a part in 10(exp 10) at 100 km, and a test of the Lense-Thirring effect by detecting the relativistic gravity magnetic terms in the gravity gradient tensor for the earth

13. 3D inversion of full gravity gradient tensor data in spherical coordinate system using local north-oriented frame

Zhang, Yi; Wu, Yulong; Yan, Jianguo; Wang, Haoran; Rodriguez, J. Alexis P.; Qiu, Yue

2018-04-01

In this paper, we propose an inverse method for full gravity gradient tensor data in the spherical coordinate system. As opposed to the traditional gravity inversion in the Cartesian coordinate system, our proposed method takes the curvature of the Earth, the Moon, or other planets into account, using tesseroid bodies to produce gravity gradient effects in forward modeling. We used both synthetic and observed datasets to test the stability and validity of the proposed method. Our results using synthetic gravity data show that our new method predicts the depth of the density anomalous body efficiently and accurately. Using observed gravity data for the Mare Smythii area on the moon, the density distribution of the crust in this area reveals its geological structure. These results validate the proposed method and potential application for large area data inversion of planetary geological structures.[Figure not available: see fulltext.

14. Testing the inverse-square law of gravity: Error and design with the upward continuation integral

Thomas, J.

1989-01-01

It has been reported that the inverse-square law of gravity is violated over a range of a few hundred meters. I present a different method for the analysis of the data from that experiment. In this method, the experimental error can be evaluated analytically and I confirm the previous analysis but show that it is a 2σ effect. The method can also be used to design new experiments that will yield minimum errors for a fixed number of data points

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

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.

16. Using Gravity Inversion to Estimate Antarctic Geothermal Heat Flux

Vaughan, Alan P. M.; Kusznir, Nick J.; Ferraccioli, Fausto; Leat, Phil T.; Jordan, Tom A. R. M.; Purucker, Michael E.; (Sasha) Golynsky, A. V.; Rogozhina, Irina

2014-05-01

New modelling studies for Greenland have recently underlined the importance of GHF for long-term ice sheet behaviour (Petrunin et al. 2013). Revised determinations of top basement heat-flow for Antarctica and adjacent rifted continental margins using gravity inversion mapping of crustal thickness and continental lithosphere thinning (Chappell & Kusznir 2008), using BedMap2 data have provided improved estimates of geothermal heat flux (GHF) in Antarctica where it is very poorly known. Continental lithosphere thinning and post-breakup residual thicknesses of continental crust determined from gravity inversion have been used to predict the preservation of continental crustal radiogenic heat productivity and the transient lithosphere heat-flow contribution within thermally equilibrating rifted continental and oceanic lithosphere. The sensitivity of present-day Antarctic top basement heat-flow to initial continental radiogenic heat productivity, continental rift and margin breakup age has been examined. Recognition of the East Antarctic Rift System (EARS), a major Permian to Cretaceous age rift system that appears to extend from the continental margin at the Lambert Rift to the South Pole region, a distance of 2500 km (Ferraccioli et al. 2011) and is comparable in scale to the well-studied East African rift system, highlights that crustal variability in interior Antarctica is much greater than previously assumed. GHF is also important to understand proposed ice accretion at the base of the EAIS in the GSM and its links to sub-ice hydrology (Bell et al. 2011). References Bell, R.E., Ferraccioli, F., Creyts, T.T., Braaten, D., Corr, H., Das, I., Damaske, D., Frearson, N., Jordan, T., Rose, K., Studinger, M. & Wolovick, M. 2011. Widespread persistent thickening of the East Antarctic Ice Sheet by freezing from the base. Science, 331 (6024), 1592-1595. Chappell, A.R. & Kusznir, N.J. 2008. Three-dimensional gravity inversion for Moho depth at rifted continental margins

17. Three-dimensional Gravity Inversion with a New Gradient Scheme on Unstructured Grids

Sun, S.; Yin, C.; Gao, X.; Liu, Y.; Zhang, B.

2017-12-01

Stabilized gradient-based methods have been proved to be efficient for inverse problems. Based on these methods, setting gradient close to zero can effectively minimize the objective function. Thus the gradient of objective function determines the inversion results. By analyzing the cause of poor resolution on depth in gradient-based gravity inversion methods, we find that imposing depth weighting functional in conventional gradient can improve the depth resolution to some extent. However, the improvement is affected by the regularization parameter and the effect of the regularization term becomes smaller with increasing depth (shown as Figure 1 (a)). In this paper, we propose a new gradient scheme for gravity inversion by introducing a weighted model vector. The new gradient can improve the depth resolution more efficiently, which is independent of the regularization parameter, and the effect of regularization term will not be weakened when depth increases. Besides, fuzzy c-means clustering method and smooth operator are both used as regularization terms to yield an internal consecutive inverse model with sharp boundaries (Sun and Li, 2015). We have tested our new gradient scheme with unstructured grids on synthetic data to illustrate the effectiveness of the algorithm. Gravity forward modeling with unstructured grids is based on the algorithm proposed by Okbe (1979). We use a linear conjugate gradient inversion scheme to solve the inversion problem. The numerical experiments show a great improvement in depth resolution compared with regular gradient scheme, and the inverse model is compact at all depths (shown as Figure 1 (b)). AcknowledgeThis research is supported by Key Program of National Natural Science Foundation of China (41530320), China Natural Science Foundation for Young Scientists (41404093), and Key National Research Project of China (2016YFC0303100, 2017YFC0601900). ReferencesSun J, Li Y. 2015. Multidomain petrophysically constrained inversion and

18. Estimating Antarctic Geothermal Heat Flux using Gravity Inversion

Vaughan, Alan P. M.; Kusznir, Nick J.; Ferraccioli, Fausto; Leat, Phil T.; Jordan, Tom A. R. M.; Purucker, Michael E.; Golynsky, A. V.; Sasha Rogozhina, Irina

2013-04-01

Geothermal heat flux (GHF) in Antarctica is very poorly known. We have determined (Vaughan et al. 2012) top basement heat-flow for Antarctica and adjacent rifted continental margins using gravity inversion mapping of crustal thickness and continental lithosphere thinning (Chappell & Kusznir 2008). Continental lithosphere thinning and post-breakup residual thicknesses of continental crust determined from gravity inversion have been used to predict the preservation of continental crustal radiogenic heat productivity and the transient lithosphere heat-flow contribution within thermally equilibrating rifted continental and oceanic lithosphere. The sensitivity of present-day Antarctic top basement heat-flow to initial continental radiogenic heat productivity, continental rift and margin breakup age has been examined. Knowing GHF distribution for East Antarctica and the Gamburtsev Subglacial Mountains (GSM) region in particular is critical because: 1) The GSM likely acted as key nucleation point for the East Antarctic Ice Sheet (EAIS); 2) the region may contain the oldest ice of the EAIS - a prime target for future ice core drilling; 3) GHF is important to understand proposed ice accretion at the base of the EAIS in the GSM and its links to sub-ice hydrology (Bell et al. 2011). An integrated multi-dataset-based GHF model for East Antarctica is planned that will resolve the wide range of estimates previously published using single datasets. The new map and existing GHF distribution estimates available for Antarctica will be evaluated using direct ice temperature measurements obtained from deep ice cores, estimates of GHF derived from subglacial lakes, and a thermodynamic ice-sheet model of the Antarctic Ice Sheet driven by past climate reconstructions and each of analysed heat flow maps, as has recently been done for the Greenland region (Rogozhina et al. 2012). References Bell, R.E., Ferraccioli, F., Creyts, T.T., Braaten, D., Corr, H., Das, I., Damaske, D., Frearson, N

19. Model study of the compact gravity reconstruction; Juryoku inversion CGR no model kento

Ishii, Y; Muraoka, A [Sogo Geophysical Exploration Co. Ltd., Tokyo (Japan)

1996-05-01

An examination was made on gravity inversion using a compact gravity reconstruction (CGR) method in gravity tomography analysis. In a model analysis, an analytical region of 100m{times}50m was divided into cells of 10m{times}10m, on the assumption that two density anomalous bodies with a density difference of 1.0g/cm{sup 3} existed with one shallow and the other deep density distribution. The result of the analysis revealed that, in a linear analysis by a general inverse matrix, blurs and blotting were plenty with a tendency of making gravity anomaly attributable to an anomalous distribution of shallow density; that CGR provided a large effect in making a clear contrast of an anomalous part; that, where structures of shallow and deep density anomalies existed, the analysis by CGR was inferior in the restoration of a deep structure with errors enlarged; that, if a gravity traverse was taken long compared with the distribution depth of density anomalies, the analytical precision of a deep part was improved; that an analytical convergence was better with the restriction of density difference given on the large side than on the small side; and so on. 3 refs., 10 figs.

20. A Combined Gravity Compensation Method for INS Using the Simplified Gravity Model and Gravity Database.

Zhou, Xiao; Yang, Gongliu; Wang, Jing; Wen, Zeyang

2018-05-14

In recent decades, gravity compensation has become an important way to reduce the position error of an inertial navigation system (INS), especially for a high-precision INS, because of the extensive application of high precision inertial sensors (accelerometers and gyros). This paper first deducts the INS's solution error considering gravity disturbance and simulates the results. Meanwhile, this paper proposes a combined gravity compensation method using a simplified gravity model and gravity database. This new combined method consists of two steps all together. Step 1 subtracts the normal gravity using a simplified gravity model. Step 2 first obtains the gravity disturbance on the trajectory of the carrier with the help of ELM training based on the measured gravity data (provided by Institute of Geodesy and Geophysics; Chinese Academy of sciences), and then compensates it into the error equations of the INS, considering the gravity disturbance, to further improve the navigation accuracy. The effectiveness and feasibility of this new gravity compensation method for the INS are verified through vehicle tests in two different regions; one is in flat terrain with mild gravity variation and the other is in complex terrain with fierce gravity variation. During 2 h vehicle tests, the positioning accuracy of two tests can improve by 20% and 38% respectively, after the gravity is compensated by the proposed method.

1. Inversion of gravity data in the Big Bear Lake Area to recover depth to basement using Cauchy-type integrals

Cai, Hongzhu; Zhdanov, Michael

2014-01-01

One of the important applications of the gravity method is evaluation of the depth to the basement, which is characterized by a significant density contrast with the sedimental layeres. We have introduced recently a new method of modeling and inversion of potential field data generated by a densi...

2. Inversion of gravity and gravity gradiometry data for density contrast surfaces using Cauchy-type integrals

Zhdanov, Michael; Cai, Hongzhu

2014-01-01

We introduce a new method of modeling and inversion of potential field data generated by a density contrast surface. Our method is based on 3D Cauchy-type integral representation of the potential fields. Traditionally, potential fields are calculated using volume integrals of the domains occupied...

3. Graphical calculus of volume, inverse volume and Hamiltonian operators in loop quantum gravity

Yang, Jinsong [Guizhou University, Department of Physics, Guiyang (China); Academia Sinica, Institute of Physics, Taipei (China); Ma, Yongge [Beijing Normal University, Department of Physics, Beijing (China)

2017-04-15

To adopt a practical method to calculate the action of geometrical operators on quantum states is a crucial task in loop quantum gravity. In this paper, the graphical calculus based on the original Brink graphical method is applied to loop quantum gravity along the line of previous work. The graphical method provides a very powerful technique for simplifying complicated calculations. The closed formula of the volume operator and the actions of the Euclidean Hamiltonian constraint operator and the so-called inverse volume operator on spin-network states with trivalent vertices are derived via the graphical method. By employing suitable and non-ambiguous graphs to represent the action of operators as well as the spin-network states, we use the simple rules of transforming graphs to obtain the resulting formula. Comparing with the complicated algebraic derivation in some literature, our procedure is more concise, intuitive and visual. The resulting matrix elements of the volume operator is compact and uniform, fitting for both gauge-invariant and gauge-variant spin-network states. Our results indicate some corrections to the existing results for the Hamiltonian operator and inverse volume operator in the literature. (orig.)

4. What goes up... gravity and scientific method

Kosso, Peter

2017-01-01

The concept of gravity provides a natural phenomenon that is simultaneously obvious and obscure; we all know what it is, but rarely question why it is. The simple observation that 'what goes up must come down' contrasts starkly with our current scientific explanation of gravity, which involves challenging and sometimes counterintuitive concepts. With such extremes between the plain and the perplexing, gravity forces a sharp focus on scientific method. Following the history of gravity from Aristotle to Einstein, this clear account highlights the logic of scientific method for non-specialists. Successive theories of gravity and the evidence for each are presented clearly and rationally, focusing on the fundamental ideas behind them. Using only high-school level algebra and geometry, the author emphasizes what the equations mean rather than how they are derived, making this accessible for all those curious about gravity and how science really works.

5. Gravity inversion of deep-crust and mantle interfaces in the Three Gorges area

Wang Jian

2012-11-01

Full Text Available To better understand the heterogeneity of deep-crust and mantle interfaces in the region of the Three Gorges, China, we used the Parker-Oldenburg iterative inversion method to invert existing Bouguer gravity data from the Three Gorges area (1 : 500000, a new gravity map of the Three Gorges Dam (1 : 200000, and the results of deep seismic soundings. The inversion results show a Moho depth of 42 km between Badong and Zigui and the depth of the B2 lower-crustal interface beneath the Jianghan Plain and surrounding areas at 21–25 km. The morphology of crustal interfaces and the surface geology present an overpass structure. The mid-crust beneath the Three Gorges Dam is approximately 9 km thick, which is the thinnest in the Three Gorges area and may be related to the shallow low-density body near the Huangling anticline. The upper crust is seismogenic, and there is a close relationship between seismicity and the deep-crust and mantle interfaces. For example, the M5. 1 Zigui earthquake occurred where the gradients of the Moho and the B2 interface are the steepest, showing that deep structure has a very important effect on regional seismicity.

6. Earthquake epicentroids in the Beijing-Tianjin-Tangshan-Zhangjiakou region inversed by gravity variation data

Zheng, Jin-Han; Song, Sheng-He; Liu, Ke-Ren; Lu, Hong-Yan; Kuo, J. T.

2003-07-01

Gravity variation data observed in the process of seismogenesis and occurrences of earthquakes show that the location with the greatest gravity changes does not necessarily coincide with the epicenter. To explain this we defined the center of effective mass of stress volume as "hypocentroid", and the vertical projection of which on the earth’s surface as "epicentroid". Here we adopt three rotating models, including spheroid, ellipsoid and cylinder, to represent the region of an impending earthquake. Based on the models of gravity variations induced by uniform dilatancy, epicentroids associated with sixteen earthquakes with M>4.0 occurred in 1981 2000 in the Beijing-Tianjin-Tangshan-Zhangjiakou region are determined by means of a proposed least squares iterative inversion method. The results indicate that cylinder model is preferable to the other two, and epicentroids obtained by the cylinder model separate from the epicenters by a range of 0 40 km. Epicentroids are inevitably located within intact tectonic blocks, and usually cluster in groups; while the epicenters are generally located at the terminations of faults or at the intersections of faults. It seems that there exist earthquake-hatching areas in the block among faults. Earthquakes hatch in these areas, but occur around these areas, meanwhile the existence of faults may play an important role in controlling the processes.

7. Inversion of gravity gradient tensor data: does it provide better resolution?

Paoletti, V.; Fedi, M.; Italiano, F.; Florio, G.; Ialongo, S.

2016-04-01

The gravity gradient tensor (GGT) has been increasingly used in practical applications, but the advantages and the disadvantages of the analysis of GGT components versus the analysis of the vertical component of the gravity field are still debated. We analyse the performance of joint inversion of GGT components versus separate inversion of the gravity field alone, or of one tensor component. We perform our analysis by inspection of the Picard Plot, a Singular Value Decomposition tool, and analyse both synthetic data and gradiometer measurements carried out at the Vredefort structure, South Africa. We show that the main factors controlling the reliability of the inversion are algebraic ambiguity (the difference between the number of unknowns and the number of available data points) and signal-to-noise ratio. Provided that algebraic ambiguity is kept low and the noise level is small enough so that a sufficient number of SVD components can be included in the regularized solution, we find that: (i) the choice of tensor components involved in the inversion is not crucial to the overall reliability of the reconstructions; (ii) GGT inversion can yield the same resolution as inversion with a denser distribution of gravity data points, but with the advantage of using fewer measurement stations.

8. Inverse Scattering Method and Soliton Solution Family for String Effective Action

Ya-Jun, Gao

2009-01-01

A modified Hauser–Ernst-type linear system is established and used to develop an inverse scattering method for solving the motion equations of the string effective action describing the coupled gravity, dilaton and Kalb–Ramond fields. The reduction procedures in this inverse scattering method are found to be fairly simple, which makes the proposed inverse scattering method applied fine and effective. As an application, a concrete family of soliton solutions for the considered theory is obtained

9. Inversion of Gravity and Magnetic Field Data for Tyrrhena Patera

Milbury, C.; Schubert, G.; Raymond, C. A.; Smrekar, S. E.

2011-01-01

Tyrrhena Patera is located to the southeast/northeast of the Isidis/Hellas impact basin. It was geologically active into the Late Amazonian, although the main edifice was formed in the Noachian(approximately 3.7-4.0 Ga). Tyrrhena Patera and the surrounding area contain gravity and magnetic anomalies that appear to be correlated. The results presented here are for the anomalies 1a and 1b (closest to Tyrrhena Patera), however other anomalies in this region have been modeled and will be presented at the conference.The Mars Global Surveyor (MGS) free-air gravity signature of Tyrrhena Patera has been studied by Kiefer, who inferred the existence of an extinct magma chamber below it. The magnetic signature has been mapped by Lillis R. J. et al., who compared electron reflectometer data, analogous to the total magnetic field, for Syrtis Major and Tyrrhena Patera and argued for demagnetization of both volcanoes.

10. On the Inversion for Mass (Re)Distribution from Global (Time-Variable) Gravity Field

Chao, Benjamin F.

2004-01-01

The well-known non-uniqueness of the gravitational inverse problem states the following: The external gravity field, even if completely and exactly known, cannot Uniquely determine the density distribution of the body that produces the gravity field. This is an intrinsic property of a field that obeys the Laplace equation, as already treated in mathematical as well as geophysical literature. In this paper we provide conceptual insight by examining the problem in terms of spherical harmonic expansion of the global gravity field. By comparing the multipoles and the moments of the density function, we show that in 3-S the degree of knowledge deficiency in trying to inversely recover the density distribution from external gravity field is (n+l)(n+2)/2 - (2n+l) = n(n-1)/2 for each harmonic degree n. On the other hand, on a 2-D spherical shell we show via a simple relationship that the inverse solution of the surface density distribution is unique. The latter applies quite readily in the inversion of time-variable gravity signals (such as those observed by the GRACE space mission) where the sources over a wide range of the scales largely come from the Earth's Surface.

11. Lectures on the inverse scattering method

Zakharov, V.E.

1983-06-01

In a series of six lectures an elementary introduction to the theory of inverse scattering is given. The first four lectures contain a detailed theory of solitons in the framework of the KdV equation, together with the inverse scattering theory of the one-dimensional Schroedinger equation. In the fifth lecture the dressing method is described, while the sixth lecture gives a brief review of the equations soluble by the inverse scattering method. (author)

12. Inversion of Density Interfaces Using the Pseudo-Backpropagation Neural Network Method

Chen, Xiaohong; Du, Yukun; Liu, Zhan; Zhao, Wenju; Chen, Xiaocheng

2018-05-01

This paper presents a new pseudo-backpropagation (BP) neural network method that can invert multi-density interfaces at one time. The new method is based on the conventional forward modeling and inverse modeling theories in addition to conventional pseudo-BP neural network arithmetic. A 3D inversion model for gravity anomalies of multi-density interfaces using the pseudo-BP neural network method is constructed after analyzing the structure and function of the artificial neural network. The corresponding iterative inverse formula of the space field is presented at the same time. Based on trials of gravity anomalies and density noise, the influence of the two kinds of noise on the inverse result is discussed and the scale of noise requested for the stability of the arithmetic is analyzed. The effects of the initial model on the reduction of the ambiguity of the result and improvement of the precision of inversion are discussed. The correctness and validity of the method were verified by the 3D model of the three interfaces. 3D inversion was performed on the observed gravity anomaly data of the Okinawa trough using the program presented herein. The Tertiary basement and Moho depth were obtained from the inversion results, which also testify the adaptability of the method. This study has made a useful attempt for the inversion of gravity density interfaces.

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

Commer, M.

2011-03-01

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

14. An inverse method for radiation transport

Favorite, J. A. (Jeffrey A.); Sanchez, R. (Richard)

2004-01-01

Adjoint functions have been used with forward functions to compute gradients in implicit (iterative) solution methods for inverse problems in optical tomography, geoscience, thermal science, and other fields, but only once has this approach been used for inverse solutions to the Boltzmann transport equation. In this paper, this approach is used to develop an inverse method that requires only angle-independent flux measurements, rather than angle-dependent measurements as was done previously. The method is applied to a simplified form of the transport equation that does not include scattering. The resulting procedure uses measured values of gamma-ray fluxes of discrete, characteristic energies to determine interface locations in a multilayer shield. The method was implemented with a Newton-Raphson optimization algorithm, and it worked very well in numerical one-dimensional spherical test cases. A more sophisticated optimization method would better exploit the potential of the inverse method.

15. Planetary wave-gravity wave interactions during mesospheric inversion layer events

Ramesh, K.; Sridharan, S.; Raghunath, K.; Vijaya Bhaskara Rao, S.; Bhavani Kumar, Y.

2013-07-01

lidar temperature observations over Gadanki (13.5°N, 79.2°E) show a few mesospheric inversion layer (MIL) events during 20-25 January 2007. The zonal mean removed SABER temperature shows warm anomalies around 50°E and 275°E indicating the presence of planetary wave of zonal wave number 2. The MIL amplitudes in SABER temperature averaged for 10°N-15°N and 70°E-90°E show a clear 2 day wave modulation during 20-28 January 2007. Prior to 20 January 2007, a strong 2day wave (zonal wave number 2) is observed in the height region of 80-90 km and it gets largely suppressed during 20-26 January 2007 as the condition for vertical propagation is not favorable, though it prevails at lower heights. The 10 day mean zonal wind over Tirunelveli (8.7°N, 77.8°E) shows deceleration of eastward winds indicating the westward drag due to wave dissipation. The nightly mean MF radar observed zonal winds show the presence of alternating eastward and westward winds during the period of 20-26 January 2007. The two dimensional spectrum of Rayleigh lidar temperature observations available for the nights of 20, 22, and 24 January 2007 shows the presence of gravity wave activity with periods 18 min, 38 min, 38 min, and vertical wavelengths 6.4 km, 4.0 km, 6.4 km respectively. From the dispersion relation of gravity waves, it is inferred that these waves are internal gravity waves rather than inertia gravity waves with the horizontal phase speeds of ~40 m/s, ~37 m/s, and ~50 m/s respectively. Assuming the gravity waves are eastward propagating waves, they get absorbed only in the eastward local wind fields of the planetary wave thereby causing turbulence and eddy diffusion which can be inferred from the estimation of large drag force due to the breaking of gravity wave leading to the formation of large amplitude inversion events in alternate nights. The present study shows that, the mesospheric temperature inversion is caused mainly due to the gravity wave breaking and the inversion

16. Gravity inversion predicts the nature of the amundsen basin and its continental borderlands near greenland

Døssing, Arne; Hansen, Thomas Mejer; Olesen, Arne Vestergaard

2014-01-01

the results of 3-D gravity inversion for predicting the sediment thickness and basement geometry within the Amundsen Basin and along its borderlands. We use the recently published LOMGRAV-09 gravity compilation and adopt a process-oriented iterative cycle approach that minimizes misfit between an Earth model...... and observations. The sensitivity of our results to lateral variations in depth and density contrast of the Moho is further tested by a stochastic inversion. Within their limitations, the approach and setup used herein provides the first detailed model of the sediment thickness and basement geometry in the Arctic...... above high-relief basement in the central Amundsen Basin. Significantly, an up to 7 km deep elongated sedimentary basin is predicted along the northern edge of the Morris Jesup Rise. This basin continues into the Klenova Valley south of the Lomonosov Ridge and correlates with an offshore continuation...

17. Ensemble Kalman methods for inverse problems

Iglesias, Marco A; Law, Kody J H; Stuart, Andrew M

2013-01-01

The ensemble Kalman filter (EnKF) was introduced by Evensen in 1994 (Evensen 1994 J. Geophys. Res. 99 10143–62) as a novel method for data assimilation: state estimation for noisily observed time-dependent problems. Since that time it has had enormous impact in many application domains because of its robustness and ease of implementation, and numerical evidence of its accuracy. In this paper we propose the application of an iterative ensemble Kalman method for the solution of a wide class of inverse problems. In this context we show that the estimate of the unknown function that we obtain with the ensemble Kalman method lies in a subspace A spanned by the initial ensemble. Hence the resulting error may be bounded above by the error found from the best approximation in this subspace. We provide numerical experiments which compare the error incurred by the ensemble Kalman method for inverse problems with the error of the best approximation in A, and with variants on traditional least-squares approaches, restricted to the subspace A. In so doing we demonstrate that the ensemble Kalman method for inverse problems provides a derivative-free optimization method with comparable accuracy to that achieved by traditional least-squares approaches. Furthermore, we also demonstrate that the accuracy is of the same order of magnitude as that achieved by the best approximation. Three examples are used to demonstrate these assertions: inversion of a compact linear operator; inversion of piezometric head to determine hydraulic conductivity in a Darcy model of groundwater flow; and inversion of Eulerian velocity measurements at positive times to determine the initial condition in an incompressible fluid. (paper)

18. 3D Gravity Inversion by Growing Bodies and Shaping Layers at Mt. Vesuvius (Southern Italy)

Berrino, Giovanna; Camacho, Antonio G.

2008-06-01

To improve our knowledge of the structural pattern of Mt. Vesuvius and its magmatic system, which represents one of the three volcanoes located in the Neapolitan area (together with Campi Flegrei and Ischia; southern Italy), we analyze here the Bouguer gravity map that is already available through its interpretation by means of 2.5-dimensional modelling. We have carried out a three-dimensional interpretation using a new and original algorithm, known as ‘Layers’, that has been especially processed for this purpose. Layers works in an automatic and non-subjective way, and allows the definition of the structural settings in terms of several layers, each representing a specific geological formation. The same data are also interpreted in terms of isolated and shallow anomalous density bodies using a well tested algorithm known as ‘Growth’. We focus our inversions on the Mt. Vesuvius volcano, while globally analyzing the entire Neapolitan area, in order to investigate the deep structures, and in particular the deep extended ‘sill’ that has been revealed by seismic tomography. The final models generally confirm the global setting of the area as outlined by previous investigations, mainly for the shape and depth of the carbonate basement below Mt. Vesuvius. The presence of lateral density contrasts inside the volcano edifice is also shown, which was only hypothesized in the 2.5-dimensional inversion. Moreover, the models allow us to note a high density body that rises from the top of the carbonate basement and further elongates above sea level. This probably represents an uprising of the same basement, which is just below the volcano and which coincides with the VP and VP/VS anomalies detected under the crater. The three-dimensional results also reveal that the two inversion methods provide very similar models, where the high density isolated body in the Growth model can be associated with the rising high density anomaly in the Layers model. Taking into account

19. Kinetic equation solution by inverse kinetic method

Salas, G.

1983-01-01

We propose a computer program (CAMU) which permits to solve the inverse kinetic equation. The CAMU code is written in HPL language for a HP 982 A microcomputer with a peripheral interface HP 9876 A ''thermal graphic printer''. The CAMU code solves the inverse kinetic equation by taking as data entry the output of the ionization chambers and integrating the equation with the help of the Simpson method. With this program we calculate the evolution of the reactivity in time for a given disturbance

20. Tectonic evolution of the Tualatin basin, northwest Oregon, as revealed by inversion of gravity data

McPhee, Darcy K.; Langenheim, Victoria E.; Wells, Ray; Blakely, Richard J.

2014-01-01

The Tualatin basin, west of Portland (Oregon, USA), coincides with a 110 mGal gravity low along the Puget-Willamette lowland. New gravity measurements (n = 3000) reveal a three-dimensional (3-D) subsurface geometry suggesting early development as a fault-bounded pull-apart basin. A strong northwest-trending gravity gradient coincides with the Gales Creek fault, which forms the southwestern boundary of the Tualatin basin. Faults along the northeastern margin in the Portland Hills and the northeast-trending Sherwood fault along the southeastern basin margin are also associated with gravity gradients, but of smaller magnitude. The gravity low reflects the large density contrast between basin fill and the mafic crust of the Siletz terrane composing basement. Inversions of gravity data indicate that the Tualatin basin is ∼6 km deep, therefore 6 times deeper than the 1 km maximum depth of the Miocene Columba River Basalt Group (CRBG) in the basin, implying that the basin contains several kilometers of low-density pre-CRBG sediments and so formed primarily before the 15 Ma emplacement of the CRBG. The shape of the basin and the location of parallel, linear basin-bounding faults along the southwest and northeast margins suggest that the Tualatin basin originated as a pull-apart rhombochasm. Pre-CRBG extension in the Tualatin basin is consistent with an episode of late Eocene extension documented elsewhere in the Coast Ranges. The present fold and thrust geometry of the Tualatin basin, the result of Neogene compression, is superimposed on the ancestral pull-apart basin. The present 3-D basin geometry may imply stronger ground shaking along basin edges, particularly along the concealed northeast edge of the Tualatin basin beneath the greater Portland area.

1. DenInv3D: a geophysical software for three-dimensional density inversion of gravity field data

Tian, Yu; Ke, Xiaoping; Wang, Yong

2018-04-01

This paper presents a three-dimensional density inversion software called DenInv3D that operates on gravity and gravity gradient data. The software performs inversion modelling, kernel function calculation, and inversion calculations using the improved preconditioned conjugate gradient (PCG) algorithm. In the PCG algorithm, due to the uncertainty of empirical parameters, such as the Lagrange multiplier, we use the inflection point of the L-curve as the regularisation parameter. The software can construct unequally spaced grids and perform inversions using such grids, which enables changing the resolution of the inversion results at different depths. Through inversion of airborne gradiometry data on the Australian Kauring test site, we discovered that anomalous blocks of different sizes are present within the study area in addition to the central anomalies. The software of DenInv3D can be downloaded from http://159.226.162.30.

2. Eastern US crustal thickness estimates from spectral analysis and inversion of onshore Bouguer gravity anaomalies

Dybus, W.; Benoit, M. H.; Ebinger, C. J.

2011-12-01

The crustal thickness beneath much of the eastern half of the US is largely unconstrained. Though there have been several controlled source seismic surveys of the region, many of these studies suffer from rays that turn in the crust above the Moho, resulting in somewhat ambiguous crustal thickness values. Furthermore, the broadband seismic station coverage east of the Mississippi has been limited, and most of the region remains largely understudied. In this study, we estimated the depth to the Moho using both spectral analysis and inversion of Bouguer gravity anomalies. We systematically estimated depths to lithospheric density contrasts from radial power spectra of Bouguer gravity within 100 km X 100 km windows eastward from the Mississippi River to the Atlantic Coast, and northward from North Carolina to Maine. The slopes and slope breaks in the radial power spectra were computed using an automated algorithm. The slope values for each window were visually inspected and then used to estimate the depth to the Moho and other lithospheric density contrasts beneath each windowed region. Additionally, we performed a standard Oldenburg-Parker inversion for lithospheric density contrasts using various reference depths and density contrasts that are realistic for the different physiographic provinces in the Eastern US. Our preliminary results suggest that the gravity-derived Moho depths are similar to those found using seismic data, and that the crust is relatively thinner (~28-33 km) than expected in beneath the Piedmont region (~35-40 km). Given the relative paucity of seismic data in the eastern US, analysis of onshore gravity data is a valuable tool for interpolating between seismic stations.

3. The quest for the perfect gravity anomaly: Part 2 - Mass effects and anomaly inversion

Keller, Gordon R.; Hildenbrand, T.G.; Hinze, W. J.; Li, X.; Ravat, D.; Webring, M.

2006-01-01

Gravity anomalies have become an important tool for geologic studies since the widespread use of high-precision gravimeters after the Second World War. More recently the development of instrumentation for airborne gravity observations, procedures for acquiring data from satellite platforms, the readily available Global Positioning System for precise vertical and horizontal control, improved global data bases, and enhancement of computational hardware and software have accelerated the use of the gravity method. As a result, efforts are being made to improve the gravity databases that are made available to the geoscience community by broadening their observational holdings and increasing the accuracy and precision of the included data. Currently the North American Gravity Database as well as the individual databases of Canada, Mexico, and the United States of America are being revised using new formats and standards. The objective of this paper is to describe the use of the revised standards for gravity data processing and modeling and there impact on geological interpretations. ?? 2005 Society of Exploration Geophysicists.

4. Multi-GPU parallel algorithm design and analysis for improved inversion of probability tomography with gravity gradiometry data

Hou, Zhenlong; Huang, Danian

2017-09-01

In this paper, we make a study on the inversion of probability tomography (IPT) with gravity gradiometry data at first. The space resolution of the results is improved by multi-tensor joint inversion, depth weighting matrix and the other methods. Aiming at solving the problems brought by the big data in the exploration, we present the parallel algorithm and the performance analysis combining Compute Unified Device Architecture (CUDA) with Open Multi-Processing (OpenMP) based on Graphics Processing Unit (GPU) accelerating. In the test of the synthetic model and real data from Vinton Dome, we get the improved results. It is also proved that the improved inversion algorithm is effective and feasible. The performance of parallel algorithm we designed is better than the other ones with CUDA. The maximum speedup could be more than 200. In the performance analysis, multi-GPU speedup and multi-GPU efficiency are applied to analyze the scalability of the multi-GPU programs. The designed parallel algorithm is demonstrated to be able to process larger scale of data and the new analysis method is practical.

5. Large Airborne Full Tensor Gradient Data Inversion Based on a Non-Monotone Gradient Method

Sun, Yong; Meng, Zhaohai; Li, Fengting

2018-03-01

Following the development of gravity gradiometer instrument technology, the full tensor gravity (FTG) data can be acquired on airborne and marine platforms. Large-scale geophysical data can be obtained using these methods, making such data sets a number of the "big data" category. Therefore, a fast and effective inversion method is developed to solve the large-scale FTG data inversion problem. Many algorithms are available to accelerate the FTG data inversion, such as conjugate gradient method. However, the conventional conjugate gradient method takes a long time to complete data processing. Thus, a fast and effective iterative algorithm is necessary to improve the utilization of FTG data. Generally, inversion processing is formulated by incorporating regularizing constraints, followed by the introduction of a non-monotone gradient-descent method to accelerate the convergence rate of FTG data inversion. Compared with the conventional gradient method, the steepest descent gradient algorithm, and the conjugate gradient algorithm, there are clear advantages of the non-monotone iterative gradient-descent algorithm. Simulated and field FTG data were applied to show the application value of this new fast inversion method.

6. Invariant models in the inversion of gravity and magnetic fields and their derivatives

Ialongo, Simone; Fedi, Maurizio; Florio, Giovanni

2014-11-01

In potential field inversion problems we usually solve underdetermined systems and realistic solutions may be obtained by introducing a depth-weighting function in the objective function. The choice of the exponent of such power-law is crucial. It was suggested to determine it from the field-decay due to a single source-block; alternatively it has been defined as the structural index of the investigated source distribution. In both cases, when k-order derivatives of the potential field are considered, the depth-weighting exponent has to be increased by k with respect that of the potential field itself, in order to obtain consistent source model distributions. We show instead that invariant and realistic source-distribution models are obtained using the same depth-weighting exponent for the magnetic field and for its k-order derivatives. A similar behavior also occurs in the gravity case. In practice we found that the depth weighting-exponent is invariant for a given source-model and equal to that of the corresponding magnetic field, in the magnetic case, and of the 1st derivative of the gravity field, in the gravity case. In the case of the regularized inverse problem, with depth-weighting and general constraints, the mathematical demonstration of such invariance is difficult, because of its non-linearity, and of its variable form, due to the different constraints used. However, tests performed on a variety of synthetic cases seem to confirm the invariance of the depth-weighting exponent. A final consideration regards the role of the regularization parameter; we show that the regularization can severely affect the depth to the source because the estimated depth tends to increase proportionally with the size of the regularization parameter. Hence, some care is needed in handling the combined effect of the regularization parameter and depth weighting.

7. Terrain Classification on Venus from Maximum-Likelihood Inversion of Parameterized Models of Topography, Gravity, and their Relation

Eggers, G. L.; Lewis, K. W.; Simons, F. J.; Olhede, S.

2013-12-01

topography and gravity, in which the INITIAL loading by topography retains the Matern form but the FINAL topography and gravity are the result of flexural compensation. In our modeling, we pay explicit attention to finite-field spectral estimation effects (and their remedy via tapering), and to the implementation of statistical tests (for anisotropy, for initial-loading process correlation, to ascertain the proper density contrasts and interface depth in a two-layer model), robustness assessment and uncertainty quantification, as well as to algorithmic intricacies related to low-dimensional but poorly scaled maximum-likelihood inversions. We conclude that Venusian geomorphic terrains are well described by their 2-D topographic and gravity (cross-)power spectra, and the spectral properties of distinct geologic provinces on Venus are worth quantifying via maximum-likelihood-based methods under idealized three-parameter Matern distributions. Analysis of fitted parameters and the fitted-data residuals reveals natural variability in the (sub)surface properties on Venus, as well as some directional anisotropy. Geologic regions tend to cluster according to terrain type in our parameter space, which we analyze to confirm their shared geologic histories and utilize for guidance in ongoing mapping efforts of Venus and other terrestrial bodies.

8. Implicit structural inversion of gravity data using linear programming, a validation study

Zon, A.T. van; Roy Chowdhury, K.

2010-01-01

In this study, a regional scale gravity data set has been inverted to infer the structure (topography) of the top of the basement underlying sub-horizontal strata. We apply our method to this real data set for further proof of concept, validation and benchmarking against results from an earlier

9. Uncertainty reduction of gravity and magnetic inversion through the integration of petrophysical constraints and geological data

Giraud, Jérémie; Jessell, Mark; Lindsay, Mark; Martin, Roland; Pakyuz-Charrier, Evren; Ogarko, Vitaliy

2016-04-01

measurements and standard values obtained from the literature. Finally, we ran the different inversions on gravity and magnetic data generated using this model. As a result, the use of petrophysical constraints permits us to retrieve sharper boundaries while prior structural information from geology on the shallow lithologies permits to retrieve the contacts more accurately. The integration of the different constraints provides a better-resolved model, with reduced uncertainties such as improved posterior covariance and resolution matrices. The analysis of the sensitivity to and resolution indicators using geological a priori information and petrophysical constraints shows complementarity between the resolution matrices. Moreover, the comparison of the posterior covariance matrices (diagonal and non-diagonal elements) shows that when geological prior information and petrophysical constraints are used together higher values coincide with poorly resolved lithologies. This is not always the case when either only geological prior information or no constraints are used. However, the improvement of the inversion results due to the constraints and prior information are more pronounced on gravity inversion than on magnetic inversion.

10. Gravity Wave Dynamics in a Mesospheric Inversion Layer: 1. Reflection, Trapping, and Instability Dynamics

Laughman, Brian; Wang, Ling; Lund, Thomas S.; Collins, Richard L.

2018-01-01

Abstract An anelastic numerical model is employed to explore the dynamics of gravity waves (GWs) encountering a mesosphere inversion layer (MIL) having a moderate static stability enhancement and a layer of weaker static stability above. Instabilities occur within the MIL when the GW amplitude approaches that required for GW breaking due to compression of the vertical wavelength accompanying the increasing static stability. Thus, MILs can cause large‐amplitude GWs to yield instabilities and turbulence below the altitude where they would otherwise arise. Smaller‐amplitude GWs encountering a MIL do not lead to instability and turbulence but do exhibit partial reflection and transmission, and the transmission is a smaller fraction of the incident GW when instabilities and turbulence arise within the MIL. Additionally, greater GW transmission occurs for weaker MILs and for GWs having larger vertical wavelengths relative to the MIL depth and for lower GW intrinsic frequencies. These results imply similar dynamics for inversions due to other sources, including the tropopause inversion layer, the high stability capping the polar summer mesopause, and lower frequency GWs or tides having sufficient amplitudes to yield significant variations in stability at large and small vertical scales. MILs also imply much stronger reflections and less coherent GW propagation in environments having significant fine structure in the stability and velocity fields than in environments that are smoothly varying. PMID:29576994

11. Inverse amplitude method and Adler zeros

Gomez Nicola, A.; Pelaez, J. R.; Rios, G.

2008-01-01

The inverse amplitude method is a powerful unitarization technique to enlarge the energy applicability region of effective Lagrangians. It has been widely used to describe resonances in hadronic physics, combined with chiral perturbation theory, as well as in the strongly interacting symmetry breaking sector. In this work we show how it can be slightly modified to also account for the subthreshold region, incorporating correctly the Adler zeros required by chiral symmetry and eliminating spurious poles. These improvements produce negligible effects on the physical region.

12. Approximate inverse preconditioning of iterative methods for nonsymmetric linear systems

Benzi, M. [Universita di Bologna (Italy); Tuma, M. [Inst. of Computer Sciences, Prague (Czech Republic)

1996-12-31

A method for computing an incomplete factorization of the inverse of a nonsymmetric matrix A is presented. The resulting factorized sparse approximate inverse is used as a preconditioner in the iterative solution of Ax = b by Krylov subspace methods.

13. Active Response Gravity Offload and Method

Dungan, Larry K. (Inventor); Valle, Paul S. (Inventor); Bankieris, Derek R. (Inventor); Lieberman, Asher P. (Inventor); Redden, Lee (Inventor); Shy, Cecil (Inventor)

2015-01-01

A variable gravity field simulator can be utilized to provide three dimensional simulations for simulated gravity fields selectively ranging from Moon, Mars, and micro-gravity environments and/or other selectable gravity fields. The gravity field simulator utilizes a horizontally moveable carriage with a cable extending from a hoist. The cable can be attached to a load which experiences the effects of the simulated gravity environment. The load can be a human being or robot that makes movements that induce swinging of the cable whereby a horizontal control system reduces swinging energy. A vertical control system uses a non-linear feedback filter to remove noise from a load sensor that is in the same frequency range as signals from the load sensor.

14. Shallow structure of the Somma Vesuvius volcano from 3D inversion of gravity data

Cella, Federico; Fedi, Maurizio; Florio, Giovanni; Grimaldi, Marino; Rapolla, Antonio

2007-04-01

A gravity investigation was carried out in the Somma-Vesuvius complex area (Campania, Italy) based on a dataset recently enlarged with new measurements. These cover the volcanic top and fill some other important spatial gaps in previous surveys. Besides the new gravity map of the Vesuvius, we also present the results of a 3D inverse modelling, carried out by using constraints from deep well exploration and seismic reflection surveys. The resulting density model provides a complete reconstruction of the top of the carbonate basement. This is relevant mostly on the western side of the survey area, where no significant information was previously available. Other new information regards the Somma-Vesuvius structure. It consists of an annular volume of rocks around the volcanic vent and that extends down to the carbonate basement. It results to be denser with respect to the surrounding sedimentary cover of the Campanian Plain and to the material located just along the central axis of the volcanic structure. The coherence between these features and other geophysical evidences from previous studies, will be discussed together with the other results of this research.

15. Structural interpretation of El Hierro (Canary Islands) rifts system from gravity inversion modelling

Sainz-Maza, S.; Montesinos, F. G.; Martí, J.; Arnoso, J.; Calvo, M.; Borreguero, A.

2017-08-01

Recent volcanism in El Hierro Island is mostly concentrated along three elongated and narrow zones which converge at the center of the island. These zones with extensive volcanism have been identified as rift zones. The presence of similar structures is common in many volcanic oceanic islands, so understanding their origin, dynamics and structure is important to conduct hazard assessment in such environments. There is still not consensus on the origin of the El Hierro rift zones, having been associated with mantle uplift or interpreted as resulting from gravitational spreading and flank instability. To further understand the internal structure and origin of the El Hierro rift systems, starting from the previous gravity studies, we developed a new 3D gravity inversion model for its shallower layers, gathering a detailed picture of this part of the island, which has permitted a new interpretation about these rifts. Previous models already identified a main central magma accumulation zone and several shallower high density bodies. The new model allows a better resolution of the pathways that connect both levels and the surface. Our results do not point to any correspondence between the upper parts of these pathways and the rift identified at the surface. Non-clear evidence of progression toward deeper parts into the volcanic system is shown, so we interpret them as very shallow structures, probably originated by local extensional stresses derived from gravitational loading and flank instability, which are used to facilitate the lateral transport of magma when it arrives close to the surface.

16. Numerical Methods for Bayesian Inverse Problems

Ernst, Oliver

2014-01-06

We present recent results on Bayesian inversion for a groundwater flow problem with an uncertain conductivity field. In particular, we show how direct and indirect measurements can be used to obtain a stochastic model for the unknown. The main tool here is Bayes’ theorem which merges the indirect data with the stochastic prior model for the conductivity field obtained by the direct measurements. Further, we demonstrate how the resulting posterior distribution of the quantity of interest, in this case travel times of radionuclide contaminants, can be obtained by Markov Chain Monte Carlo (MCMC) simulations. Moreover, we investigate new, promising MCMC methods which exploit geometrical features of the posterior and which are suited to infinite dimensions.

17. Numerical Methods for Bayesian Inverse Problems

Ernst, Oliver; Sprungk, Bjorn; Cliffe, K. Andrew; Starkloff, Hans-Jorg

2014-01-01

We present recent results on Bayesian inversion for a groundwater flow problem with an uncertain conductivity field. In particular, we show how direct and indirect measurements can be used to obtain a stochastic model for the unknown. The main tool here is Bayes’ theorem which merges the indirect data with the stochastic prior model for the conductivity field obtained by the direct measurements. Further, we demonstrate how the resulting posterior distribution of the quantity of interest, in this case travel times of radionuclide contaminants, can be obtained by Markov Chain Monte Carlo (MCMC) simulations. Moreover, we investigate new, promising MCMC methods which exploit geometrical features of the posterior and which are suited to infinite dimensions.

18. Crustal and Upper Mantle Structure from Joint Inversion of Body Wave and Gravity Data

2012-09-01

We use both free-air and Bouguer gravity anomalies derived from the global gravity model of the GRACE satellite mission. The gravity data provide...relocation analysis. We use both free-air and Bouguer gravity anomalies derived from the global gravity model of the GRACE satellite mission. The gravity...topographic relief this effect needs to be removed; thus, we converted free-air anomalies into Bouguer anomalies assuming a standard density for crustal rocks

19. Characterising East Antarctic Lithosphere and its Rift Systems using Gravity Inversion

Vaughan, Alan P. M.; Kusznir, Nick J.; Ferraccioli, Fausto; Leat, Phil T.; Jordan, Tom A. R. M.; Purucker, Michael E.; Golynsky, A. V. Sasha; Rogozhina, Irina

2013-04-01

Since the International Geophysical Year (1957), a view has prevailed that East Antarctica has a relatively homogeneous lithospheric structure, consisting of a craton-like mosaic of Precambrian terranes, stable since the Pan-African orogeny ~500 million years ago (e.g. Ferracioli et al. 2011). Recent recognition of a continental-scale rift system cutting the East Antarctic interior has crystallised an alternative view of much more recent geological activity with important implications. The newly defined East Antarctic Rift System (EARS) (Ferraccioli et al. 2011) appears to extend from at least the South Pole to the continental margin at the Lambert Rift, a distance of 2500 km. This is comparable in scale to the well-studied East African rift system. New analysis of RadarSat data by Golynsky & Golynsky (2009) indicates that further rift zones may form widely distributed extension zones within the continent. A pilot study (Vaughan et al. 2012), using a newly developed gravity inversion technique (Chappell & Kusznir 2008) with existing public domain satellite data, shows distinct crustal thickness provinces with overall high average thickness separated by thinner, possibly rifted, crust. Understanding the nature of crustal thickness in East Antarctica is critical because: 1) this is poorly known along the ocean-continent transition, but is necessary to improve the plate reconstruction fit between Antarctica, Australia and India in Gondwana, which will also better define how and when these continents separated; 2) lateral variation in crustal thickness can be used to test supercontinent reconstructions and assess the effects of crystalline basement architecture and mechanical properties on rifting; 3) rift zone trajectories through East Antarctica will define the geometry of zones of crustal and lithospheric thinning at plate-scale; 4) it is not clear why or when the crust of East Antarctica became so thick and elevated, but knowing this can be used to test models of

20. Surface mass redistribution inversion from global GPS deformation and Gravity Recovery and Climate Experiment (GRACE) gravity data

Kusche, J.; Schrama, E.J.O.

2005-01-01

Monitoring hydrological redistributions through their integrated gravitational effect is the primary aim of the Gravity Recovery and Climate Experiment (GRACE) mission. Time?variable gravity data from GRACE can be uniquely inverted to hydrology, since mass transfers located at or near the Earth's

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

CUI, C.; Hou, W.

2017-12-01

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

2. On quasiclassical approximation in the inverse scattering method

Geogdzhaev, V.V.

1985-01-01

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

3. Radiation Source Mapping with Bayesian Inverse Methods

Hykes, Joshua Michael

We present a method to map the spectral and spatial distributions of radioactive sources using a small number of detectors. Locating and identifying radioactive materials is important for border monitoring, accounting for special nuclear material in processing facilities, and in clean-up operations. Most methods to analyze these problems make restrictive assumptions about the distribution of the source. In contrast, the source-mapping method presented here allows an arbitrary three-dimensional distribution in space and a flexible group and gamma peak distribution in energy. To apply the method, the system's geometry and materials must be known. A probabilistic Bayesian approach is used to solve the resulting inverse problem (IP) since the system of equations is ill-posed. The probabilistic approach also provides estimates of the confidence in the final source map prediction. A set of adjoint flux, discrete ordinates solutions, obtained in this work by the Denovo code, are required to efficiently compute detector responses from a candidate source distribution. These adjoint fluxes are then used to form the linear model to map the state space to the response space. The test for the method is simultaneously locating a set of 137Cs and 60Co gamma sources in an empty room. This test problem is solved using synthetic measurements generated by a Monte Carlo (MCNP) model and using experimental measurements that we collected for this purpose. With the synthetic data, the predicted source distributions identified the locations of the sources to within tens of centimeters, in a room with an approximately four-by-four meter floor plan. Most of the predicted source intensities were within a factor of ten of their true value. The chi-square value of the predicted source was within a factor of five from the expected value based on the number of measurements employed. With a favorable uniform initial guess, the predicted source map was nearly identical to the true distribution

4. Some technical details concerning a new method of gravimetric-seismic inversion

Strykowski, Gabriel

1999-01-01

In this paper a number of technical details related to a new method of gravimetric-seismic inversion, which is still under development, are explained. Although the present contribution aims on providing general statements on how to formulate and solve complex gravimetric-seismic modeling; problems......, the inspiration comes from the practical modeling problems in the area of Jutland peninsula (Denmark). More specifically, the methodological aspects of the proposed inversion method are illustrated on a problem of 3D modeling of the intra crustal intrusion associated with the Silkeborg Gravity High. The existing...... refraction seismic profile locates the source of the anomaly in depths 10 km - 18 km. In an earlier publication, (Strykowski, 1998), and for the same test area, a method of complex geological stripping is described. The present contribution is a continuation of this paper in the direction of inversion...

5. Moho geometry gravity inversion experiment (MoGGIE): A refined model of the Australian Moho, and its tectonic and isostatic implications

Aitken, Alan R. A.

2010-08-01

At the continent-scale, models of Moho depth based on seismic estimates alone can be inadequate due to irregular or sparse data. Gravity-based Moho modelling provides better coverage, however, the methods used are typically hampered by an inability to explicitly honour seismic constraints and are also limited by over simplistic model conditions, e.g. laterally-homogenous layering. I present a new method to generate a continent-scale Moho model, based on the constrained inversion of free-air gravity data. This method explicitly honours seismic Moho estimates and accounts for a laterally heterogeneous crust and mantle. Resolution and sensitivity testing shows that, for wavelengths greater than 200 km, crustal density and Moho depth are recovered with reasonable accuracy, ± 30 kg m - 3 and ± 3 km respectively. MoGGIE uses a six layer model incorporating ocean, sedimentary basin, upper crust, lower/oceanic crust, eclogitised crust and mantle. Inversion variables were the density of the crustal layers, constrained by a standard density model, and the depths to intra-crustal boundaries and the Moho, constrained by 230 seismic depth estimates. The results demonstrate that a balanced approach to seismically-constrained gravity inversion has the capability to generate detailed and well-constrained models of the Moho and crustal density at the continent-scale. For Australia, this is a clear improvement on the sparse and irregular resolution of the Moho provided by seismic estimates of crustal thickness, which fail to resolve short-wavelength features. Newly defined tectonic features include extensive magmatic underplates, crustal-scale shear zones, and the boundaries between tectonic blocks. Isostatic analysis reveals that little of the continent is close to isostatic equilibrium, with isostatic disequilibria preserved at multiple scales, from hundreds of kilometres to the entire continent. These disequilibria are interpreted to indicate long-wavelength flexure of highly

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

Matoba, Tohru; Funahashi, Akimasa

1975-09-01

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

7. Improved artificial bee colony algorithm based gravity matching navigation method.

Gao, Wei; Zhao, Bo; Zhou, Guang Tao; Wang, Qiu Ying; Yu, Chun Yang

2014-07-18

Gravity matching navigation algorithm is one of the key technologies for gravity aided inertial navigation systems. With the development of intelligent algorithms, the powerful search ability of the Artificial Bee Colony (ABC) algorithm makes it possible to be applied to the gravity matching navigation field. However, existing search mechanisms of basic ABC algorithms cannot meet the need for high accuracy in gravity aided navigation. Firstly, proper modifications are proposed to improve the performance of the basic ABC algorithm. Secondly, a new search mechanism is presented in this paper which is based on an improved ABC algorithm using external speed information. At last, modified Hausdorff distance is introduced to screen the possible matching results. Both simulations and ocean experiments verify the feasibility of the method, and results show that the matching rate of the method is high enough to obtain a precise matching position.

8. Systems and Methods for Gravity-Independent Gripping and Drilling

Parness, Aaron (Inventor); Frost, Matthew A. (Inventor); Thatte, Nitish (Inventor); King, Jonathan P. (Inventor)

2016-01-01

Systems and methods for gravity independent gripping and drilling are described. The gripping device can also comprise a drill or sampling devices for drilling and/or sampling in microgravity environments, or on vertical or inverted surfaces in environments where gravity is present. A robotic system can be connected with the gripping and drilling devices via an ankle interface adapted to distribute the forces realized from the robotic system.

9. REGULARIZED D-BAR METHOD FOR THE INVERSE CONDUCTIVITY PROBLEM

Knudsen, Kim; Lassas, Matti; Mueller, Jennifer

2009-01-01

A strategy for regularizing the inversion procedure for the two-dimensional D-bar reconstruction algorithm based on the global uniqueness proof of Nachman [Ann. Math. 143 (1996)] for the ill-posed inverse conductivity problem is presented. The strategy utilizes truncation of the boundary integral...... the convergence of the reconstructed conductivity to the true conductivity as the noise level tends to zero. The results provide a link between two traditions of inverse problems research: theory of regularization and inversion methods based on complex geometrical optics. Also, the procedure is a novel...

10. Hybrid inverse design method for nonlifting bodies in incompressible flow

Broughton, BA

2006-11-01

Full Text Available A methodology for the inverse design of non-lifting axisymmetric bodies in compressible flow is presented. In this method, an inverse design approach based on conformal mapping is used to design a set of airfoils in isolation. These airfoils...

11. Gravity enhanced acoustic levitation method and apparatus

Barmatz, M. B.; Allen, J. L.; Granett, D. (Inventor)

1985-01-01

An acoustic levitation system is provided for acoustically levitating an object by applying a single frequency from a transducer into a resonant chamber surrounding the object. The chamber includes a stabilizer location along its height, where the side walls of the chamber are angled so they converge in an upward direction. When an acoustic standing wave pattern is applied between the top and bottom of the chamber, a levitation surface within the stabilizer does not lie on a horizontal plane, but instead is curved with a lowermost portion near the vertical axis of the chamber. As a result, an acoustically levitated object is urged by gravity towards the lowermost location on the levitation surface, so the object is kept away from the side walls of the chamber.

12. Inverse dualization and non-local dualities between Einstein gravity and supergravities

Chen Chiangmei; Gal'tsov, Dmitri V; Sharakin, Sergei A

2002-01-01

We investigate non-local dualities between suitably compactified higher dimensional Einstein gravity and supergravities which can be revealed if one reinterprets the dualized Kaluza-Klein 2-forms in D>4 as antisymmetric forms belonging to supergravities. We find several examples of such a correspondence including one between the six-dimensional Einstein gravity and the four-dimensional Einstein-Maxwell-dilaton-axion theory (truncated N=4 supergravity), and others between the compactified eleven- and ten-dimensional supergravities and the eight- or ten-dimensional pure gravity. The Killing spinor equation of the D=11 supergravity is shown to be equivalent to the geometric Killing spinor equation in the dual gravity. We give several examples of using new dualities for solution generation and demonstrate how p-branes can be interpreted as non-local duals of pure gravity solutions. New supersymmetric solutions are presented including M2 subset of 5-brane with two rotation parameters

13. A direct sampling method to an inverse medium scattering problem

Ito, Kazufumi; Jin, Bangti; Zou, Jun

2012-01-01

In this work we present a novel sampling method for time harmonic inverse medium scattering problems. It provides a simple tool to directly estimate the shape of the unknown scatterers (inhomogeneous media), and it is applicable even when

14. A two-stage method for inverse medium scattering

Ito, Kazufumi; Jin, Bangti; Zou, Jun

2013-01-01

We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from noisy near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer

15. A direct sampling method for inverse electromagnetic medium scattering

Ito, Kazufumi; Jin, Bangti; Zou, Jun

2013-01-01

In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric/magnetic near-field data. We shall develop a novel direct sampling method based

16. Review of Electrical and Gravity Methods of Near-Surface ...

USER

ABSTRACT: The theory and practice of electrical and gravity methods of geophysics for groundwater exploration was reviewed with illustrations and data examples. With the goal of reducing cases of borehole/water-well failure attributed to the lack of the knowledge of the methods of geophysics for groundwater exploration ...

17. Gravity

Gamow, George

2003-01-01

A distinguished physicist and teacher, George Gamow also possessed a special gift for making the intricacies of science accessible to a wide audience. In Gravity, he takes an enlightening look at three of the towering figures of science who unlocked many of the mysteries behind the laws of physics: Galileo, the first to take a close look at the process of free and restricted fall; Newton, originator of the concept of gravity as a universal force; and Einstein, who proposed that gravity is no more than the curvature of the four-dimensional space-time continuum.Graced with the author's own draw

18. Full Waveform Inversion Using Oriented Time Migration Method

Zhang, Zhendong

2016-04-12

Full waveform inversion (FWI) for reflection events is limited by its linearized update requirements given by a process equivalent to migration. Unless the background velocity model is reasonably accurate the resulting gradient can have an inaccurate update direction leading the inversion to converge into what we refer to as local minima of the objective function. In this thesis, I first look into the subject of full model wavenumber to analysis the root of local minima and suggest the possible ways to avoid this problem. And then I analysis the possibility of recovering the corresponding wavenumber components through the existing inversion and migration algorithms. Migration can be taken as a generalized inversion method which mainly retrieves the high wavenumber part of the model. Conventional impedance inversion method gives a mapping relationship between the migration image (high wavenumber) and model parameters (full wavenumber) and thus provides a possible cascade inversion strategy to retrieve the full wavenumber components from seismic data. In the proposed approach, consider a mild lateral variation in the model, I find an analytical Frechet derivation corresponding to the new objective function. In the proposed approach, the gradient is given by the oriented time-domain imaging method. This is independent of the background velocity. Specifically, I apply the oriented time-domain imaging (which depends on the reflection slope instead of a background velocity) on the data residual to obtain the geometrical features of the velocity perturbation. Assuming that density is constant, the conventional 1D impedance inversion method is also applicable for 2D or 3D velocity inversion within the process of FWI. This method is not only capable of inverting for velocity, but it is also capable of retrieving anisotropic parameters relying on linearized representations of the reflection response. To eliminate the cross-talk artifacts between different parameters, I

19. Inversions

Brown, Malcolm

2009-01-01

Inversions are fascinating phenomena. They are reversals of the normal or expected order. They occur across a wide variety of contexts. What do inversions have to do with learning spaces? The author suggests that they are a useful metaphor for the process that is unfolding in higher education with respect to education. On the basis of…

20. Review of Electrical and Gravity Methods of Near-Surface ...

USER

In every big city, dozen of new boreholes or hand-dug wells are .... This paper is a review of the electrical and gravity methods of ... audience/readership. II. ..... W. W. Northon and Company, New York. Butler ... McGraw Hill Books Co. New York ...

1. Estimating surface acoustic impedance with the inverse method.

Piechowicz, Janusz

2011-01-01

Sound field parameters are predicted with numerical methods in sound control systems, in acoustic designs of building and in sound field simulations. Those methods define the acoustic properties of surfaces, such as sound absorption coefficients or acoustic impedance, to determine boundary conditions. Several in situ measurement techniques were developed; one of them uses 2 microphones to measure direct and reflected sound over a planar test surface. Another approach is used in the inverse boundary elements method, in which estimating acoustic impedance of a surface is expressed as an inverse boundary problem. The boundary values can be found from multipoint sound pressure measurements in the interior of a room. This method can be applied to arbitrarily-shaped surfaces. This investigation is part of a research programme on using inverse methods in industrial room acoustics.

2. Inverse thermal analysis method to study solidification in cast iron

Dioszegi, Atilla; Hattel, Jesper

2004-01-01

Solidification modelling of cast metals is widely used to predict final properties in cast components. Accurate models necessitate good knowledge of the solidification behaviour. The present study includes a re-examination of the Fourier thermal analysis method. This involves an inverse numerical...... solution of a 1-dimensional heat transfer problem connected to solidification of cast alloys. In the analysis, the relation between the thermal state and the fraction solid of the metal is evaluated by a numerical method. This method contains an iteration algorithm controlled by an under relaxation term...... inverse thermal analysis was tested on both experimental and simulated data....

3. A Stochastic Inversion Method for Potential Field Data: Ant Colony Optimization

Liu, Shuang; Hu, Xiangyun; Liu, Tianyou

2014-07-01

Simulating natural ants' foraging behavior, the ant colony optimization (ACO) algorithm performs excellently in combinational optimization problems, for example the traveling salesman problem and the quadratic assignment problem. However, the ACO is seldom used to inverted for gravitational and magnetic data. On the basis of the continuous and multi-dimensional objective function for potential field data optimization inversion, we present the node partition strategy ACO (NP-ACO) algorithm for inversion of model variables of fixed shape and recovery of physical property distributions of complicated shape models. We divide the continuous variables into discrete nodes and ants directionally tour the nodes by use of transition probabilities. We update the pheromone trails by use of Gaussian mapping between the objective function value and the quantity of pheromone. It can analyze the search results in real time and promote the rate of convergence and precision of inversion. Traditional mapping, including the ant-cycle system, weaken the differences between ant individuals and lead to premature convergence. We tested our method by use of synthetic data and real data from scenarios involving gravity and magnetic anomalies. The inverted model variables and recovered physical property distributions were in good agreement with the true values. The ACO algorithm for binary representation imaging and full imaging can recover sharper physical property distributions than traditional linear inversion methods. The ACO has good optimization capability and some excellent characteristics, for example robustness, parallel implementation, and portability, compared with other stochastic metaheuristics.

4. An inverse method for color uniformity in white LED spotlights

Prins, C.R.; Thije Boonkkamp, ten J.H.M.; Tukker, T.W.; IJzerman, W.L.

2013-01-01

Color over Angle (CoA) variation in the light output of white phosphor-converted LEDs is a common problem in LED lighting technology. In this article we propose an inverse method to design an optical element that eliminates the color variation for a point light source. The method in this article is

5. An inverse method for color uniformity in white LED spotlights

Prins, C.R.; Thije Boonkkamp, ten J.H.M.; Tukker, T.W.; IJzerman, W.L.

2014-01-01

Color over Angle (CoA) variation in the light output of white phosphor-converted LEDs is a common problem in LED lighting technology. In this article we propose an inverse method to design an optical element that eliminates the color variation for a point light source. The method in this article is

6. gravity

We study the cosmological dynamics for R p exp( λ R ) gravity theory in the metric formalism, using dynamical systems approach. Considering higher-dimensional FRW geometries in case of an imperfect fluid which has two different scale factors in the normal and extra dimensions, we find the exact solutions, and study its ...

7. Uniqueness and numerical methods in inverse obstacle scattering

Kress, Rainer

2007-01-01

The inverse problem we consider in this tutorial is to determine the shape of an obstacle from the knowledge of the far field pattern for scattering of time-harmonic plane waves. In the first part we will concentrate on the issue of uniqueness, i.e., we will investigate under what conditions an obstacle and its boundary condition can be identified from a knowledge of its far field pattern for incident plane waves. We will review some classical and some recent results and draw attention to open problems. In the second part we will survey on numerical methods for solving inverse obstacle scattering problems. Roughly speaking, these methods can be classified into three groups. Iterative methods interpret the inverse obstacle scattering problem as a nonlinear ill-posed operator equation and apply iterative schemes such as regularized Newton methods, Landweber iterations or conjugate gradient methods for its solution. Decomposition methods, in principle, separate the inverse scattering problem into an ill-posed linear problem to reconstruct the scattered wave from its far field and the subsequent determination of the boundary of the scatterer from the boundary condition. Finally, the third group consists of the more recently developed sampling methods. These are based on the numerical evaluation of criteria in terms of indicator functions that decide whether a point lies inside or outside the scatterer. The tutorial will give a survey by describing one or two representatives of each group including a discussion on the various advantages and disadvantages

8. Structural appraisal of the Gadag schist belt from gravity investigations

R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22

From qualitative analysis of the gravity data, several tectonic features are ... major types of schist belts are identified in the ... Dharwar craton; Gadag schist belt; gravity method; inversion. ..... the Research Associateship of Dr D Himabindu.

9. Estimating Moho basement and faults using gravity inversion in Yushu-earthquake area, China

Yang Guangliang

2012-05-01

Full Text Available A gravity survey was conducted one month after the 2010 Yushu earthquake in the epicenter area. The cross-fault survey line was 500 km long, from Langqian county to Qingshuihe county, in a transition zone between Bayan Har block and Qiangtang block, in an area of high elevation, large undulating terrain, and complex geological features. An interpretation of the data was carried out together with other kinds of data, such as seismic exploration and magnetic exploration. The result shows that gravity is sensitive to fault boundary; the geologic structure of the region is complex at middle and upper depths, and the density profile reveals an eastward-pushing fault movement.

10. On multiple level-set regularization methods for inverse problems

DeCezaro, A; Leitão, A; Tai, X-C

2009-01-01

We analyze a multiple level-set method for solving inverse problems with piecewise constant solutions. This method corresponds to an iterated Tikhonov method for a particular Tikhonov functional G α based on TV–H 1 penalization. We define generalized minimizers for our Tikhonov functional and establish an existence result. Moreover, we prove convergence and stability results of the proposed Tikhonov method. A multiple level-set algorithm is derived from the first-order optimality conditions for the Tikhonov functional G α , similarly as the iterated Tikhonov method. The proposed multiple level-set method is tested on an inverse potential problem. Numerical experiments show that the method is able to recover multiple objects as well as multiple contrast levels

11. A high-order SPH method by introducing inverse kernels

Le Fang

2017-02-01

Full Text Available The smoothed particle hydrodynamics (SPH method is usually expected to be an efficient numerical tool for calculating the fluid-structure interactions in compressors; however, an endogenetic restriction is the problem of low-order consistency. A high-order SPH method by introducing inverse kernels, which is quite easy to be implemented but efficient, is proposed for solving this restriction. The basic inverse method and the special treatment near boundary are introduced with also the discussion of the combination of the Least-Square (LS and Moving-Least-Square (MLS methods. Then detailed analysis in spectral space is presented for people to better understand this method. Finally we show three test examples to verify the method behavior.

12. Multi-frequency direct sampling method in inverse scattering problem

Kang, Sangwoo; Lambert, Marc; Park, Won-Kwang

2017-10-01

We consider the direct sampling method (DSM) for the two-dimensional inverse scattering problem. Although DSM is fast, stable, and effective, some phenomena remain unexplained by the existing results. We show that the imaging function of the direct sampling method can be expressed by a Bessel function of order zero. We also clarify the previously unexplained imaging phenomena and suggest multi-frequency DSM to overcome traditional DSM. Our method is evaluated in simulation studies using both single and multiple frequencies.

13. Gaining insight into food webs reconstructed by the inverse method

Kones, J.; Soetaert, K.E.R.; Van Oevelen, D.; Owino, J.; Mavuti, K.

2006-01-01

The use of the inverse method to analyze flow patterns of organic components in ecological systems has had wide application in ecological modeling. Through this approach, an infinite number of food web flows describing the food web and satisfying biological constraints are generated, from which one

14. A variational Bayesian method to inverse problems with impulsive noise

Jin, Bangti

2012-01-01

We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise to achieve

15. Supersymmetry, reflectionless symmetric potentials and the inverse method

Bagchi, B.

1990-01-01

The role of inverse scattering method is illustrated to examine the connection between the multi-soliton solutions of Korteweg-de Vries (KdV) equation and discrete eigenvalues of Schrodinger equation. The necessity of normalization of the Schrodinger wave functions, which are constructed purely from a supersymmetric consideration is pointed out

16. Gradient-type methods in inverse parabolic problems

Kabanikhin, Sergey; Penenko, Aleksey

2008-01-01

17. A method of inversion of satellite magnetic anomaly data

Mayhew, M. A.

1977-01-01

A method of finding a first approximation to a crustal magnetization distribution from inversion of satellite magnetic anomaly data is described. Magnetization is expressed as a Fourier Series in a segment of spherical shell. Input to this procedure is an equivalent source representation of the observed anomaly field. Instability of the inversion occurs when high frequency noise is present in the input data, or when the series is carried to an excessively high wave number. Preliminary results are given for the United States and adjacent areas.

18. Gravity interpretation of dipping faults using the variance analysis method

Essa, Khalid S

2013-01-01

A new algorithm is developed to estimate simultaneously the depth and the dip angle of a buried fault from the normalized gravity gradient data. This algorithm utilizes numerical first horizontal derivatives computed from the observed gravity anomaly, using filters of successive window lengths to estimate the depth and the dip angle of a buried dipping fault structure. For a fixed window length, the depth is estimated using a least-squares sense for each dip angle. The method is based on computing the variance of the depths determined from all horizontal gradient anomaly profiles using the least-squares method for each dip angle. The minimum variance is used as a criterion for determining the correct dip angle and depth of the buried structure. When the correct dip angle is used, the variance of the depths is always less than the variances computed using wrong dip angles. The technique can be applied not only to the true residuals, but also to the measured Bouguer gravity data. The method is applied to synthetic data with and without random errors and two field examples from Egypt and Scotland. In all cases examined, the estimated depths and other model parameters are found to be in good agreement with the actual values. (paper)

19. Indium oxide inverse opal films synthesized by structure replication method

Amrehn, Sabrina; Berghoff, Daniel; Nikitin, Andreas; Reichelt, Matthias; Wu, Xia; Meier, Torsten; Wagner, Thorsten

2016-04-01

We present the synthesis of indium oxide (In2O3) inverse opal films with photonic stop bands in the visible range by a structure replication method. Artificial opal films made of poly(methyl methacrylate) (PMMA) spheres are utilized as template. The opal films are deposited via sedimentation facilitated by ultrasonication, and then impregnated by indium nitrate solution, which is thermally converted to In2O3 after drying. The quality of the resulting inverse opal film depends on many parameters; in this study the water content of the indium nitrate/PMMA composite after drying is investigated. Comparison of the reflectance spectra recorded by vis-spectroscopy with simulated data shows a good agreement between the peak position and calculated stop band positions for the inverse opals. This synthesis is less complex and highly efficient compared to most other techniques and is suitable for use in many applications.

20. Refractive index inversion based on Mueller matrix method

Fan, Huaxi; Wu, Wenyuan; Huang, Yanhua; Li, Zhaozhao

2016-03-01

Based on Stokes vector and Jones vector, the correlation between Mueller matrix elements and refractive index was studied with the result simplified, and through Mueller matrix way, the expression of refractive index inversion was deduced. The Mueller matrix elements, under different incident angle, are simulated through the expression of specular reflection so as to analyze the influence of the angle of incidence and refractive index on it, which is verified through the measure of the Mueller matrix elements of polished metal surface. Research shows that, under the condition of specular reflection, the result of Mueller matrix inversion is consistent with the experiment and can be used as an index of refraction of inversion method, and it provides a new way for target detection and recognition technology.

1. Solution of 3D inverse scattering problems by combined inverse equivalent current and finite element methods

Kılıç, Emre; Eibert, Thomas F.

2015-01-01

An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained

2. Solution of 3D inverse scattering problems by combined inverse equivalent current and finite element methods

Kılıç, Emre, E-mail: emre.kilic@tum.de; Eibert, Thomas F.

2015-05-01

An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.

3. A finite-difference contrast source inversion method

Abubakar, A; Hu, W; Habashy, T M; Van den Berg, P M

2008-01-01

We present a contrast source inversion (CSI) algorithm using a finite-difference (FD) approach as its backbone for reconstructing the unknown material properties of inhomogeneous objects embedded in a known inhomogeneous background medium. Unlike the CSI method using the integral equation (IE) approach, the FD-CSI method can readily employ an arbitrary inhomogeneous medium as its background. The ability to use an inhomogeneous background medium has made this algorithm very suitable to be used in through-wall imaging and time-lapse inversion applications. Similar to the IE-CSI algorithm the unknown contrast sources and contrast function are updated alternately to reconstruct the unknown objects without requiring the solution of the full forward problem at each iteration step in the optimization process. The FD solver is formulated in the frequency domain and it is equipped with a perfectly matched layer (PML) absorbing boundary condition. The FD operator used in the FD-CSI method is only dependent on the background medium and the frequency of operation, thus it does not change throughout the inversion process. Therefore, at least for the two-dimensional (2D) configurations, where the size of the stiffness matrix is manageable, the FD stiffness matrix can be inverted using a non-iterative inversion matrix approach such as a Gauss elimination method for the sparse matrix. In this case, an LU decomposition needs to be done only once and can then be reused for multiple source positions and in successive iterations of the inversion. Numerical experiments show that this FD-CSI algorithm has an excellent performance for inverting inhomogeneous objects embedded in an inhomogeneous background medium

4. Regularization method for solving the inverse scattering problem

Denisov, A.M.; Krylov, A.S.

1985-01-01

The inverse scattering problem for the Schroedinger radial equation consisting in determining the potential according to the scattering phase is considered. The problem of potential restoration according to the phase specified with fixed error in a finite range is solved by the regularization method based on minimization of the Tikhonov's smoothing functional. The regularization method is used for solving the problem of neutron-proton potential restoration according to the scattering phases. The determined potentials are given in the table

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

Fang Jinqing

1993-01-01

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

6. Preliminary limits on deviation from the inverse-square law of gravity in the solar system: a power-law parameterization

Liu Meng-Yao; Zhong Ze-Hao; Han Yi-Chen; Wang Xiao-Yu; Yang Zong-Shui; Xie Yi

2014-01-01

New physics beyond the standard model of particles might cause a deviation from the inverse-square law of gravity. In some theories, it is parameterized by a power-law correction to the Newtonian gravitational force, which might originate from the simultaneous exchange of particles or modified and extended theories of gravity. Using the supplementary advances of the perihelia provided by INPOP10a (IMCCE, France) and EPM2011 (IAA RAS, Russia) ephemerides, we obtain preliminary limits on this correction. In our estimation, we take the Lense-Thirring effect due to the Sun's angular momentum into account. The parameters of the power-law correction and the uncertainty of the Sun's quadrupole moment are simultaneously estimated with the method of minimizing χ 2 . From INPOP10a, we find N = 0.605 for the exponent of the power-law correction. However, from EPM2011, we find that, although it yields N = 3.001, the estimated uncertainty in the Sun's quadrupole moment is much larger than the value given by current observations. This might be caused by the intrinsic nonlinearity in the power-law correction, which makes the estimation very sensitive to the supplementary advances of the perihelia. (research papers)

7. Total variation regularization of the 3-D gravity inverse problem using a randomized generalized singular value decomposition

Vatankhah, Saeed; Renaut, Rosemary A.; Ardestani, Vahid E.

2018-04-01

We present a fast algorithm for the total variation regularization of the 3-D gravity inverse problem. Through imposition of the total variation regularization, subsurface structures presenting with sharp discontinuities are preserved better than when using a conventional minimum-structure inversion. The associated problem formulation for the regularization is nonlinear but can be solved using an iteratively reweighted least-squares algorithm. For small-scale problems the regularized least-squares problem at each iteration can be solved using the generalized singular value decomposition. This is not feasible for large-scale, or even moderate-scale, problems. Instead we introduce the use of a randomized generalized singular value decomposition in order to reduce the dimensions of the problem and provide an effective and efficient solution technique. For further efficiency an alternating direction algorithm is used to implement the total variation weighting operator within the iteratively reweighted least-squares algorithm. Presented results for synthetic examples demonstrate that the novel randomized decomposition provides good accuracy for reduced computational and memory demands as compared to use of classical approaches.

8. Study of inverse methods in remote sensing with laser

Jesus, Wellington Carlos de

2009-01-01

The Laboratory of Environmental Applications of Lasers at IPEN realizes a study about atmospherics properties, such as extinction and backscattering coefficient. These coefficient are estimated by an inverse method, whose estimate quality is difficult to measure. This work presents a method with good statistic approach to retrieval the same coefficients. The new method, however, offers a number of advantages compared to the first method in use, including (1) the ability to incorporate different kinds of information under a common retrieval philosophy and (2) the method provides number of ways for evaluating the quality of the retrieval. Thus we hope improve the accuracy of estimates. (author)

9. Complexity analysis of accelerated MCMC methods for Bayesian inversion

Hoang, Viet Ha; Schwab, Christoph; Stuart, Andrew M

2013-01-01

The Bayesian approach to inverse problems, in which the posterior probability distribution on an unknown field is sampled for the purposes of computing posterior expectations of quantities of interest, is starting to become computationally feasible for partial differential equation (PDE) inverse problems. Balancing the sources of error arising from finite-dimensional approximation of the unknown field, the PDE forward solution map and the sampling of the probability space under the posterior distribution are essential for the design of efficient computational Bayesian methods for PDE inverse problems. We study Bayesian inversion for a model elliptic PDE with an unknown diffusion coefficient. We provide complexity analyses of several Markov chain Monte Carlo (MCMC) methods for the efficient numerical evaluation of expectations under the Bayesian posterior distribution, given data δ. Particular attention is given to bounds on the overall work required to achieve a prescribed error level ε. Specifically, we first bound the computational complexity of ‘plain’ MCMC, based on combining MCMC sampling with linear complexity multi-level solvers for elliptic PDE. Our (new) work versus accuracy bounds show that the complexity of this approach can be quite prohibitive. Two strategies for reducing the computational complexity are then proposed and analyzed: first, a sparse, parametric and deterministic generalized polynomial chaos (gpc) ‘surrogate’ representation of the forward response map of the PDE over the entire parameter space, and, second, a novel multi-level Markov chain Monte Carlo strategy which utilizes sampling from a multi-level discretization of the posterior and the forward PDE. For both of these strategies, we derive asymptotic bounds on work versus accuracy, and hence asymptotic bounds on the computational complexity of the algorithms. In particular, we provide sufficient conditions on the regularity of the unknown coefficients of the PDE and on the

10. 2D Inversion of Transient Electromagnetic Method (TEM)

Bortolozo, Cassiano Antonio; Luís Porsani, Jorge; Acácio Monteiro dos Santos, Fernando

2017-04-01

A new methodology was developed for 2D inversion of Transient Electromagnetic Method (TEM). The methodology consists in the elaboration of a set of routines in Matlab code for modeling and inversion of TEM data and the determination of the most efficient field array for the problem. In this research, the 2D TEM modeling uses the finite differences discretization. To solve the inversion problem, were applied an algorithm based on Marquardt technique, also known as Ridge Regression. The algorithm is stable and efficient and it is widely used in geoelectrical inversion problems. The main advantage of 1D survey is the rapid data acquisition in a large area, but in regions with two-dimensional structures or that need more details, is essential to use two-dimensional interpretation methodologies. For an efficient field acquisition we used in an innovative form the fixed-loop array, with a square transmitter loop (200m x 200m) and 25m spacing between the sounding points. The TEM surveys were conducted only inside the transmitter loop, in order to not deal with negative apparent resistivity values. Although it is possible to model the negative values, it makes the inversion convergence more difficult. Therefore the methodology described above has been developed in order to achieve maximum optimization of data acquisition. Since it is necessary only one transmitter loop disposition in the surface for each series of soundings inside the loop. The algorithms were tested with synthetic data and the results were essential to the interpretation of the results with real data and will be useful in future situations. With the inversion of the real data acquired over the Paraná Sedimentary Basin (PSB) was successful realized a 2D TEM inversion. The results indicate a robust geoelectrical characterization for the sedimentary and crystalline aquifers in the PSB. Therefore, using a new and relevant approach for 2D TEM inversion, this research effectively contributed to map the most

11. Joint inversion of gravity and seismic data along a profile across the seismogenic fault of 2010 Yushu Ms7.1 earthquake

Yang Guangliang

2011-11-01

Full Text Available Yushu Ms7.1 earthquake occurred on the Ganzi-Yushu fault zone, across which we carried out a joint relative-gravity and seismic-reflection survey, and then performed a gravity inversion constrained by the seismic-reflection result. Based on the data of complete Bouguer gravity anomaly and seismic reflection, we obtained a layered interface structure in deep crust down to Moho. Our study showed that the inversion could reveal the interfaces of strata along the survey profile and the directions of regional faults in two-dimension. From the characteristics of the observed topography of the Moho basement, we tentatively confirmed that the uplift of eastern edge of Qinghai-Tibet plateau was caused by the subduction of the Indian plate.

12. A three-dimensional gravity inversion applied to São Miguel Island (Azores)

Camacho, A. G.; Montesinos, F. G.; Vieira, R.

1997-04-01

Gravimetric studies are becoming more and more widely acknowledged as a useful tool for studying and modeling the distributions of subsurface masses that are associated with volcanic activity. In this paper, new gravimetric data for the volcanic island of São Miguel (Azores) were analyzed and interpreted by a stabilized linear inversion methodology. An inversion model of higher resolution was calculated for the Caldera of Furnas, which has a larger density of data. In order to filter out the noncorrelatable anomalies, least squares prediction was used, resulting in a correlated gravimetric signal model with an accuracy of the order of 0.9 mGal. The gravimetric inversion technique is based on the adjustment of a three-dimensional (3-D) model of cubes of unknown density that represents the island's subsurface. The problem of non-uniqueness is solved by minimization with appropriate covariance matrices of the data (resulting from the least squares prediction) and of the unknowns. We also propose a criterion for choosing a balance between the data fit (which in this case corresponds to residues with rms of the order of 0.6 mGal) and the smoothness of the solution. The global model of the island includes a low-density zone in a WNW-ESE direction and a depth of the order of 20 km, associated with the Terceira rift spreading center. The minimums located at a depth of 4 km may be associated with shallow magmatic chambers beneath the main volcanoes of the island. The main high-density area is related to the Nordeste basaltic shield. With regard to the Caldera Furnas, in addition to the minimum that can be associated with a magmatic chamber, there are other shallow minimums that correspond to eruptive processes.

13. Maximum-likelihood method for numerical inversion of Mellin transform

Iqbal, M.

1997-01-01

A method is described for inverting the Mellin transform which uses an expansion in Laguerre polynomials and converts the Mellin transform to Laplace transform, then the maximum-likelihood regularization method is used to recover the original function of the Mellin transform. The performance of the method is illustrated by the inversion of the test functions available in the literature (J. Inst. Math. Appl., 20 (1977) 73; Math. Comput., 53 (1989) 589). Effectiveness of the method is shown by results obtained through demonstration by means of tables and diagrams

14. A variational Bayesian method to inverse problems with impulsive noise

Jin, Bangti

2012-01-01

We propose a novel numerical method for solving inverse problems subject to impulsive noises which possibly contain a large number of outliers. The approach is of Bayesian type, and it exploits a heavy-tailed t distribution for data noise to achieve robustness with respect to outliers. A hierarchical model with all hyper-parameters automatically determined from the given data is described. An algorithm of variational type by minimizing the Kullback-Leibler divergence between the true posteriori distribution and a separable approximation is developed. The numerical method is illustrated on several one- and two-dimensional linear and nonlinear inverse problems arising from heat conduction, including estimating boundary temperature, heat flux and heat transfer coefficient. The results show its robustness to outliers and the fast and steady convergence of the algorithm. © 2011 Elsevier Inc.

15. Lag profile inversion method for EISCAT data analysis

I. I. Virtanen

2008-03-01

Full Text Available The present standard EISCAT incoherent scatter experiments are based on alternating codes that are decoded in power domain by simple summation and subtraction operations. The signal is first digitised and then different lagged products are calculated and decoded in real time. Only the decoded lagged products are saved for further analysis so that both the original data samples and the undecoded lagged products are lost. A fit of plasma parameters can be later performed using the recorded lagged products. In this paper we describe a different analysis method, which makes use of statistical inversion in removing range ambiguities from the lag profiles. An analysis program carrying out both the lag profile inversion and the fit of the plasma parameters has been constructed. Because recording the received signal itself instead of the lagged products allows very flexible data analysis, the program is constructed to use raw data, i.e. IQ-sampled signal recorded from an IF stage of the radar. The program is now capable of analysing standard alternating-coded EISCAT experiments as well as experiments with any other kind of radar modulation if raw data is available. The program calculates the ambiguous lag profiles and is capable of inverting them as such but, for analysis in real time, time integration is needed before inversion. We demonstrate the method using alternating code experiments in the EISCAT UHF radar and specific hardware connected to the second IF stage of the receiver. This method produces a data stream of complex samples, which are stored for later processing. The raw data is analysed with lag profile inversion and the results are compared to those given by the standard method.

16. Quantum method of the inverse scattering problem. Pt. 1

1978-12-01

In this work the authors use a formulation for the method of the inverse scattering problem for quantum-mechanical models of the field theory, that can be found in a quantization of these fully integrable systems. As the most important example serves the system (sinγ) 2 with the movement equation: γtt -γxx + m 2 /β sinβγ = 0 that is known under the specification Sine-Gordon-equation. (orig.) [de

17. Deep structure of Pyrenees range (SW Europe) imaged by joint inversion of gravity and teleseismic delay time

Dufréchou, G.; Tiberi, C.; Martin, R.; Bonvalot, S.; Chevrot, S.; Seoane, L.

2018-04-01

We present a new model of the lithosphere and asthenosphere structure down to 300 km depth beneath the Pyrenees from the joint inversion of recent gravity and teleseismic data. Unlike previous studies, crustal correction were not applied on teleseismic data in order (i) to preserve the consistency between gravity data, which are mainly sensitive to the density structure of the crust.lithosphere, and travel time data, and (ii) to avoid the introduction of biases resulting from crustal reductions. The density model down to 100 km depth is preferentially used here to discuss the lithospheric structure of the Pyrenees, whereas the asthenospheric structure from 100 km to 300 km depth is discussed from our velocity model. The absence of a high density anomaly in our model between 30-100 km depth (except the Labourd density anomaly) in the northern part of the Pyrenees seems to preclude eclogitization of the subducted Iberian crust at the scale of the entire Pyrenean range. Local eclogitization of the deep Pyrenean crust beneath the western part of the Axial Zone (West of Andorra) associated with the positive Central density anomaly is proposed. The Pyrenean lithosphere in density and velocity models appears segmented from East to West. No clear relation between the along-strike segmentation and mapped major faults is visible in our models. The Pyrenees' lithosphere segments are associated to different seismicity pattern in the Pyrenees suggesting a possible relation between the deep structure of the Pyrenees and its seismicity in the upper crust. The concentration of earthquakes localized just straight up the Central density anomaly can result of the subsidence and/or delamination of an eclogitized Pyrenean deep root. The velocity model in the asthenosphere is similar to previous studies. The absence of a high-velocity anomaly in the upper mantle and transition zone (i.e. 125 to 225 km depth) seems to preclude the presence of a detached oceanic lithosphere beneath the

18. Inversion methods for analysis of neutron brightness measurements in tokamaks

Gorini, G.; Gottardi, N.

1990-02-01

The problem of determining neutron emissivity from neutron brightness measurements in magnetic fusion plasmas is addressed. In the case of two-dimensional measurements with two orthogonal cameras, a complete, tomographic analysis of the data can in principle be performed. The results depend critically on the accuracy of the measurements and alternative solutions can be sought under the assumption of a known emissivity topology (Generalized Abel Inversion). In this work, neutron brightness data from the JET tokamak have been studied with both methods. We find that with the present experimental uncertainty (levels 10-20%) the Abel inversion method works best, while two-dimensional information cannot in general be deduced. This is confirmed by studies of the error propagation in the inversion using artificial data, which are also presented here. An important application of emissivity profile information is the determination of the plasma deuterium temperature profile, T D (R). Results are presented here from the analysis of JET data and the errors in T D (R) are discussed in some detail. It is found that, for typical JET plasma conditions, the dominant source of uncertainty arises from the high plasma impurity level and the fact that it is poorly known; these problems can be expected to be remedied and neutron brightness measurements would be expected to be very effective (especially in high density plasmas) as a T D (R) diagnostics. (author)

19. Application of the kernel method to the inverse geosounding problem.

Hidalgo, Hugo; Sosa León, Sonia; Gómez-Treviño, Enrique

2003-01-01

Determining the layered structure of the earth demands the solution of a variety of inverse problems; in the case of electromagnetic soundings at low induction numbers, the problem is linear, for the measurements may be represented as a linear functional of the electrical conductivity distribution. In this paper, an application of the support vector (SV) regression technique to the inversion of electromagnetic data is presented. We take advantage of the regularizing properties of the SV learning algorithm and use it as a modeling technique with synthetic and field data. The SV method presents better recovery of synthetic models than Tikhonov's regularization. As the SV formulation is solved in the space of the data, which has a small dimension in this application, a smaller problem than that considered with Tikhonov's regularization is produced. For field data, the SV formulation develops models similar to those obtained via linear programming techniques, but with the added characteristic of robustness.

20. A direct sampling method to an inverse medium scattering problem

Ito, Kazufumi

2012-01-10

In this work we present a novel sampling method for time harmonic inverse medium scattering problems. It provides a simple tool to directly estimate the shape of the unknown scatterers (inhomogeneous media), and it is applicable even when the measured data are only available for one or two incident directions. A mathematical derivation is provided for its validation. Two- and three-dimensional numerical simulations are presented, which show that the method is accurate even with a few sets of scattered field data, computationally efficient, and very robust with respect to noises in the data. © 2012 IOP Publishing Ltd.

1. The Adjoint Method for the Inverse Problem of Option Pricing

Shou-Lei Wang

2014-01-01

Full Text Available The estimation of implied volatility is a typical PDE inverse problem. In this paper, we propose the TV-L1 model for identifying the implied volatility. The optimal volatility function is found by minimizing the cost functional measuring the discrepancy. The gradient is computed via the adjoint method which provides us with an exact value of the gradient needed for the minimization procedure. We use the limited memory quasi-Newton algorithm (L-BFGS to find the optimal and numerical examples shows the effectiveness of the presented method.

2. Simulation of bubble motion under gravity by lattice Boltzmann method

Takada, Naoki; Misawa, Masaki; Tomiyama, Akio; Hosokawa, Shigeo

2001-01-01

We describe the numerical simulation results of bubble motion under gravity by the lattice Boltzmann method (LBM), which assumes that a fluid consists of mesoscopic fluid particles repeating collision and translation and a multiphase interface is reproduced in a self-organizing way by repulsive interaction between different kinds of particles. The purposes in this study are to examine the applicability of LBM to the numerical analysis of bubble motions, and to develop a three-dimensional version of the binary fluid model that introduces a free energy function. We included the buoyancy terms due to the density difference in the lattice Boltzmann equations, and simulated single-and two-bubble motions, setting flow conditions according to the Eoetvoes and Morton numbers. The two-dimensional results by LBM agree with those by the Volume of Fluid method based on the Navier-Stokes equations. The three-dimensional model possesses the surface tension satisfying the Laplace's law, and reproduces the motion of single bubble and the two-bubble interaction of their approach and coalescence in circular tube. There results prove that the buoyancy terms and the 3D model proposed here are suitable, and that LBM is useful for the numerical analysis of bubble motion under gravity. (author)

3. Improved algorithm for three-dimensional inverse method

Qiu, Xuwen

4. Numerical computation of FCT equilibria by inverse equilibrium method

Tokuda, Shinji; Tsunematsu, Toshihide; Takeda, Tatsuoki

1986-11-01

FCT (Flux Conserving Tokamak) equilibria were obtained numerically by the inverse equilibrium method. The high-beta tokamak ordering was used to get the explicit boundary conditions for FCT equilibria. The partial differential equation was reduced to the simultaneous quasi-linear ordinary differential equations by using the moment method. The regularity conditions for solutions at the singular point of the equations can be expressed correctly by this reduction and the problem to be solved becomes a tractable boundary value problem on the quasi-linear ordinary differential equations. This boundary value problem was solved by the method of quasi-linearization, one of the shooting methods. Test calculations show that this method provides high-beta tokamak equilibria with sufficiently high accuracy for MHD stability analysis. (author)

5. Using Inverse Problem Methods with Surveillance Data in Pneumococcal Vaccination

Sutton, Karyn L.; Banks, H. T.; Castillo-Chavez, Carlos

2010-01-01

The design and evaluation of epidemiological control strategies is central to public health policy. While inverse problem methods are routinely used in many applications, this remains an area in which their use is relatively rare, although their potential impact is great. We describe methods particularly relevant to epidemiological modeling at the population level. These methods are then applied to the study of pneumococcal vaccination strategies as a relevant example which poses many challenges common to other infectious diseases. We demonstrate that relevant yet typically unknown parameters may be estimated, and show that a calibrated model may used to assess implemented vaccine policies through the estimation of parameters if vaccine history is recorded along with infection and colonization information. Finally, we show how one might determine an appropriate level of refinement or aggregation in the age-structured model given age-stratified observations. These results illustrate ways in which the collection and analysis of surveillance data can be improved using inverse problem methods. PMID:20209093

6. Solution of the radiative enclosure with a hybrid inverse method

Silva, Rogerio Brittes da; Franca, Francis Henrique Ramos [Universidade Federal do Rio Grande do Sul (UFRGS), Porto Alegre, RS (Brazil). Dept. de Engenharia Mecanica], E-mail: frfranca@mecanica.ufrgs.br

2010-07-01

This work applies the inverse analysis to solve a three-dimensional radiative enclosure - which the surfaces are diffuse-grays - filled with transparent medium. The aim is determine the powers and locations of the heaters to attain both uniform heat flux and temperature on the design surface. A hybrid solution that couples two methods, the generalized extremal optimization (GEO) and the truncated singular value decomposition (TSVD) is proposed. The determination of the heat sources distribution is treated as an optimization problem, by GEO algorithm , whereas the solution of the system of equation, that embodies the Fredholm equation of first kind and therefore is expected to be ill conditioned, is build up through TSVD regularization method. The results show that the hybrid method can lead to a heat flux on the design surface that satisfies the imposed conditions with maximum error of less than 1,10%. The results illustrated the relevance of a hybrid method as a prediction tool. (author)

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

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

1979-01-01

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

8. Comparison of publically available Moho depth and crustal thickness grids with newly derived grids by 3D gravity inversion for the High Arctic region.

Lebedeva-Ivanova, Nina; Gaina, Carmen; Minakov, Alexander; Kashubin, Sergey

2016-04-01

We derived Moho depth and crustal thickness for the High Arctic region by 3D forward and inverse gravity modelling method in the spectral domain (Minakov et al. 2012) using lithosphere thermal gravity anomaly correction (Alvey et al., 2008); a vertical density variation for the sedimentary layer and lateral crustal variation density. Recently updated grids of bathymetry (Jakobsson et al., 2012), gravity anomaly (Gaina et al, 2011) and dynamic topography (Spasojevic & Gurnis, 2012) were used as input data for the algorithm. TeMAr sedimentary thickness grid (Petrov et al., 2013) was modified according to the most recently published seismic data, and was re-gridded and utilized as input data. Other input parameters for the algorithm were calibrated using seismic crustal scale profiles. The results are numerically compared with publically available grids of the Moho depth and crustal thickness for the High Arctic region (CRUST 1 and GEMMA global grids; the deep Arctic Ocean grids by Glebovsky et al., 2013) and seismic crustal scale profiles. The global grids provide coarser resolution of 0.5-1.0 geographic degrees and not focused on the High Arctic region. Our grids better capture all main features of the region and show smaller error in relation to the seismic crustal profiles compare to CRUST 1 and GEMMA grids. Results of 3D gravity modelling by Glebovsky et al. (2013) with separated geostructures approach show also good fit with seismic profiles; however these grids cover the deep part of the Arctic Ocean only. Alvey A, Gaina C, Kusznir NJ, Torsvik TH (2008). Integrated crustal thickness mapping and plate recon-structions for the high Arctic. Earth Planet Sci Lett 274:310-321. Gaina C, Werner SC, Saltus R, Maus S (2011). Circum-Arctic mapping project: new magnetic and gravity anomaly maps of the Arctic. Geol Soc Lond Mem 35, 39-48. Glebovsky V.Yu., Astafurova E.G., Chernykh A.A., Korneva M.A., Kaminsky V.D., Poselov V.A. (2013). Thickness of the Earth's crust in the

9. Measuring the Change in Water Table with Gravity Methods - a Controlled Experiment

Lund, S; Christiansen, Lars; Andersen, O. B.

2009-01-01

Gravity changes linearly with the change in soil water content. With the GRACE satellite mission the interest for ground-based gravity methods in hydrology has gained new attention. Time-lapse gravity data have the potential to constrain hydrological model parameters in a calibration scheme....... The greatest potential is seen for specific yield. The gravity signal from hydrology is small (10^-8 m/s^2 level) and the application of ground-based methods is mainly limited by the sensitivity of available instruments. In order to demonstrate the ability of the Scintrex CG-5 gravity meter to detect a change...... in water content, a controlled experiment was set up in 30 m by 20 m basin. The water table was lowered 0.69 m within 1½ hours and the corresponding gravity signal measured using two different approaches: a time series measurements at one location and a gravity network measurement including four points...

10. GePb Alloy Growth Using Layer Inversion Method

Alahmad, Hakimah; Mosleh, Aboozar; Alher, Murtadha; Banihashemian, Seyedeh Fahimeh; Ghetmiri, Seyed Amir; Al-Kabi, Sattar; Du, Wei; Li, Bauhoa; Yu, Shui-Qing; Naseem, Hameed A.

2018-04-01

Germanium-lead films have been investigated as a new direct-bandgap group IV alloy. GePb films were deposited on Si via thermal evaporation of Ge and Pb solid sources using the layer inversion metal-induced crystallization method for comparison with the current laser-induced recrystallization method. Material characterization of the films using x-ray diffraction analysis revealed highly oriented crystallinity and Pb incorporation as high as 13.5% before and 5.2% after annealing. Transmission electron microscopy, scanning electron microscopy, and energy-dispersive x-ray mapping of the samples revealed uniform incorporation of elements and complete layer inversion. Optical characterization of the GePb films by Raman spectroscopy and photoluminescence techniques showed that annealing the samples resulted in higher crystalline quality as well as bandgap reduction. The bandgap reduction from 0.67 eV to 0.547 eV observed for the highest-quality material confirms the achievement of a direct-bandgap material.

11. GePb Alloy Growth Using Layer Inversion Method

Alahmad, Hakimah; Mosleh, Aboozar; Alher, Murtadha; Banihashemian, Seyedeh Fahimeh; Ghetmiri, Seyed Amir; Al-Kabi, Sattar; Du, Wei; Li, Bauhoa; Yu, Shui-Qing; Naseem, Hameed A.

2018-07-01

Germanium-lead films have been investigated as a new direct-bandgap group IV alloy. GePb films were deposited on Si via thermal evaporation of Ge and Pb solid sources using the layer inversion metal-induced crystallization method for comparison with the current laser-induced recrystallization method. Material characterization of the films using x-ray diffraction analysis revealed highly oriented crystallinity and Pb incorporation as high as 13.5% before and 5.2% after annealing. Transmission electron microscopy, scanning electron microscopy, and energy-dispersive x-ray mapping of the samples revealed uniform incorporation of elements and complete layer inversion. Optical characterization of the GePb films by Raman spectroscopy and photoluminescence techniques showed that annealing the samples resulted in higher crystalline quality as well as bandgap reduction. The bandgap reduction from 0.67 eV to 0.547 eV observed for the highest-quality material confirms the achievement of a direct-bandgap material.

12. A New Self-Constrained Inversion Method of Potential Fields Based on Probability Tomography

Sun, S.; Chen, C.; WANG, H.; Wang, Q.

2014-12-01

The self-constrained inversion method of potential fields uses a priori information self-extracted from potential field data. Differing from external a priori information, the self-extracted information are generally parameters derived exclusively from the analysis of the gravity and magnetic data (Paoletti et al., 2013). Here we develop a new self-constrained inversion method based on probability tomography. Probability tomography doesn't need any priori information, as well as large inversion matrix operations. Moreover, its result can describe the sources, especially the distribution of which is complex and irregular, entirely and clearly. Therefore, we attempt to use the a priori information extracted from the probability tomography results to constrain the inversion for physical properties. The magnetic anomaly data was taken as an example in this work. The probability tomography result of magnetic total field anomaly(ΔΤ) shows a smoother distribution than the anomalous source and cannot display the source edges exactly. However, the gradients of ΔΤ are with higher resolution than ΔΤ in their own direction, and this characteristic is also presented in their probability tomography results. So we use some rules to combine the probability tomography results of ∂ΔΤ⁄∂x, ∂ΔΤ⁄∂y and ∂ΔΤ⁄∂z into a new result which is used for extracting a priori information, and then incorporate the information into the model objective function as spatial weighting functions to invert the final magnetic susceptibility. Some magnetic synthetic examples incorporated with and without a priori information extracted from the probability tomography results were made to do comparison, results of which show that the former are more concentrated and with higher resolution of the source body edges. This method is finally applied in an iron mine in China with field measured ΔΤ data and performs well. ReferencesPaoletti, V., Ialongo, S., Florio, G., Fedi, M

13. A two-stage method for inverse medium scattering

Ito, Kazufumi

2013-03-01

We present a novel numerical method to the time-harmonic inverse medium scattering problem of recovering the refractive index from noisy near-field scattered data. The approach consists of two stages, one pruning step of detecting the scatterer support, and one resolution enhancing step with nonsmooth mixed regularization. The first step is strictly direct and of sampling type, and it faithfully detects the scatterer support. The second step is an innovative application of nonsmooth mixed regularization, and it accurately resolves the scatterer size as well as intensities. The nonsmooth model can be efficiently solved by a semi-smooth Newton-type method. Numerical results for two- and three-dimensional examples indicate that the new approach is accurate, computationally efficient, and robust with respect to data noise. © 2012 Elsevier Inc.

14. Electromagnetic heating method to improve steam assisted gravity drainage

Koolman, M.; Huber, N.; Diehl, D.; Wacker, B. [Siemens AG, Munich (Germany)

2008-10-15

The in-situ recovery of heavy and highly viscous bitumen has become economically feasible with the use of steam assisted gravity drainage (SAGD). However, several challenges exist, such as the energy cost for production of bitumen; environmental concerns over the consumption of water; limited recovery of bitumen; shallowness of the reservoirs; and the propagation of steam chambers leading to limited recovery. This paper described an opportunity to improve the widely applied SAGD process for in-situ production of bitumen from oil sands deposits. The technical concept was directed at electromagnetic (EM-SAGD) heating methods assisting the process. The paper described a preliminary investigation that was conducted in order to confirm the feasibility of different solutions and evaluate aspects of energy efficiency and environmental impact. A comparison of electrical heating methods showed that the inductive method was the most reasonable in terms of technical and economical feasibility. The paper also discussed a small scale sandbox test to verify a three-dimensional simulation provided with two different simulation tools. The results of reservoir simulation were also presented. Last, the paper examined health and safety considerations. It was concluded that inductive heating provides an additional, easy to handle control parameter. The study showed that if the geometries of the inductors related to the producer wells were selected in a tailor-made manner, individual reservoir conditions could be handled by an optimized operating strategy. 4 refs., 3 tabs., 15 figs.

15. Determination of brazed joint constitutive law by inverse method

Lovato, G.; Moret, F.; Gallo, P. le; Cailletaud, G.; Pilvin, P.

1993-01-01

An important parameter often neglected for the calculation of residual stresses in brazed ceramic/metal assemblies is the joint constitutive law. In situ camber measurements on a model system (axisymmetric TZM/InCuSil ABA/316L samples) performed using a special vertical dilatometer during the whole brazing thermal cycle are compared with results of FEM calculations based on published filler metal constitutive laws. A strong disagreement is observed. Actual constitutive law of the joint is determined from these measurements using a numerical inverse method. Calculated displacements are fully consistent with experimental ones. True solidification temperature of the joint is determined. The identified constitutive law of the joint exhibits a low flow stress from solidification temperature to 320 C. (orig.)

16. A direct sampling method for inverse electromagnetic medium scattering

Ito, Kazufumi

2013-09-01

In this paper, we study the inverse electromagnetic medium scattering problem of estimating the support and shape of medium scatterers from scattered electric/magnetic near-field data. We shall develop a novel direct sampling method based on an analysis of electromagnetic scattering and the behavior of the fundamental solution. It is applicable to a few incident fields and needs only to compute inner products of the measured scattered field with the fundamental solutions located at sampling points. Hence, it is strictly direct, computationally very efficient and highly robust to the presence of data noise. Two- and three-dimensional numerical experiments indicate that it can provide reliable support estimates for multiple scatterers in the case of both exact and highly noisy data. © 2013 IOP Publishing Ltd.

17. Direct sampling methods for inverse elastic scattering problems

Ji, Xia; Liu, Xiaodong; Xi, Yingxia

2018-03-01

We consider the inverse elastic scattering of incident plane compressional and shear waves from the knowledge of the far field patterns. Specifically, three direct sampling methods for location and shape reconstruction are proposed using the different component of the far field patterns. Only inner products are involved in the computation, thus the novel sampling methods are very simple and fast to be implemented. With the help of the factorization of the far field operator, we give a lower bound of the proposed indicator functionals for sampling points inside the scatterers. While for the sampling points outside the scatterers, we show that the indicator functionals decay like the Bessel functions as the sampling point goes away from the boundary of the scatterers. We also show that the proposed indicator functionals continuously dependent on the far field patterns, which further implies that the novel sampling methods are extremely stable with respect to data error. For the case when the observation directions are restricted into the limited aperture, we firstly introduce some data retrieval techniques to obtain those data that can not be measured directly and then use the proposed direct sampling methods for location and shape reconstructions. Finally, some numerical simulations in two dimensions are conducted with noisy data, and the results further verify the effectiveness and robustness of the proposed sampling methods, even for multiple multiscale cases and limited-aperture problems.

18. Microstrip natural wave spectrum mathematical model using partial inversion method

Pogarsky, S.A.; Litvinenko, L.N.; Prosvirnin, S.L.

1995-01-01

It is generally agreed that both microstrip lines itself and different discontinuities based on microstrips are the most difficult problem for accurate electrodynamic analysis. Over the last years much has been published about principles and accurate (or full wave) methods of microstrip lines investigations. The growing interest for this problem may be explained by the microstrip application in the millimeter-wave range for purpose of realizing interconnects and a variety of passive components. At these higher operating rating frequencies accurate component modeling becomes more critical. A creation, examination and experimental verification of the accurate method for planar electrodynamical structures natural wave spectrum investigations are the objects of this manuscript. The moment method with partial inversion operator method using may be considered as a basical way for solving this problem. This method is outlook for accurate analysis of different planar discontinuities in microstrip: such as step discontinuities, microstrip turns, Y- and X-junctions and etc., substrate space steps dielectric constants and other anisotropy types

19. Comparison of survey and photogrammetry methods to position gravity data, Yucca Mountain, Nevada

Ponce, D.A.; Wu, S.S.C.; Spielman, J.B.

1985-01-01

Locations of gravity stations at Yucca Mountain, Nevada, were determined by a survey using an electronic distance-measuring device and by a photogram-metric method. The data from both methods were compared to determine if horizontal and vertical coordinates developed from photogrammetry are sufficently accurate to position gravity data at the site. The results show that elevations from the photogrammetric data have a mean difference of 0.57 +- 0.70 m when compared with those of the surveyed data. Comparison of the horizontal control shows that the two methods agreed to within 0.01 minute. At a latitude of 45 0 , an error of 0.01 minute (18 m) corresponds to a gravity anomaly error of 0.015 mGal. Bouguer gravity anomalies are most sensitive to errors in elevation, thus elevation is the determining factor for use of photogrammetric or survey methods to position gravity data. Because gravity station positions are difficult to locate on aerial photographs, photogrammetric positions are not always exactly at the gravity station; therefore, large disagreements may appear when comparing electronic and photogrammetric measurements. A mean photogrammetric elevation error of 0.57 m corresponds to a gravity anomaly error of 0.11 mGal. Errors of 0.11 mGal are too large for high-precision or detailed gravity measurements but acceptable for regional work. 1 ref. 2 figs., 4 tabs

20. Comparison of optimal design methods in inverse problems

Banks, H T; Holm, K; Kappel, F

2011-01-01

Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix. A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criterion with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst–Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am. J. Physiol. 236 E667–77; De Gaetano A and Arino O 2000 J. Math. Biol. 40 136–68; Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979–90)

1. Comparison of optimal design methods in inverse problems

Banks, H. T.; Holm, K.; Kappel, F.

2011-07-01

Typical optimal design methods for inverse or parameter estimation problems are designed to choose optimal sampling distributions through minimization of a specific cost function related to the resulting error in parameter estimates. It is hoped that the inverse problem will produce parameter estimates with increased accuracy using data collected according to the optimal sampling distribution. Here we formulate the classical optimal design problem in the context of general optimization problems over distributions of sampling times. We present a new Prohorov metric-based theoretical framework that permits one to treat succinctly and rigorously any optimal design criteria based on the Fisher information matrix. A fundamental approximation theory is also included in this framework. A new optimal design, SE-optimal design (standard error optimal design), is then introduced in the context of this framework. We compare this new design criterion with the more traditional D-optimal and E-optimal designs. The optimal sampling distributions from each design are used to compute and compare standard errors; the standard errors for parameters are computed using asymptotic theory or bootstrapping and the optimal mesh. We use three examples to illustrate ideas: the Verhulst-Pearl logistic population model (Banks H T and Tran H T 2009 Mathematical and Experimental Modeling of Physical and Biological Processes (Boca Raton, FL: Chapman and Hall/CRC)), the standard harmonic oscillator model (Banks H T and Tran H T 2009) and a popular glucose regulation model (Bergman R N, Ider Y Z, Bowden C R and Cobelli C 1979 Am. J. Physiol. 236 E667-77 De Gaetano A and Arino O 2000 J. Math. Biol. 40 136-68 Toffolo G, Bergman R N, Finegood D T, Bowden C R and Cobelli C 1980 Diabetes 29 979-90).

2. Research on inverse methods and optimization in Italy

Larocca, Francesco

1991-01-01

The research activities in Italy on inverse design and optimization are reviewed. The review is focused on aerodynamic aspects in turbomachinery and wing section design. Inverse design of blade rows and ducts of turbomachinery in subsonic and transonic regime are illustrated by the Politecnico di Torino and turbomachinery industry (FIAT AVIO).

3. Level set methods for inverse scattering—some recent developments

Dorn, Oliver; Lesselier, Dominique

2009-01-01

We give an update on recent techniques which use a level set representation of shapes for solving inverse scattering problems, completing in that matter the exposition made in (Dorn and Lesselier 2006 Inverse Problems 22 R67) and (Dorn and Lesselier 2007 Deformable Models (New York: Springer) pp 61–90), and bringing it closer to the current state of the art

4. Centrifugal compressor shape modification using a proposed inverse design method

2013-01-01

This paper is concerned with a quasi-3D design method for the radial and axial diffusers of a centrifugal compressor on the meridional plane. The method integrates a novel inverse design algorithm, called ball-spine algorithm (BSA), and a quasi-3D analysis code. The Euler equation is solved on the meridional plane for a numerical domain, of which unknown boundaries (hub and shroud) are iteratively modified under the BSA until a prescribed pressure distribution is reached. In BSA, unknown walls are composed of a set of virtual balls that move freely along specified directions called spines. The difference between target and current pressure distributions causes the flexible boundary to deform at each modification step. In validating the quasi-3D analysis code, a full 3D Navier-Stokes code is used to analyze the existing and designed compressors numerically. Comparison of the quasi-3D analysis results with full 3D analysis results shows viable agreement. The 3D numerical analysis of the current compressor shows a huge total pressure loss on the 90 .deg. bend between the radial and axial diffusers. Geometric modification of the meridional plane causes the efficiency to improve by about 10%.

5. Stress estimation in reservoirs using an integrated inverse method

Mazuyer, Antoine; Cupillard, Paul; Giot, Richard; Conin, Marianne; Leroy, Yves; Thore, Pierre

2018-05-01

Estimating the stress in reservoirs and their surroundings prior to the production is a key issue for reservoir management planning. In this study, we propose an integrated inverse method to estimate such initial stress state. The 3D stress state is constructed with the displacement-based finite element method assuming linear isotropic elasticity and small perturbations in the current geometry of the geological structures. The Neumann boundary conditions are defined as piecewise linear functions of depth. The discontinuous functions are determined with the CMA-ES (Covariance Matrix Adaptation Evolution Strategy) optimization algorithm to fit wellbore stress data deduced from leak-off tests and breakouts. The disregard of the geological history and the simplified rheological assumptions mean that only the stress field, statically admissible and matching the wellbore data should be exploited. The spatial domain of validity of this statement is assessed by comparing the stress estimations for a synthetic folded structure of finite amplitude with a history constructed assuming a viscous response.

6. Centrifugal compressor shape modification using a proposed inverse design method

2013-03-15

This paper is concerned with a quasi-3D design method for the radial and axial diffusers of a centrifugal compressor on the meridional plane. The method integrates a novel inverse design algorithm, called ball-spine algorithm (BSA), and a quasi-3D analysis code. The Euler equation is solved on the meridional plane for a numerical domain, of which unknown boundaries (hub and shroud) are iteratively modified under the BSA until a prescribed pressure distribution is reached. In BSA, unknown walls are composed of a set of virtual balls that move freely along specified directions called spines. The difference between target and current pressure distributions causes the flexible boundary to deform at each modification step. In validating the quasi-3D analysis code, a full 3D Navier-Stokes code is used to analyze the existing and designed compressors numerically. Comparison of the quasi-3D analysis results with full 3D analysis results shows viable agreement. The 3D numerical analysis of the current compressor shows a huge total pressure loss on the 90 .deg. bend between the radial and axial diffusers. Geometric modification of the meridional plane causes the efficiency to improve by about 10%.

7. Comparison of the Effect of Horizontal Vibrations on Interfacial Waves in a Two-Layer System of Inviscid Liquids to Effective Gravity Inversion

Pimenova, Anastasiya V.; Goldobin, Denis S.; Lyubimova, Tatyana P.

2018-02-01

We study the waves at the interface between two thin horizontal layers of immiscible liquids subject to high-frequency tangential vibrations. Nonlinear governing equations are derived for the cases of two- and three-dimensional flows and arbitrary ratio of layer thicknesses. The derivation is performed within the framework of the long-wavelength approximation, which is relevant as the linear instability of a thin-layers system is long-wavelength. The dynamics of equations is integrable and the equations themselves can be compared to the Boussinesq equation for the gravity waves in shallow water, which allows one to compare the action of the vibrational field to the action of the gravity and its possible effective inversion.

8. Comparison of inverse Laplace and numerical inversion methods for obtaining z-depth profiles of diffraction data

Xiaojing Zhu; Predecki, P.; Ballard, B.

1995-01-01

Two different inversion methods, the inverse Laplace method and the linear constrained numerical method, for retrieving the z-profiles of diffraction data from experimentally obtained i-profiles were compared using tests with a known function as the original z-profile. Two different real data situations were simulated to determine the effects of specimen thickness and missing τ-profile data at small τ-values on the retrieved z-profiles. The results indicate that although both methods are able to retrieve the z-profiles in the bulk specimens satisfactorily, the numerical method can be used for thin film samples as well. Missing τ-profile data at small τ values causes error in the retrieved z-profiles with both methods, particularly when the trend of the τ-profile at small τ is significantly changed because of the missing data. 6 refs., 3 figs

9. Full Waveform Inversion Using Oriented Time Migration Method

Zhang, Zhendong

2016-01-01

Full waveform inversion (FWI) for reflection events is limited by its linearized update requirements given by a process equivalent to migration. Unless the background velocity model is reasonably accurate the resulting gradient can have

10. Source Parameter Inversion for Recent Great Earthquakes from a Decade-long Observation of Global Gravity Fields

Han, Shin-Chan; Riva, Ricccardo; Sauber, Jeanne; Okal, Emile

2013-01-01

We quantify gravity changes after great earthquakes present within the 10 year long time series of monthly Gravity Recovery and Climate Experiment (GRACE) gravity fields. Using spherical harmonic normal-mode formulation, the respective source parameters of moment tensor and double-couple were estimated. For the 2004 Sumatra-Andaman earthquake, the gravity data indicate a composite moment of 1.2x10(exp 23)Nm with a dip of 10deg, in agreement with the estimate obtained at ultralong seismic periods. For the 2010 Maule earthquake, the GRACE solutions range from 2.0 to 2.7x10(exp 22)Nm for dips of 12deg-24deg and centroid depths within the lower crust. For the 2011 Tohoku-Oki earthquake, the estimated scalar moments range from 4.1 to 6.1x10(exp 22)Nm, with dips of 9deg-19deg and centroid depths within the lower crust. For the 2012 Indian Ocean strike-slip earthquakes, the gravity data delineate a composite moment of 1.9x10(exp 22)Nm regardless of the centroid depth, comparing favorably with the total moment of the main ruptures and aftershocks. The smallest event we successfully analyzed with GRACE was the 2007 Bengkulu earthquake with M(sub 0) approx. 5.0x10(exp 21)Nm. We found that the gravity data constrain the focal mechanism with the centroid only within the upper and lower crustal layers for thrust events. Deeper sources (i.e., in the upper mantle) could not reproduce the gravity observation as the larger rigidity and bulk modulus at mantle depths inhibit the interior from changing its volume, thus reducing the negative gravity component. Focal mechanisms and seismic moments obtained in this study represent the behavior of the sources on temporal and spatial scales exceeding the seismic and geodetic spectrum.

11. A high-order 3-D spectral-element method for the forward modelling and inversion of gravimetric data—Application to the western Pyrenees

Martin, Roland; Chevrot, Sébastien; Komatitsch, Dimitri; Seoane, Lucia; Spangenberg, Hannah; Wang, Yi; Dufréchou, Grégory; Bonvalot, Sylvain; Bruinsma, Sean

2017-04-01

We image the internal density structure of the Pyrenees by inverting gravity data using an a priori density model derived by scaling a Vp model obtained by full waveform inversion of teleseismic P-waves. Gravity anomalies are computed via a 3-D high-order finite-element integration in the same high-order spectral-element grid as the one used to solve the wave equation and thus to obtain the velocity model. The curvature of the Earth and surface topography are taken into account in order to obtain a density model as accurate as possible. The method is validated through comparisons with exact semi-analytical solutions. We show that the spectral-element method drastically accelerates the computations when compared to other more classical methods. Different scaling relations between compressional velocity and density are tested, and the Nafe-Drake relation is the one that leads to the best agreement between computed and observed gravity anomalies. Gravity data inversion is then performed and the results allow us to put more constraints on the density structure of the shallow crust and on the deep architecture of the mountain range.

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

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

2018-04-01

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

13. Novel inversion method for land mine imaging and detection

Sindoni, Orazio I.; Cohoon, David K.

2000-08-01

We have developed, using both partial differential equation approaches and integral equation formulations, a precise method to invert acoustic or electromagnetic scattering data from macroscopic concealed objects. Our approach makes use of the ideas associated with our exact solution of partial differential equations as described in our paper where we were able to collapse the number of equations by elimination of transcendentals therefore preserving the absolute mathematical precision inherent in the partial differential equation formulation. Our mathematical method, as a consequence, has not encountered the traditional loss of precision when inverting the scattered data. The unrestricted wavelength range allows us to penetrate any material which may surround the object and differentiate between the object and the media. For this reason we have applied our inversion scheme to landmine detection as we can penetrate and differentiate under both wet and dry conditions. Also, we are able to account, under certain conditions, for dielectric nonlinearities of material in the concealed object. Therefore, we are able to build in density dependent false colors a 3D grid representative of both the media and of the embedded object including the internal structure of the object. We have surveyed the literature on the subject of recovery of physical location of concealed objects and we have found that most of the present applications such as land mine detection, and we have found that most of the present applications have shortcomings due to the physical changes that are present in the surrounding media or the discontinuities of physical properties of the media. For all the above reasons we believe that we may have the most versatile and mathematically precise approach to the solution of this problem.

14. Reconstruction Methods for Inverse Problems with Partial Data

Hoffmann, Kristoffer

This thesis presents a theoretical and numerical analysis of a general mathematical formulation of hybrid inverse problems in impedance tomography. This includes problems from several existing hybrid imaging modalities such as Current Density Impedance Imaging, Magnetic Resonance Electrical...... Impedance Tomography, and Ultrasound Modulated Electrical Impedance Tomography. After giving an introduction to hybrid inverse problems in impedance tomography and the mathematical tools that facilitate the related analysis, we explain in detail the stability properties associated with the classification...... of a linearised hybrid inverse problem. This is done using pseudo-differential calculus and theory for overdetermined boundary value problem. Using microlocal analysis we then present novel results on the propagation of singularities, which give a precise description of the distinct features of solutions...

15. 3D density model of the upper mantle of Asia based on inversion of gravity and seismic tomography data

Kaban, Mikhail K.; Stolk, Ward; Tesauro, Magdala; El Khrepy, Sami; Al-Arifi, Nassir; Beekman, Fred; Cloetingh, Sierd A P L

2016-01-01

We construct a new-generation 3D density model of the upper mantle of Asia and its surrounding areas based on a joint interpretation of several data sets. A recent model of the crust combining nearly all available seismic data is employed to calculate the impact of the crust on the gravity anomalies

16. A time domain inverse dynamic method for the end point tracking control of a flexible manipulator

Kwon, Dong-Soo; Book, Wayne J.

1991-01-01

The inverse dynamic equation of a flexible manipulator was solved in the time domain. By dividing the inverse system equation into the causal part and the anticausal part, we calculated the torque and the trajectories of all state variables for a given end point trajectory. The interpretation of this method in the frequency domain was explained in detail using the two-sided Laplace transform and the convolution integral. The open loop control of the inverse dynamic method shows an excellent result in simulation. For real applications, a practical control strategy is proposed by adding a feedback tracking control loop to the inverse dynamic feedforward control, and its good experimental performance is presented.

17. Regularization parameter estimation for underdetermined problems by the χ 2 principle with application to 2D focusing gravity inversion

Vatankhah, Saeed; Ardestani, Vahid E; Renaut, Rosemary A

2014-01-01

The χ 2 principle generalizes the Morozov discrepancy principle to the augmented residual of the Tikhonov regularized least squares problem. For weighting of the data fidelity by a known Gaussian noise distribution on the measured data, when the stabilizing, or regularization, term is considered to be weighted by unknown inverse covariance information on the model parameters, the minimum of the Tikhonov functional becomes a random variable that follows a χ 2 -distribution with m+p−n degrees of freedom for the model matrix G of size m×n, m⩾n, and regularizer L of size p × n. Then, a Newton root-finding algorithm, employing the generalized singular value decomposition, or singular value decomposition when L = I, can be used to find the regularization parameter α. Here the result and algorithm are extended to the underdetermined case, m 2 algorithms when m 2 and unbiased predictive risk estimator of the regularization parameter are used for the first time in this context. For a simulated underdetermined data set with noise, these regularization parameter estimation methods, as well as the generalized cross validation method, are contrasted with the use of the L-curve and the Morozov discrepancy principle. Experiments demonstrate the efficiency and robustness of the χ 2 principle and unbiased predictive risk estimator, moreover showing that the L-curve and Morozov discrepancy principle are outperformed in general by the other three techniques. Furthermore, the minimum support stabilizer is of general use for the χ 2 principle when implemented without the desirable knowledge of the mean value of the model. (paper)

18. Evaluation of Inversion Methods Applied to Ionospheric ro Observations

Rios Caceres, Arq. Estela Alejandra; Rios, Victor Hugo; Guyot, Elia

The new technique of radio-occultation can be used to study the Earth's ionosphere. The retrieval processes of ionospheric profiling from radio occultation observations usually assume spherical symmetry of electron density distribution at the locality of occultation and use the Abel integral transform to invert the measured total electron content (TEC) values. This pa-per presents a set of ionospheric profiles obtained from SAC-C satellite with the Abel inversion technique. The effects of the ionosphere on the GPS signal during occultation, such as bending and scintillation, are examined. Electron density profiles are obtained using the Abel inversion technique. Ionospheric radio occultations are validated using vertical profiles of electron con-centration from inverted ionograms , obtained from ionosonde sounding in the vicinity of the occultation. Results indicate that the Abel transform works well in the mid-latitudes during the daytime, but is less accurate during the night-time.

19. Inverse mass matrix via the method of localized lagrange multipliers

González, José A.; Kolman, Radek; Cho, S.S.; Felippa, C.A.; Park, K.C.

2018-01-01

Roč. 113, č. 2 (2018), s. 277-295 ISSN 0029-5981 R&D Projects: GA MŠk(CZ) EF15_003/0000493; GA ČR GA17-22615S Institutional support: RVO:61388998 Keywords : explicit time integration * inverse mass matrix * localized Lagrange multipliers * partitioned analysis Subject RIV: BI - Acoustics OBOR OECD: Applied mechanics Impact factor: 2.162, year: 2016 https://onlinelibrary.wiley.com/doi/10.1002/nme.5613

20. Iterative Reconstruction Methods for Hybrid Inverse Problems in Impedance Tomography

Hoffmann, Kristoffer; Knudsen, Kim

2014-01-01

For a general formulation of hybrid inverse problems in impedance tomography the Picard and Newton iterative schemes are adapted and four iterative reconstruction algorithms are developed. The general problem formulation includes several existing hybrid imaging modalities such as current density...... impedance imaging, magnetic resonance electrical impedance tomography, and ultrasound modulated electrical impedance tomography, and the unified approach to the reconstruction problem encompasses several algorithms suggested in the literature. The four proposed algorithms are implemented numerically in two...

1. A new method for optimization of low-thrust gravity-assist sequences

Maiwald, V.

2017-09-01

Recently missions like Hayabusa and Dawn have shown the relevance and benefits of low-thrust spacecraft concerning the exploration of our solar system. In general, the efficiency of low-thrust propulsion is one means of improving mission payload mass. At the same time, gravity-assist maneuvers can serve as mission enablers, as they have the capability to provide "free energy." A combination of both, gravity-assist and low-thrust propulsion, has the potential to generally improve mission performance, i.e. planning and optimization of gravity-assist sequences for low-thrust missions is a desirable asset. Currently no established methods exist to include the gravity-assist partners as optimization variable for low-thrust missions. The present paper explains how gravity-assists are planned and optimized, including the gravity-assist partners, for high-thrust missions and discusses the possibility to transfer the established method, based on the Tisserand Criterion, to low-thrust missions. It is shown how the Tisserand Criterion needs to be adapted using a correction term for the low-thrust situation. It is explained why this necessary correction term excludes an a priori evaluation of sequences and therefore their planning and an alternate approach is proposed. Preliminary results of this method, by application of a Differential Evolution optimization algorithm, are presented and discussed, showing that the method is valid but can be improved. Two constraints on the search space are briefly presented for that aim.

2. Calculation of gravity and magnetic anomalies along profiles with end corrections and inverse solutions for density and magnetization

1977-01-01

An equation derived for the vertical gravity field due to a body with polygonal cross section and finite strike length.  The equations consists of the 2-dimensional equation of Talwani, Worzel, and Landisman (1959), with the addition of end corrections.  Equations for the magnetic field due to a similar body were derived by Shuey and Pasquale (1973).  They coined the term "2 1/2-dimensional" to describe the geometry.

3. An inverse hyperbolic heat conduction problem in estimating surface heat flux by the conjugate gradient method

Huang, C.-H.; Wu, H.-H.

2006-01-01

In the present study an inverse hyperbolic heat conduction problem is solved by the conjugate gradient method (CGM) in estimating the unknown boundary heat flux based on the boundary temperature measurements. Results obtained in this inverse problem will be justified based on the numerical experiments where three different heat flux distributions are to be determined. Results show that the inverse solutions can always be obtained with any arbitrary initial guesses of the boundary heat flux. Moreover, the drawbacks of the previous study for this similar inverse problem, such as (1) the inverse solution has phase error and (2) the inverse solution is sensitive to measurement error, can be avoided in the present algorithm. Finally, it is concluded that accurate boundary heat flux can be estimated in this study

4. Model Based Beamforming and Bayesian Inversion Signal Processing Methods for Seismic Localization of Underground Source

Oh, Geok Lian

properties such as the elastic wave speeds and soil densities. One processing method is casting the estimation problem into an inverse problem to solve for the unknown material parameters. The forward model for the seismic signals used in the literatures include ray tracing methods that consider only...... density values of the discretized ground medium, which leads to time-consuming computations and instability behaviour of the inversion process. In addition, the geophysics inverse problem is generally ill-posed due to non-exact forward model that introduces errors. The Bayesian inversion method through...... the first arrivals of the reflected compressional P-waves from the subsurface structures, or 3D elastic wave models that model all the seismic wave components. The ray tracing forward model formulation is linear, whereas the full 3D elastic wave model leads to a nonlinear inversion problem. In this Ph...

5. Four-dimensional variational data assimilation for inverse modelling of atmospheric methane emissions: method and comparison with synthesis inversion

J. F. Meirink

2008-11-01

Full Text Available A four-dimensional variational (4D-Var data assimilation system for inverse modelling of atmospheric methane emissions is presented. The system is based on the TM5 atmospheric transport model. It can be used for assimilating large volumes of measurements, in particular satellite observations and quasi-continuous in-situ observations, and at the same time it enables the optimization of a large number of model parameters, specifically grid-scale emission rates. Furthermore, the variational method allows to estimate uncertainties in posterior emissions. Here, the system is applied to optimize monthly methane emissions over a 1-year time window on the basis of surface observations from the NOAA-ESRL network. The results are rigorously compared with an analogous inversion by Bergamaschi et al. (2007, which was based on the traditional synthesis approach. The posterior emissions as well as their uncertainties obtained in both inversions show a high degree of consistency. At the same time we illustrate the advantage of 4D-Var in reducing aggregation errors by optimizing emissions at the grid scale of the transport model. The full potential of the assimilation system is exploited in Meirink et al. (2008, who use satellite observations of column-averaged methane mixing ratios to optimize emissions at high spatial resolution, taking advantage of the zooming capability of the TM5 model.

6. Canonical methods in classical and quantum gravity: An invitation to canonical LQG

Reyes, Juan D.

2018-04-01

Loop Quantum Gravity (LQG) is a candidate quantum theory of gravity still under construction. LQG was originally conceived as a background independent canonical quantization of Einstein’s general relativity theory. This contribution provides some physical motivations and an overview of some mathematical tools employed in canonical Loop Quantum Gravity. First, Hamiltonian classical methods are reviewed from a geometric perspective. Canonical Dirac quantization of general gauge systems is sketched next. The Hamiltonian formultation of gravity in geometric ADM and connection-triad variables is then presented to finally lay down the canonical loop quantization program. The presentation is geared toward advanced undergradute or graduate students in physics and/or non-specialists curious about LQG.

7. Full waveform inversion using oriented time-domain imaging method for vertical transverse isotropic media

Zhang, Zhendong

2017-07-11

Full waveform inversion for reection events is limited by its linearized update re-quirements given by a process equivalent to migration. Unless the background velocity model is reasonably accurate, the resulting gradient can have an inaccurate update direction leading the inversion to converge what we refer to as local minima of the objective function. In our approach, we consider mild lateral variation in the model, and thus, use a gradient given by the oriented time-domain imaging method. Specifically, we apply the oriented time-domain imaging on the data residual to obtain the geometrical features of the velocity perturbation. After updating the model in the time domain, we convert the perturbation from the time domain to depth using the average velocity. Considering density is constant, we can expand the conventional 1D impedance inversion method to 2D or 3D velocity inversion within the process of full waveform inversion. This method is not only capable of inverting for velocity, but it is also capable of retrieving anisotropic parameters relying on linearized representations of the reection response. To eliminate the cross-talk artifacts between different parameters, we utilize what we consider being an optimal parametrization for this step. To do so, we extend the prestack time-domain migration image in incident angle dimension to incorporate angular dependence needed by the multiparameter inversion. For simple models, this approach provides an efficient and stable way to do full waveform inversion or modified seismic inversion and makes the anisotropic inversion more practicable. The proposed method still needs kinematically accurate initial models since it only recovers the high-wavenumber part as conventional full waveform inversion method does. Results on synthetic data of isotropic and anisotropic cases illustrate the benefits and limitations of this method.

8. Method for the preparation of metal colloids in inverse micelles and product preferred by the method

Wilcoxon, Jess P.

1992-01-01

A method is provided for preparing catalytic elemental metal colloidal particles (e.g. gold, palladium, silver, rhodium, iridium, nickel, iron, platinum, molybdenum) or colloidal alloy particles (silver/iridium or platinum/gold). A homogeneous inverse micelle solution of a metal salt is first formed in a metal-salt solvent comprised of a surfactant (e.g. a nonionic or cationic surfactant) and an organic solvent. The size and number of inverse micelles is controlled by the proportions of the surfactant and the solvent. Then, the metal salt is reduced (by chemical reduction or by a pulsed or continuous wave UV laser) to colloidal particles of elemental metal. After their formation, the colloidal metal particles can be stabilized by reaction with materials that permanently add surface stabilizing groups to the surface of the colloidal metal particles. The sizes of the colloidal elemental metal particles and their size distribution is determined by the size and number of the inverse micelles. A second salt can be added with further reduction to form the colloidal alloy particles. After the colloidal elemental metal particles are formed, the homogeneous solution distributes to two phases, one phase rich in colloidal elemental metal particles and the other phase rich in surfactant. The colloidal elemental metal particles from one phase can be dried to form a powder useful as a catalyst. Surfactant can be recovered and recycled from the phase rich in surfactant.

9. Testing joint inversion techniques of gravity data and cosmic ray muon flux at a well-characterized site for use in the detection of subsurface density structures beneath volcanoes.

Cosburn, K.; Roy, M.; Rowe, C. A.; Guardincerri, E.

2017-12-01

Obtaining accurate static and time-dependent shallow subsurface density structure beneath volcanic, hydrogeologic, and tectonic targets can help illuminate active processes of fluid flow and magma transport. A limitation of using surface gravity measurements for such imaging is that these observations are vastly underdetermined and non-unique. In order to hone in on a more accurate solution, other data sets are needed to provide constraints, typically seismic or borehole observations. The spatial resolution of these techniques, however, is relatively poor, and a novel solution to this problem in recent years has been to use attenuation of the cosmic ray muon flux, which provides an independent constraint on density. In this study we present a joint inversion of gravity and cosmic ray muon flux observations to infer the density structure of a target rock volume at a well-characterized site near Los Alamos, New Mexico, USA. We investigate the shallow structure of a mesa formed by the Quaternary ash-flow tuffs on the Pajarito Plateau, flanking the Jemez volcano in New Mexico. Gravity measurements were made using a Lacoste and Romberg D meter on the surface of the mesa and inside a tunnel beneath the mesa. Muon flux measurements were also made at the mesa surface and at various points within the same tunnel using a muon detector having an acceptance region of 45 degrees from the vertical and a track resolution of several milliradians. We expect the combination of muon and gravity data to provide us with enhanced resolution as well as the ability to sense deeper structures in our region of interest. We use Bayesian joint inversion techniques on the gravity-muon dataset to test these ideas, building upon previous work using gravity inversion alone to resolve density structure in our study area. Both the regional geology and geometry of our study area is well-known and we assess the inferred density structure from our gravity-muon joint inversion within this known

10. Joint inversion of ambient noise surface wave and gravity data to image the upper crustal structure of the Tanlu fault zone to the southeast of Hefei, China

Wang, K.; Gu, N.; Zhang, H.; Zhou, G.

2017-12-01

The Tanlu fault is a major fault located in the eastern China, which stretches 2400 km long from Tancheng in the north to Lujiang in the south. It is generally believed that the Tanlu fault zone was formed in Proterozoic era and underwent a series of complicated processes since then. To understand the upper crustal structure around the southern segment of the Tanlu fault zone, in 2017 we deployed 53 short period seismic stations around the fault zone to the southeast of Hefei, capital city of Anhui province. The temporary array continuously recorded the data for about one month from 17 March to 26 April 2017. The seismic array spans an area of about 30km x 30Km with an average station spacing of about 5-6km. The vertical component data were used for extracting Rayleigh wave phase and group velocity dispersion data for the period of 0.2 to 5 seconds. To improve imaging the upper crustal structure of the fault zone, we jointly inverted the surface wave dispersion data and the gravity data because they have complementary strengths. To combine surface wave dispersion data and gravity observations into a single inversion framework, we used an empirical relationship between seismic velocity and density of Maceira and Ammon (2009). By finding the optimal relative weighting between two data types, we are able to find a shear wave velocity (Vs) model that fits both data types. The joint inversion can resolve the upper crustal fault zone structure down to about 7 km in depth. The Vs model shows that in this region the Tanlu fault is associated with high velocity anomalies, corresponding well to the Feidong complex seen on the surface. This indicates that the Tanlu fault zone may provide a channel for the intrusion of hot materials.

11. The inverse method parametric verification of real-time embedded systems

André , Etienne

2013-01-01

This book introduces state-of-the-art verification techniques for real-time embedded systems, based on the inverse method for parametric timed automata. It reviews popular formalisms for the specification and verification of timed concurrent systems and, in particular, timed automata as well as several extensions such as timed automata equipped with stopwatches, linear hybrid automata and affine hybrid automata.The inverse method is introduced, and its benefits for guaranteeing robustness in real-time systems are shown. Then, it is shown how an iteration of the inverse method can solv

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

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...

13. Optimization method for an evolutional type inverse heat conduction problem

Deng Zuicha; Yu Jianning; Yang Liu

2008-01-01

This paper deals with the determination of a pair (q, u) in the heat conduction equation u t -u xx +q(x,t)u=0, with initial and boundary conditions u(x,0)=u 0 (x), u x vertical bar x=0 =u x vertical bar x=1 =0, from the overspecified data u(x, t) = g(x, t). By the time semi-discrete scheme, the problem is transformed into a sequence of inverse problems in which the unknown coefficients are purely space dependent. Based on the optimal control framework, the existence, uniqueness and stability of the solution (q, u) are proved. A necessary condition which is a couple system of a parabolic equation and parabolic variational inequality is deduced

14. Optimization method for an evolutional type inverse heat conduction problem

Deng, Zui-Cha; Yu, Jian-Ning; Yang, Liu

2008-01-01

This paper deals with the determination of a pair (q, u) in the heat conduction equation u_t-u_{xx}+q(x,t)u=0, with initial and boundary conditions u(x,0)=u_0(x),\\qquad u_x|_{x=0}=u_x|_{x=1}=0, from the overspecified data u(x, t) = g(x, t). By the time semi-discrete scheme, the problem is transformed into a sequence of inverse problems in which the unknown coefficients are purely space dependent. Based on the optimal control framework, the existence, uniqueness and stability of the solution (q, u) are proved. A necessary condition which is a couple system of a parabolic equation and parabolic variational inequality is deduced.

15. Effect of templates on inverse opals fabricated through annular self-assembly/sol-gel method

Ge Dengteng; Yang Lili; Fan Zeng; Zhao Jiupeng; Li Yao

2011-01-01

Highlights: → Flexible inverse opals could be facilely prepared through annular growth method. → The infiltrated materials are highly densified due to the existence of templates. → The crystalline grains are refined due to the the existence of templates. - Abstract: There is a strong interest in simple preparation of flexible inverse opals for applications. In this article, indium tin oxides (ITO) flexible inverse opals were prepared through annular growth of templates and sol-gel process. It is shown that this method provides a facile route for large scale flexible inverse opals with excellent ordered structures. ITO materials are found much denser in inverse opals, which is due to the increased capillary force during drying process and enhanced shrinkage during annealing process. It is also found that the crystalline grains are refined and the photoluminescence performance is strengthened in low frequency.

16. Optimization of gold ore Sumbawa separation using gravity method: Shaking table

2018-04-01

Most of artisanal small gold mining in Indonesia has been using amalgamation method, which caused negative impact to the environment around ore processing area due to the usage of mercury. One of the more environmental-friendly method for gold processing is gravity method. Shaking table is one of separation equipment of gravity method used to increase concentrate based on difference of specific gravity. The optimum concentration result is influenced by several variables, such as rotational speed shaking, particle size and deck slope. In this research, the range of rotational speed shaking was between 100 rpm and 200 rpm, the particle size was between -100 + 200 mesh and -200 + 300 mesh and deck slope was between 3° and 7°. Gold concentration in concentrate was measured by EDX. The result shows that the optimum condition is obtained at a shaking speed of 200 rpm, with a slope of 7° and particle size of -100 + 200 mesh.

17. Shrinkage-thresholding enhanced born iterative method for solving 2D inverse electromagnetic scattering problem

Desmal, Abdulla; Bagci, Hakan

2014-01-01

A numerical framework that incorporates recently developed iterative shrinkage thresholding (IST) algorithms within the Born iterative method (BIM) is proposed for solving the two-dimensional inverse electromagnetic scattering problem. IST

18. Micro-seismic imaging using a source function independent full waveform inversion method

Wang, Hanchen; Alkhalifah, Tariq Ali

2018-01-01

hand, the conventional micro-seismic source locating methods require, in many cases manual picking of traveltime arrivals, which do not only lead to manual effort and human interaction, but also prone to errors. Using full waveform inversion (FWI

19. A Frequency Matching Method: Solving Inverse Problems by Use of Geologically Realistic Prior Information

Lange, Katrine; Frydendall, Jan; Cordua, Knud Skou

2012-01-01

The frequency matching method defines a closed form expression for a complex prior that quantifies the higher order statistics of a proposed solution model to an inverse problem. While existing solution methods to inverse problems are capable of sampling the solution space while taking into account...... arbitrarily complex a priori information defined by sample algorithms, it is not possible to directly compute the maximum a posteriori model, as the prior probability of a solution model cannot be expressed. We demonstrate how the frequency matching method enables us to compute the maximum a posteriori...... solution model to an inverse problem by using a priori information based on multiple point statistics learned from training images. We demonstrate the applicability of the suggested method on a synthetic tomographic crosshole inverse problem....

20. Resampling: An optimization method for inverse planning in robotic radiosurgery

Schweikard, Achim; Schlaefer, Alexander; Adler, John R. Jr.

2006-01-01

By design, the range of beam directions in conventional radiosurgery are constrained to an isocentric array. However, the recent introduction of robotic radiosurgery dramatically increases the flexibility of targeting, and as a consequence, beams need be neither coplanar nor isocentric. Such a nonisocentric design permits a large number of distinct beam directions to be used in one single treatment. These major technical differences provide an opportunity to improve upon the well-established principles for treatment planning used with GammaKnife or LINAC radiosurgery. With this objective in mind, our group has developed over the past decade an inverse planning tool for robotic radiosurgery. This system first computes a set of beam directions, and then during an optimization step, weights each individual beam. Optimization begins with a feasibility query, the answer to which is derived through linear programming. This approach offers the advantage of completeness and avoids local optima. Final beam selection is based on heuristics. In this report we present and evaluate a new strategy for utilizing the advantages of linear programming to improve beam selection. Starting from an initial solution, a heuristically determined set of beams is added to the optimization problem, while beams with zero weight are removed. This process is repeated to sample a set of beams much larger compared with typical optimization. Experimental results indicate that the planning approach efficiently finds acceptable plans and that resampling can further improve its efficiency

1. An optical method for measuring the thickness of a falling condensate in gravity assisted heat pipe

Kasanický Martin

2015-01-01

Full Text Available A large number of variables is the main problem of designing systems which uses heat pipes, whether it is a traditional - gravity, or advanced - capillary, pulsating, advanced heat pipes. This article is a methodology for measuring the thickness of the falling condensate in gravitational heat pipes, with using the optical triangulation method, and the evaluation of risks associated with this method.

2. Moving Least Squares Method for a One-Dimensional Parabolic Inverse Problem

Baiyu Wang

2014-01-01

Full Text Available This paper investigates the numerical solution of a class of one-dimensional inverse parabolic problems using the moving least squares approximation; the inverse problem is the determination of an unknown source term depending on time. The collocation method is used for solving the equation; some numerical experiments are presented and discussed to illustrate the stability and high efficiency of the method.

3. Optimization method for identifying the source term in an inverse wave equation

Arumugam Deiveegan

2017-08-01

Full Text Available In this work, we investigate the inverse problem of identifying a space-wise dependent source term of wave equation from the measurement on the boundary. On the basis of the optimal control framework, the inverse problem is transformed into an optimization problem. The existence and necessary condition of the minimizer for the cost functional are obtained. The projected gradient method and two-parameter model function method are applied to the minimization problem and numerical results are illustrated.

4. Response of Gravity, Magnetic, and Geoelectrical Resistivity Methods on Ngeni Southern Blitar Mineralization Zone

Sunaryo

2018-03-01

The research with entitle response of gravity, magnetic, and geoelectrical resistivity methods on Ngeni Southern Blitar mineralization zone has been done. This study aims to find the response of several geophysical methods of gravity, magnetic, and geoelectrical resistivity in an integrated manner. Gravity data acquisition was acquired 224 data which covers the whole region of Blitar district by using Gravity Meter La Coste & Romberg Model “G”, and magnetic data acquisition were acquired 195 data which covers the southern Blitar district only by using Proton Precession Magnetometer G-856. Meanwhile geoelectrical resistivity data only done in Ngeni village which is the location of phyropilite mining with the composition content of Fe, Si, Ca, S, Cu, and Mn by using ABEM Terrameter SAS 300C. Gravity data processing was performed to obtain the Bouguer anomaly value, which included unit conversion, tidal correction, drift correction, correction of tie point, base station correction, free air correction, and Bouguer correction. Magnetic data processing has been done by some corrections i.e daily, drift, and IGRF(International Geomagnetic Refference Field) to obtain the total magnetic anomaly. From gravity data processing has been obtained the simple Bouguer anomaly value in range from -10mGal until 115mGal. From this data processing has been obtained the total magnetic anomaly value in range from -650nT until 800nT. Meanwhile from geoelectrical resistivity 3.03Ωm until 11249.91 Ωm. There is a correlation between gravity anomaly, magnetic anomaly, and geoelectrical resistivity anomaly that are associated with deep anomaly, middle anomaly, and shallow anomaly.

5. Estimation of Bouguer Density Precision: Development of Method for Analysis of La Soufriere Volcano Gravity Data

Gunawan, Hendra; Micheldiament, Micheldiament; Mikhailov, Valentin

2008-01-01

http://dx.doi.org/10.17014/ijog.vol3no3.20084The precision of topographic density (Bouguer density) estimation by the Nettleton approach is based on a minimum correlation of Bouguer gravity anomaly and topography. The other method, the Parasnis approach, is based on a minimum correlation of Bouguer gravity anomaly and Bouguer correction. The precision of Bouguer density estimates was investigated by both methods on simple 2D syntetic models and under an assumption free-air anomaly consisting ...

6. Metamodel-based inverse method for parameter identification: elastic-plastic damage model

Huang, Changwu; El Hami, Abdelkhalak; Radi, Bouchaïb

2017-04-01

This article proposed a metamodel-based inverse method for material parameter identification and applies it to elastic-plastic damage model parameter identification. An elastic-plastic damage model is presented and implemented in numerical simulation. The metamodel-based inverse method is proposed in order to overcome the disadvantage in computational cost of the inverse method. In the metamodel-based inverse method, a Kriging metamodel is constructed based on the experimental design in order to model the relationship between material parameters and the objective function values in the inverse problem, and then the optimization procedure is executed by the use of a metamodel. The applications of the presented material model and proposed parameter identification method in the standard A 2017-T4 tensile test prove that the presented elastic-plastic damage model is adequate to describe the material's mechanical behaviour and that the proposed metamodel-based inverse method not only enhances the efficiency of parameter identification but also gives reliable results.

7. A simple method for solving the inverse scattering problem

Melnikov, V.N.; Rudyak, B.V.; Zakhariev, V.N.

1977-01-01

A new method is proposed for approximate reconstruction of a potential as a step function from scattering data using the completeness relation of solutions of the Schroedinger equation. The suggested method allows one to take into account exactly the additional centrifugal barrier for partial waves with angular momentum l>0, and also the Coulomb potential. The method admits different generalizations. Numerical calculations for checking the method have been performed

8. Assessment of Groundwater Chemical Quality, Using Inverse Distance Weighted Method

Sh. Ashraf

2013-04-01

Full Text Available An interpolation technique, ordinary Inverse Distance Weighted (IDW, was used to obtain the spatial distribution of groundwater quality parameters in Damghan plain of Iran. According to Scofield guidelines for TDS value, 60% of the water samples were harmful for irrigation purposes. Regarding to EC parameter, more than 60% of studied area was laid in bad range for irrigation purposes. The most dominant anion was Cl- and 10% of water samples showed a very hazardous class. According to Doneen guidelines for chloride value, 100% of collected water from the aquifer had slight to moderate problems for irrigation water purposes. The predominant cations in Damghan plain aquifer were according to Na+> Ca++> Mg++> K+. Sodium ion was the dominant cation and regarding to Na+ content guidelines, almost all groundwater samples had problem for foliar application. Calcium ion distribution was within usual range. The magnesium ion concentration is generally lower than sodium and calcium. The majority of the samples showed Mg++amount within usual range. Also K+ value ranged from 0.1 to 0.23 meq/L and all the water samples had potassium values within the permissible limit. Based on SAR criterion 80 % of collected water had slight to moderate problems. The SSP values were found from 2.87 to 6.87%. According to SAR value, thirty percent of ground water samples were doubtful class. The estimated amounts of RSC were ranged from 0.4-2 and based on RSC criterion, twenty percent of groundwater samples had slight to moderate problems.

9. Implementing gravity method on geological contacts in Bukit Bunuh, Lenggong, Perak (Malaysia)

Hidayah, I N E; Saad, Rosli; Nordiana, M M; Azwin, I N; Bery, Andy Anderson; Saidin, Mokhtar

2015-01-01

Using gravity method, a study of responses of different geological settings towards gravity was conducted in Bukit Bunuh, Lenggong, Perak (Malaysia). Gravity method provides different responses towards different rock types depending on the rock density. The survey area cover an area of 12 km 2 , with a total 404 survey stations with stations interval of approximately 50 m and 500 m. The Bouguer anomaly map identifies the shallow granite rock with a value of -6 to -10.5 mGal while shallow limestone is -11 to -15 mGal. The sediment/overburden was identified with value of < -15.5 mGal. Few fractures are also identified and the boundary between limestone and granite rocks identified at the north part of the study area

10. Application of specific gravity method for normalization of urinary excretion rates of radionuclides

Thakur, Smita S.; Yadav, J.R.; Rao, D.D.

2015-01-01

In vitro bioassay monitoring is based on the determination of activity concentration in biological samples excreted from the body and is most suitable for alpha and beta emitters. For occupational workers handling actinides in reprocessing facilities possibility of internal exposure exists and urine assay is preferred method for monitoring such exposure. Urine samples collected for 24 h duration, is the true representative of bioassay sample and hence in the case of insufficient collection time, specific gravity applied method of normalization of urine sample is used. The present study reports the data of specific gravity generated for controlled group of Indian population by the use of densitometer and its application in urinary sample activity normalization. The average specific gravity value obtained for the controlled group was 1.008±0.005 gm/ml. (author)

11. The use of gravity methods in the internal characterization of landfills—a case study

Mantlík, František; Matias, Manuel; Grangeia, Carlos; Tareco, Hélder; Lourenço, Jose

2009-01-01

Some examples of the use of gravity exploration methods in landfills were published recently. However, density contrast between the landfill and the host media as well as the cost involved may be limiting factors to the application of gravimetry to this problem. Herein a case study of the application of gravity methods to the internal characterization of a sealed landfill is presented. This landfill is installed in recent low-density quaternary sand formations. Two north–south gravity profiles were carried out. The first profile crossed the landfill at its centre, whilst a second profile was done some distance away from the landfill to provide general regional information. The first profile was modelled in order to obtain lateral variations of density within the landfill that might be caused by different types of waste and/or the age of the waste deposits. Gravity modelling and interpretation were supported with data from resistivity profiles carried out in the immediate vicinity of the gravity measurements, i.e. the resistivity profiles interpretation results constrained the thickness of landfill deposits

12. FOREWORD: 5th International Workshop on New Computational Methods for Inverse Problems

Vourc'h, Eric; Rodet, Thomas

2015-11-01

This volume of Journal of Physics: Conference Series is dedicated to the scientific research presented during the 5th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2015 (http://complement.farman.ens-cachan.fr/NCMIP_2015.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 29, 2015. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011, and secondly at the initiative of Institut Farman, in May 2012, May 2013 and May 2014. The New Computational Methods for Inverse Problems (NCMIP) workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, Kernel methods, learning methods

13. FOREWORD: 4th International Workshop on New Computational Methods for Inverse Problems (NCMIP2014)

2014-10-01

This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 4th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2014 (http://www.farman.ens-cachan.fr/NCMIP_2014.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 23, 2014. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/), and secondly at the initiative of Institut Farman, in May 2012 and May 2013, (http://www.farman.ens-cachan.fr/NCMIP_2012.html), (http://www.farman.ens-cachan.fr/NCMIP_2013.html). The New Computational Methods for Inverse Problems (NCMIP) Workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the

14. Assessment of Groundwater Chemical Quality, Using Inverse Distance Weighted Method

Sh. Ashraf

2014-02-01

Full Text Available An interpolation technique, ordinary Inverse Distance Weighted (IDW, was used to obtain the spatial distribution of groundwater quality parameters in Damghan plain of Iran. According to Scofield guidelines for TDS   value, 60% of the water samples were harmful for irrigation purposes. Regarding to EC parameter, more than 60% of studied area was laid in bad range for irrigation purposes. The most dominant anion was Cl- and 10% of water samples showed a very hazardous class. According to  Doneen  guidelines for  chloride value, 100%  of  collected  water  from the  aquifer  had  slight to moderate problems  for  irrigation water purposes. The predominant cations in Damghan plain aquifer were according to Na+> Ca++> Mg++> K+. Sodium ion was the dominant cation and regarding to Na+ content guidelines, almost all groundwater samples had problem for foliar application. Calcium ion distribution was within usual range. The magnesium ion concentration is generally lower than sodium and calcium. The majority of the samples showed   Mg++amount within usual range. Also K+ value ranged from 0.1 to 0.23 meq/L and all the water samples had potassium values within the permissible limit. Based on SAR criterion 80 % of collected water had slight to moderate problems. The SSP values were found from 2.87 to 6.87%. According to SAR value, thirty percent of ground water samples were doubtful class. The estimated amounts of RSC were ranged from 0.4-2 and based on RSC criterion, twenty percent of groundwater samples had slight to moderate problems Normal 0 false false false EN-US X-NONE AR-SA /* Style Definitions */ table.MsoNormalTable {mso-style-name:"Table Normal"; mso-tstyle-rowband-size:0; mso-tstyle-colband-size:0; mso-style-noshow:yes; mso-style-priority:99; mso-style-parent:""; mso-padding-alt:0cm 5.4pt 0cm 5.4pt; mso-para-margin:0cm; mso-para-margin-bottom:.0001pt; mso-pagination:widow-orphan; font-size:10.0pt; font

15. Joint inversion of seismic and gravity data for imaging seismic velocity structure of the crust and upper mantle beneath Utah, United States

Syracuse, E. M.; Zhang, H.; Maceira, M.

2017-10-01

We present a method for using any combination of body wave arrival time measurements, surface wave dispersion observations, and gravity data to simultaneously invert for three-dimensional P- and S-wave velocity models. The simultaneous use of disparate data types takes advantage of the differing sensitivities of each data type, resulting in a comprehensive and higher resolution three-dimensional geophysical model. In a case study for Utah, we combine body wave first arrivals mainly from the USArray Transportable Array, Rayleigh wave group and phase velocity dispersion data, and Bouguer gravity anomalies to invert for crustal and upper mantle structure of the region. Results show clear delineations, visible in both P- and S-wave velocities, between the three main tectonic provinces in the region. Without the inclusion of the surface wave and gravity constraints, these delineations are less clear, particularly for S-wave velocities. Indeed, checkerboard tests confirm that the inclusion of the additional datasets dramatically improves S-wave velocity recovery, with more subtle improvements to P-wave velocity recovery, demonstrating the strength of the method in successfully recovering seismic velocity structure from multiple types of constraints.

16. Instructions for applying inverse method for reactivity measurement

Milosevic, M.

1988-11-01

This report is a brief description of the completed method for reactivity measurement. It contains description of the experimental procedure needed instrumentation and computer code IM for determining reactivity. The objective of this instructions manual is to enable experiments and reactivity measurement on any critical system according to the methods adopted at the RB reactor

17. Inversion of quasi-periodic deviations between low-degree solar gravity mode eigenfrequencies and asymptotic theory eigenfrequencies

Hill, H.A.; Gao, Qiang; Rosenwald, R.D.

1988-01-01

The fine structure found by Gu, Hill and Rosenwald between asymptotic theory eigenfrequencies and the observed eigenfrequencies reported by Hill and Gu is interpreted as the result of conditions not being met for the applicability of asymptotic theory at one or more radii in the solar interior. From an inversion of the observed fine structure, reasonably good agreement is obtained between observation and theory for either a localized perturbation in internal structure at r/R ∼ 0.06 or at r/R ∼ 0.23. The latter solution is, however, the better one. The amplitude of the perturbation in the mean molecular weight required to produce the fine structure is also inferred. 11 refs., 2 figs

18. Solution of axisymmetric transient inverse heat conduction problems using parameter estimation and multi block methods

Azimi, A.; Hannani, S.K.; Farhanieh, B.

2005-01-01

In this article, a comparison between two iterative inverse techniques to solve simultaneously two unknown functions of axisymmetric transient inverse heat conduction problems in semi complex geometries is presented. The multi-block structured grid together with blocked-interface nodes is implemented for geometric decomposition of physical domain. Numerical scheme for solution of transient heat conduction equation is the finite element method with frontal technique to solve algebraic system of discrete equations. The inverse heat conduction problem involves simultaneous unknown time varying heat generation and time-space varying boundary condition estimation. Two parameter-estimation techniques are considered, Levenberg-Marquardt scheme and conjugate gradient method with adjoint problem. Numerically computed exact and noisy data are used for the measured transient temperature data needed in the inverse solution. The results of the present study for a configuration including two joined disks with different heights are compared to those of exact heat source and temperature boundary condition, and show good agreement. (author)

19. A fully general and adaptive inverse analysis method for cementitious materials

Jepsen, Michael S.; Damkilde, Lars; Lövgren, Ingemar

2016-01-01

The paper presents an adaptive method for inverse determination of the tensile σ - w relationship, direct tensile strength and Young’s modulus of cementitious materials. The method facilitates an inverse analysis with a multi-linear σ - w function. Usually, simple bi- or tri-linear functions...... are applied when modeling the fracture mechanisms in cementitious materials, but the vast development of pseudo-strain hardening, fiber reinforced cementitious materials require inverse methods, capable of treating multi-linear σ - w functions. The proposed method is fully general in the sense that it relies...... of notched specimens and simulated data from a nonlinear hinge model. The paper shows that the results obtained by means of the proposed method is independent on the initial shape of the σ - w function and the initial guess of the tensile strength. The method provides very accurate fits, and the increased...

20. Intelligent inversion method for pre-stack seismic big data based on MapReduce

Yan, Xuesong; Zhu, Zhixin; Wu, Qinghua

2018-01-01

Seismic exploration is a method of oil exploration that uses seismic information; that is, according to the inversion of seismic information, the useful information of the reservoir parameters can be obtained to carry out exploration effectively. Pre-stack data are characterised by a large amount of data, abundant information, and so on, and according to its inversion, the abundant information of the reservoir parameters can be obtained. Owing to the large amount of pre-stack seismic data, existing single-machine environments have not been able to meet the computational needs of the huge amount of data; thus, the development of a method with a high efficiency and the speed to solve the inversion problem of pre-stack seismic data is urgently needed. The optimisation of the elastic parameters by using a genetic algorithm easily falls into a local optimum, which results in a non-obvious inversion effect, especially for the optimisation effect of the density. Therefore, an intelligent optimisation algorithm is proposed in this paper and used for the elastic parameter inversion of pre-stack seismic data. This algorithm improves the population initialisation strategy by using the Gardner formula and the genetic operation of the algorithm, and the improved algorithm obtains better inversion results when carrying out a model test with logging data. All of the elastic parameters obtained by inversion and the logging curve of theoretical model are fitted well, which effectively improves the inversion precision of the density. This algorithm was implemented with a MapReduce model to solve the seismic big data inversion problem. The experimental results show that the parallel model can effectively reduce the running time of the algorithm.

1. Solving inverse problems for biological models using the collage method for differential equations.

Capasso, V; Kunze, H E; La Torre, D; Vrscay, E R

2013-07-01

In the first part of this paper we show how inverse problems for differential equations can be solved using the so-called collage method. Inverse problems can be solved by minimizing the collage distance in an appropriate metric space. We then provide several numerical examples in mathematical biology. We consider applications of this approach to the following areas: population dynamics, mRNA and protein concentration, bacteria and amoeba cells interaction, tumor growth.

2. A general method for closed-loop inverse simulation of helicopter maneuver flight

Wei WU

2017-01-01

Maneuverability is a key factor to determine whether a helicopter could finish certain flight missions successfully or not. Inverse simulation is commonly used to calculate the pilot controls of a helicopter to complete a certain kind of maneuver flight and to assess its maneuverability. A general method for inverse simulation of maneuver flight for helicopters with the flight control system online is developed in this paper. A general mathematical describing function is established to provid...

3. Review of Electrical and Gravity Methods of Near-Surface Exploration for Groundwater

W. O. Raji

2014-12-01

Full Text Available The theory and practice of electrical and gravity methods of geophysics for groundwater exploration was reviewed with illustrations and data examples. With the goal of reducing cases of borehole/water-well failure attributed to the lack of the knowledge of the methods of geophysics for groundwater exploration and development, the paper reviews the basic concepts, field procedures for data acquisition, data processing, and interpretation as applied to the subject matter. Given a case study of groundwater exploration in University of Ilorin Campus, the three important techniques of electrical method of groundwater exploration are explained and illustrated using field data obtained in a previous study. Interpretation of resistivity data shows that an area measuring low resistivity (high conductivity, having thick pile of unconsolidated rock, and underlained by fracture crystalline is a ‘bright spot’ for citing borehole for groundwater abstraction in a basement complex area. Further to this, gravity method of groundwater exploration was discussed with field data from Wokbedilo community in Ethopia. Bouguer and reduced gravity anomaly results were presented as maps and contours to demonstrate how gravity data can be inverted to map groundwater aquifers and subsurface geological structures during groundwater exploration.

4. GOCE in ocean modelling - Point mass method applied on GOCE gravity gradients

Herceg, Matija; Knudsen, Per

This presentation is an introduction to my Ph.D project. The main objective of the study is to improve the methodology for combining GOCE gravity field models with satellite altimetry to derive optimal dynamic ocean topography models for oceanography. Here a method for geoid determination using...

5. Constructing inverse probability weights for continuous exposures: a comparison of methods.

Naimi, Ashley I; Moodie, Erica E M; Auger, Nathalie; Kaufman, Jay S

2014-03-01

Inverse probability-weighted marginal structural models with binary exposures are common in epidemiology. Constructing inverse probability weights for a continuous exposure can be complicated by the presence of outliers, and the need to identify a parametric form for the exposure and account for nonconstant exposure variance. We explored the performance of various methods to construct inverse probability weights for continuous exposures using Monte Carlo simulation. We generated two continuous exposures and binary outcomes using data sampled from a large empirical cohort. The first exposure followed a normal distribution with homoscedastic variance. The second exposure followed a contaminated Poisson distribution, with heteroscedastic variance equal to the conditional mean. We assessed six methods to construct inverse probability weights using: a normal distribution, a normal distribution with heteroscedastic variance, a truncated normal distribution with heteroscedastic variance, a gamma distribution, a t distribution (1, 3, and 5 degrees of freedom), and a quantile binning approach (based on 10, 15, and 20 exposure categories). We estimated the marginal odds ratio for a single-unit increase in each simulated exposure in a regression model weighted by the inverse probability weights constructed using each approach, and then computed the bias and mean squared error for each method. For the homoscedastic exposure, the standard normal, gamma, and quantile binning approaches performed best. For the heteroscedastic exposure, the quantile binning, gamma, and heteroscedastic normal approaches performed best. Our results suggest that the quantile binning approach is a simple and versatile way to construct inverse probability weights for continuous exposures.

6. Inverse analysis of a rectangular fin using the lattice Boltzmann method

2015-01-01

Highlights: • Lattice Boltzmann method is used to study a transient conductive-convective fin. • LBM and Conjugate Gradient Method (CGM) are used to solve an inverse problem in fins. • LBM–ACGM estimates the unknown boundary conditions of fins accurately. • The accuracy and CPU time of LBM–ACGM are compared to IFDM–ACGM. • LBM–ACGM could be a good alternative for the conventional inverse methods. - Abstract: Inverse methods have many applications in determining unknown variables in heat transfer problems when direct measurements are impossible. As most common inverse methods are iterative and time consuming especially for complex geometries, developing more efficient methods seems necessary. In this paper, a direct transient conduction–convection heat transfer problem (fin) under several boundary conditions was solved by using lattice Boltzmann method (LBM), and then the results were successfully validated against both the finite difference method and analytical solution. Then, in the inverse problem both unknown base temperatures and heat fluxes in the rectangular fin were estimated by combining the adjoint conjugate gradient method (ACGM) and LBM. A close agreement between the exact values and estimated results confirmed the validity and accuracy of the ACGM–LBM. To compare the calculation time of ACGM–LBM, the inverse problem was solved by implicit finite difference methods as well. This comparison proved that the ACGM–LBM was an accurate and fast method to determine unknown thermal boundary conditions in transient conduction–convection heat transfer problems. The findings can efficiently determine the unknown variables in fins when a desired temperature distribution is available

7. An inverse method for the design of TIR collimators to achieve a uniform color light beam

Prins, C.R.; Thije Boonkkamp, ten J.H.M.; Tukker, T.W.; IJzerman, W.L.

2012-01-01

Color over Angle (CoA) variation in the light output of white LEDs is a common and unsolved problem. In this article we introduce a new method to reduce CoA variation using a special collimator. The method is based on analytical inverse design methods. We present a numerical algorithm to solve the

8. An inverse method for the design of TIR collimators to achieve a uniform color light beam

Prins, C.R.; Thije Boonkkamp, ten J.H.M.; Tukker, T.W.; IJzerman, W.L.

2013-01-01

Color-over-angle (CoA) variation in the light output of white LEDs is a common and unsolved problem. In this article we introduce a new method to reduce CoA variation using a special collimator. The method is based on analytical inverse design methods. We present a numerical algorithm to solve the

9. Liouville's theorem and the method of the inverse problem

Its, A.R.

1985-01-01

An approach to the investigation of the Zakharov-Shabat equations is developed. This approach is based on a classical theorem of Liouville and is the synthesis of ''finite-zone'' integration, the matrix Riemann problem method and the theory of isomonodromy deformations of differential equations. The effectiveness of the proposed scheme is demonstrated by developing ''dressing procedures'' for the Bullough-Dodd equation

10. Active Subspace Methods for Data-Intensive Inverse Problems

Wang, Qiqi [Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

2017-04-27

The project has developed theory and computational tools to exploit active subspaces to reduce the dimension in statistical calibration problems. This dimension reduction enables MCMC methods to calibrate otherwise intractable models. The same theoretical and computational tools can also reduce the measurement dimension for calibration problems that use large stores of data.

11. Spatial homogenization method based on the inverse problem

Tóta, Ádám; Makai, Mihály

2015-01-01

Highlights: • We derive a spatial homogenization method in slab and cylindrical geometries. • The fluxes and the currents on the boundary are preserved. • The reaction rates and the integral of the fluxes are preserved. • We present verification computations utilizing two- and four-energy groups. - Abstract: We present a method for deriving homogeneous multi-group cross sections to replace a heterogeneous region’s multi-group cross sections; providing that the fluxes, the currents on the external boundary, the reaction rates and the integral of the fluxes are preserved. We consider one-dimensional geometries: a symmetric slab and a homogeneous cylinder. Assuming that the boundary fluxes are given, two response matrices (RMs) can be defined concerning the current and the flux integral. The first one derives the boundary currents from the boundary fluxes, while the second one derives the flux integrals from the boundary fluxes. Further RMs can be defined that connects reaction rates to the boundary fluxes. Assuming that these matrices are known, we present formulae that reconstruct the multi-group diffusion cross-section matrix, the diffusion coefficients and the reaction cross sections in case of one-dimensional (1D) homogeneous regions. We apply these formulae to 1D heterogeneous regions and thus obtain a homogenization method. This method produces such an equivalent homogeneous material, that the fluxes and the currents on the external boundary, the reaction rates and the integral of the fluxes are preserved for any boundary fluxes. We carry out the exact derivations in 1D slab and cylindrical geometries. Verification computations for the presented homogenization method were performed using two- and four-group material cross sections, both in a slab and in a cylindrical geometry

12. 3D CSEM inversion based on goal-oriented adaptive finite element method

Zhang, Y.; Key, K.

2016-12-01

We present a parallel 3D frequency domain controlled-source electromagnetic inversion code name MARE3DEM. Non-linear inversion of observed data is performed with the Occam variant of regularized Gauss-Newton optimization. The forward operator is based on the goal-oriented finite element method that efficiently calculates the responses and sensitivity kernels in parallel using a data decomposition scheme where independent modeling tasks contain different frequencies and subsets of the transmitters and receivers. To accommodate complex 3D conductivity variation with high flexibility and precision, we adopt the dual-grid approach where the forward mesh conforms to the inversion parameter grid and is adaptively refined until the forward solution converges to the desired accuracy. This dual-grid approach is memory efficient, since the inverse parameter grid remains independent from fine meshing generated around the transmitter and receivers by the adaptive finite element method. Besides, the unstructured inverse mesh efficiently handles multiple scale structures and allows for fine-scale model parameters within the region of interest. Our mesh generation engine keeps track of the refinement hierarchy so that the map of conductivity and sensitivity kernel between the forward and inverse mesh is retained. We employ the adjoint-reciprocity method to calculate the sensitivity kernels which establish a linear relationship between changes in the conductivity model and changes in the modeled responses. Our code uses a direcy solver for the linear systems, so the adjoint problem is efficiently computed by re-using the factorization from the primary problem. Further computational efficiency and scalability is obtained in the regularized Gauss-Newton portion of the inversion using parallel dense matrix-matrix multiplication and matrix factorization routines implemented with the ScaLAPACK library. We show the scalability, reliability and the potential of the algorithm to deal with

13. Numerical Methods for Forward and Inverse Problems in Discontinuous Media

Chartier, Timothy P.

2011-03-08

The research emphasis under this grant's funding is in the area of algebraic multigrid methods. The research has two main branches: 1) exploring interdisciplinary applications in which algebraic multigrid can make an impact and 2) extending the scope of algebraic multigrid methods with algorithmic improvements that are based in strong analysis.The work in interdisciplinary applications falls primarily in the field of biomedical imaging. Work under this grant demonstrated the effectiveness and robustness of multigrid for solving linear systems that result from highly heterogeneous finite element method models of the human head. The results in this work also give promise to medical advances possible with software that may be developed. Research to extend the scope of algebraic multigrid has been focused in several areas. In collaboration with researchers at the University of Colorado, Lawrence Livermore National Laboratory, and Los Alamos National Laboratory, the PI developed an adaptive multigrid with subcycling via complementary grids. This method has very cheap computing costs per iterate and is showing promise as a preconditioner for conjugate gradient. Recent work with Los Alamos National Laboratory concentrates on developing algorithms that take advantage of the recent advances in adaptive multigrid research. The results of the various efforts in this research could ultimately have direct use and impact to researchers for a wide variety of applications, including, astrophysics, neuroscience, contaminant transport in porous media, bi-domain heart modeling, modeling of tumor growth, and flow in heterogeneous porous media. This work has already led to basic advances in computational mathematics and numerical linear algebra and will continue to do so into the future.

14. Novel TMS coils designed using an inverse boundary element method

Cobos Sánchez, Clemente; María Guerrero Rodriguez, Jose; Quirós Olozábal, Ángel; Blanco-Navarro, David

2017-01-01

In this work, a new method to design TMS coils is presented. It is based on the inclusion of the concept of stream function of a quasi-static electric current into a boundary element method. The proposed TMS coil design approach is a powerful technique to produce stimulators of arbitrary shape, and remarkably versatile as it permits the prototyping of many different performance requirements and constraints. To illustrate the power of this approach, it has been used for the design of TMS coils wound on rectangular flat, spherical and hemispherical surfaces, subjected to different constraints, such as minimum stored magnetic energy or power dissipation. The performances of such coils have been additionally described; and the torque experienced by each stimulator in the presence of a main magnetic static field have theoretically found in order to study the prospect of using them to perform TMS and fMRI concurrently. The obtained results show that described method is an efficient tool for the design of TMS stimulators, which can be applied to a wide range of coil geometries and performance requirements.

15. A Decoupling Control Method for Shunt Hybrid Active Power Filter Based on Generalized Inverse System

Xin Li

2017-01-01

Full Text Available In this paper, a novel decoupling control method based on generalized inverse system is presented to solve the problem of SHAPF (Shunt Hybrid Active Power Filter possessing the characteristics of 2-input-2-output nonlinearity and strong coupling. Based on the analysis of operation principle, the mathematical model of SHAPF is firstly built, which is verified to be invertible using interactor algorithm; then the generalized inverse system of SHAPF is obtained to connect in series with the original system so that the composite system is decoupled under the generalized inverse system theory. The PI additional controller is finally designed to control the decoupled 1-order pseudolinear system to make it possible to adjust the performance of the subsystem. The simulation results demonstrated by MATLAB show that the presented generalized inverse system strategy can realise the dynamic decoupling of SHAPF. And the control system has fine dynamic and static performance.

16. On the feasibility of inversion methods based on models of urban sky glow

Kolláth, Z.; Kránicz, B.

2014-01-01

Multi-wavelength imaging luminance photometry of sky glow provides a huge amount of information on light pollution. However, the understanding of the measured data involves the combination of different processes and data of radiation transfer, atmospheric physics and atmospheric constitution. State-of-the-art numerical radiation transfer models provide the possibility to define an inverse problem to obtain information on the emission intensity distribution of a city and perhaps the physical properties of the atmosphere. We provide numerical tests on the solvability and feasibility of such procedures. - Highlights: • A method of urban sky glow inversion is introduced based on Monte-Carlo calculations. • Imaging photometry can provide enough information for basic inversions. • The inversion technique can be used to construct maps of light pollution. • The inclusion of multiple scattering in the models plays an important role

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

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.

18. Treating experimental data of inverse kinetic method by unitary linear regression analysis

Zhao Yusen; Chen Xiaoliang

2009-01-01

The theory of treating experimental data of inverse kinetic method by unitary linear regression analysis was described. Not only the reactivity, but also the effective neutron source intensity could be calculated by this method. Computer code was compiled base on the inverse kinetic method and unitary linear regression analysis. The data of zero power facility BFS-1 in Russia were processed and the results were compared. The results show that the reactivity and the effective neutron source intensity can be obtained correctly by treating experimental data of inverse kinetic method using unitary linear regression analysis and the precision of reactivity measurement is improved. The central element efficiency can be calculated by using the reactivity. The result also shows that the effect to reactivity measurement caused by external neutron source should be considered when the reactor power is low and the intensity of external neutron source is strong. (authors)

19. Sharp Boundary Inversion of 2D Magnetotelluric Data using Bayesian Method.

Zhou, S.; Huang, Q.

2017-12-01

Normally magnetotelluric(MT) inversion method cannot show the distribution of underground resistivity with clear boundary, even if there are obviously different blocks. Aiming to solve this problem, we develop a Bayesian structure to inverse 2D MT sharp boundary data, using boundary location and inside resistivity as the random variables. Firstly, we use other MT inversion results, like ModEM, to analyze the resistivity distribution roughly. Then, we select the suitable random variables and change its data format to traditional staggered grid parameters, which can be used to do finite difference forward part. Finally, we can shape the posterior probability density(PPD), which contains all the prior information and model-data correlation, by Markov Chain Monte Carlo(MCMC) sampling from prior distribution. The depth, resistivity and their uncertainty can be valued. It also works for sensibility estimation. We applied the method to a synthetic case, which composes two large abnormal blocks in a trivial background. We consider the boundary smooth and the near true model weight constrains that mimic joint inversion or constrained inversion, then we find that the model results a more precise and focused depth distribution. And we also test the inversion without constrains and find that the boundary could also be figured, though not as well. Both inversions have a good valuation of resistivity. The constrained result has a lower root mean square than ModEM inversion result. The data sensibility obtained via PPD shows that the resistivity is the most sensible, center depth comes second and both sides are the worst.

20. On rational approximation methods for inverse source problems

Rundell, William

2011-02-01

The basis of most imaging methods is to detect hidden obstacles or inclusions within a body when one can only make measurements on an exterior surface. Such is the ubiquity of these problems, the underlying model can lead to a partial differential equation of any of the major types, but here we focus on the case of steady-state electrostatic or thermal imaging and consider boundary value problems for Laplace\\'s equation. Our inclusions are interior forces with compact support and our data consists of a single measurement of (say) voltage/current or temperature/heat flux on the external boundary. We propose an algorithm that under certain assumptions allows for the determination of the support set of these forces by solving a simpler "equivalent point source" problem, and which uses a Newton scheme to improve the corresponding initial approximation. © 2011 American Institute of Mathematical Sciences.

1. On rational approximation methods for inverse source problems

Rundell, William; Hanke, Martin

2011-01-01

The basis of most imaging methods is to detect hidden obstacles or inclusions within a body when one can only make measurements on an exterior surface. Such is the ubiquity of these problems, the underlying model can lead to a partial differential equation of any of the major types, but here we focus on the case of steady-state electrostatic or thermal imaging and consider boundary value problems for Laplace's equation. Our inclusions are interior forces with compact support and our data consists of a single measurement of (say) voltage/current or temperature/heat flux on the external boundary. We propose an algorithm that under certain assumptions allows for the determination of the support set of these forces by solving a simpler "equivalent point source" problem, and which uses a Newton scheme to improve the corresponding initial approximation. © 2011 American Institute of Mathematical Sciences.

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

Desmal, Abdulla

2014-07-01

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

3. Statistical method for resolving the photon-photoelectron-counting inversion problem

Wu Jinlong; Li Tiejun; Peng, Xiang; Guo Hong

2011-01-01

A statistical inversion method is proposed for the photon-photoelectron-counting statistics in quantum key distribution experiment. With the statistical viewpoint, this problem is equivalent to the parameter estimation for an infinite binomial mixture model. The coarse-graining idea and Bayesian methods are applied to deal with this ill-posed problem, which is a good simple example to show the successful application of the statistical methods to the inverse problem. Numerical results show the applicability of the proposed strategy. The coarse-graining idea for the infinite mixture models should be general to be used in the future.

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

Desmal, Abdulla; Bagci, Hakan

2014-01-01

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

5. Inverse problem theory methods for data fitting and model parameter estimation

Tarantola, A

2002-01-01

Inverse Problem Theory is written for physicists, geophysicists and all scientists facing the problem of quantitative interpretation of experimental data. Although it contains a lot of mathematics, it is not intended as a mathematical book, but rather tries to explain how a method of acquisition of information can be applied to the actual world.The book provides a comprehensive, up-to-date description of the methods to be used for fitting experimental data, or to estimate model parameters, and to unify these methods into the Inverse Problem Theory. The first part of the book deals wi

6. Method and software to solution of inverse and inverse design fluid flow and heat transfer problems is compatible with CFD-software

Krukovsky, P G [Institute of Engineering Thermophysics, National Academy of Sciences of Ukraine, Kiev (Ukraine)

1998-12-31

The description of method and software FRIEND which provide a possibility of solution of inverse and inverse design problems on the basis of existing (base) CFD-software for solution of direct problems (in particular, heat-transfer and fluid-flow problems using software PHOENICS) are presented. FRIEND is an independent additional module that widens the operational capacities of the base software unified with this module. This unifying does not require any change or addition to the base software. Interfacing of FRIEND and the base software takes place through input and output files of the base software. A brief description of the computational technique applied for the inverse problem solution, same detailed information on the interfacing of FRIEND and CFD-software and solution results for testing inverse and inverse design problems, obtained using the tandem CFD-software PHOENICS and FRIEND, are presented. (author) 9 refs.

7. Method and software to solution of inverse and inverse design fluid flow and heat transfer problems is compatible with CFD-software

Krukovsky, P.G. [Institute of Engineering Thermophysics, National Academy of Sciences of Ukraine, Kiev (Ukraine)

1997-12-31

The description of method and software FRIEND which provide a possibility of solution of inverse and inverse design problems on the basis of existing (base) CFD-software for solution of direct problems (in particular, heat-transfer and fluid-flow problems using software PHOENICS) are presented. FRIEND is an independent additional module that widens the operational capacities of the base software unified with this module. This unifying does not require any change or addition to the base software. Interfacing of FRIEND and the base software takes place through input and output files of the base software. A brief description of the computational technique applied for the inverse problem solution, same detailed information on the interfacing of FRIEND and CFD-software and solution results for testing inverse and inverse design problems, obtained using the tandem CFD-software PHOENICS and FRIEND, are presented. (author) 9 refs.

8. Elastic frequency-domain finite-difference contrast source inversion method

He, Qinglong; Chen, Yong; Han, Bo; Li, Yang

2016-01-01

In this work, we extend the finite-difference contrast source inversion (FD-CSI) method to the frequency-domain elastic wave equations, where the parameters describing the subsurface structure are simultaneously reconstructed. The FD-CSI method is an iterative nonlinear inversion method, which exhibits several strengths. First, the finite-difference operator only relies on the background media and the given angular frequency, both of which are unchanged during inversion. Therefore, the matrix decomposition is performed only once at the beginning of the iteration if a direct solver is employed. This makes the inversion process relatively efficient in terms of the computational cost. In addition, the FD-CSI method automatically normalizes different parameters, which could avoid the numerical problems arising from the difference of the parameter magnitude. We exploit a parallel implementation of the FD-CSI method based on the domain decomposition method, ensuring a satisfactory scalability for large-scale problems. A simple numerical example with a homogeneous background medium is used to investigate the convergence of the elastic FD-CSI method. Moreover, the Marmousi II model proposed as a benchmark for testing seismic imaging methods is presented to demonstrate the performance of the elastic FD-CSI method in an inhomogeneous background medium. (paper)

9. Estimation of Bouguer Density Precision: Development of Method for Analysis of La Soufriere Volcano Gravity Data

Hendra Gunawan

2014-06-01

Full Text Available http://dx.doi.org/10.17014/ijog.vol3no3.20084The precision of topographic density (Bouguer density estimation by the Nettleton approach is based on a minimum correlation of Bouguer gravity anomaly and topography. The other method, the Parasnis approach, is based on a minimum correlation of Bouguer gravity anomaly and Bouguer correction. The precision of Bouguer density estimates was investigated by both methods on simple 2D syntetic models and under an assumption free-air anomaly consisting of an effect of topography, an effect of intracrustal, and an isostatic compensation. Based on simulation results, Bouguer density estimates were then investigated for a gravity survey of 2005 on La Soufriere Volcano-Guadeloupe area (Antilles Islands. The Bouguer density based on the Parasnis approach is 2.71 g/cm3 for the whole area, except the edifice area where average topography density estimates are 2.21 g/cm3 where Bouguer density estimates from previous gravity survey of 1975 are 2.67 g/cm3. The Bouguer density in La Soufriere Volcano was uncertainly estimated to be 0.1 g/cm3. For the studied area, the density deduced from refraction seismic data is coherent with the recent Bouguer density estimates. New Bouguer anomaly map based on these Bouguer density values allows to a better geological intepretation.

10. Moho depth variations over the Maldive Ridge and adjoining Arabian and Central Indian Basins, Western Indian Ocean, from three dimensional inversion of gravity anomalies

Kunnummal, Priyesh; Anand, S. P.; Haritha, C.; Rama Rao, P.

2018-05-01

Analysis of high resolution satellite derived free air gravity data has been undertaken in the Greater Maldive Ridge (GMR) (Maldive Ridge, Deep Sea Channel, northern limit of Chagos Bank) segment of the Chagos Laccadive Ridge and the adjoining Arabian and Central Indian Basins. A Complete Bouguer Anomaly (CBA) map was generated from the Indian Ocean Geoidal Low removed Free Air Gravity (hereinafter referred to as "FAG-IOGL") data by incorporating Bullard A, B and C corrections. Using the Parker method, Moho topography was initially computed by inverting the CBA data. From the CBA the Mantle Residual Gravity Anomalies (MRGA) were computed by incorporating gravity effects of sediments and lithospheric temperature and pressure induced anomalies. Further, the MRGA was inverted to get Moho undulations from which the crustal thickness was also estimated. It was found that incorporating the lithospheric thermal and pressure anomaly correction has provided substantial improvement in the computed Moho depths especially in the oceanic areas. But along the GMR, there was not much variation in the Moho thickness computed with and without the thermal and pressure gravity correction implying that the crustal thickness of the ridge does not depend on the oceanic isochrones used for the thermal corrections. The estimated Moho depths in the study area ranges from 7 km to 28 km and the crustal thickness from 2 km to 27 km. The Moho depths are shallower in regions closer to Central Indian Ridge in the Arabian Basin i.e., the region to the west of the GMR is thinner compared to the region in the east (Central Indian Basin). The thickest crust and the deepest Moho are found below the N-S trending GMR segment of the Chagos-Laccadive Ridge. Along the GMR the crustal thickness decreases from north to south with thickness of 27 km below the Maldives Ridge reducing to ∼9 km at 3°S and further increasing towards Chagos Bank. Even though there are similarities in crustal thickness between

11. The contribution of gravity method in geothermal exploration of southern part of the Gulf of Suez–Sinai region, Egypt

H. Atef

2016-06-01

The Bouguer anomaly map of the study area was used for delineating the subsurface structures and tectonic trends that have resulted in a potential heat source. The gravity inversion revealed a good correlation between areas of high temperature gradients, high heat flow and positive gravity anomalies. The high temperature gradient and heat flow values suggested being associated with a noticeable hydrothermal source of heat anomaly located at relatively shallow depths which is expected to be due to the uplift of the basement in the area.

12. Efficient generalized Golub-Kahan based methods for dynamic inverse problems

Chung, Julianne; Saibaba, Arvind K.; Brown, Matthew; Westman, Erik

2018-02-01

We consider efficient methods for computing solutions to and estimating uncertainties in dynamic inverse problems, where the parameters of interest may change during the measurement procedure. Compared to static inverse problems, incorporating prior information in both space and time in a Bayesian framework can become computationally intensive, in part, due to the large number of unknown parameters. In these problems, explicit computation of the square root and/or inverse of the prior covariance matrix is not possible, so we consider efficient, iterative, matrix-free methods based on the generalized Golub-Kahan bidiagonalization that allow automatic regularization parameter and variance estimation. We demonstrate that these methods for dynamic inversion can be more flexible than standard methods and develop efficient implementations that can exploit structure in the prior, as well as possible structure in the forward model. Numerical examples from photoacoustic tomography, space-time deblurring, and passive seismic tomography demonstrate the range of applicability and effectiveness of the described approaches. Specifically, in passive seismic tomography, we demonstrate our approach on both synthetic and real data. To demonstrate the scalability of our algorithm, we solve a dynamic inverse problem with approximately 43 000 measurements and 7.8 million unknowns in under 40 s on a standard desktop.

13. Method of T2 spectrum inversion with conjugate gradient algorithm from NMR data

Li Pengju; Shi Shangming; Song Yanjie

2010-01-01

Based on the optimization techniques, the T 2 spectrum inversion method of conjugate gradient that is easy to realize non-negativity constraint of T2 spectrum is proposed. The method transforms the linear mixed-determined problem of T2 spectrum inversion into the typical optimization problem of searching the minimum of objective function by building up the objective function according to the basic idea of geophysics modeling. The optimization problem above is solved with the conjugate gradient algorithm that has quick convergence rate and quadratic termination. The method has been applied to the inversion of noise free echo train generated from artificial spectrum, artificial echo train with signal-to-noise ratio (SNR)=25 and NMR experimental data of drilling core. The comparison between the inversion results of this paper and artificial spectrum or the result of software imported in NMR laboratory shows that the method can correctly invert T 2 spectrum from artificial NMR relaxation data even though SNR=25 and that inversion T 2 spectrum with good continuity and smoothness from core NMR experimental data accords perfectly with that of laboratory software imported, and moreover,the absolute error between the NMR porosity computed from T 2 spectrum and helium (He) porosity in laboratory is 0.65%. (authors)

14. Simple analytical methods for computing the gravity-wave contribution to the cosmic background radiation anisotropy

Wang, Y.

1996-01-01

We present two simple analytical methods for computing the gravity-wave contribution to the cosmic background radiation (CBR) anisotropy in inflationary models; one method uses a time-dependent transfer function, the other methods uses an approximate gravity-mode function which is a simple combination of the lowest order spherical Bessel functions. We compare the CBR anisotropy tensor multipole spectrum computed using our methods with the previous result of the highly accurate numerical method, the open-quote open-quote Boltzmann close-quote close-quote method. Our time-dependent transfer function is more accurate than the time-independent transfer function found by Turner, White, and Lindsey; however, we find that the transfer function method is only good for l approx-lt 120. Using our approximate gravity-wave mode function, we obtain much better accuracy; the tensor multipole spectrum we find differs by less than 2% for l approx-lt 50, less than 10% for l approx-lt 120, and less than 20% for l≤300 from the open-quote open-quote Boltzmann close-quote close-quote result. Our approximate graviton mode function should be quite useful in studying tensor perturbations from inflationary models. copyright 1996 The American Physical Society

15. An improved gravity compensation method for high-precision free-INS based on MEC–BP–AdaBoost

Zhou, Xiao; Yang, Gongliu; Wang, Jing; Li, Jing

2016-01-01

In recent years, with the rapid improvement of inertial sensors (accelerometers and gyroscopes), gravity compensation has become more important for improving navigation accuracy in inertial navigation systems (INS), especially for high-precision INS. This paper proposes a mind evolutionary computation (MEC) back propagation (BP) AdaBoost algorithm neural-network-based gravity compensation method that estimates the gravity disturbance on the track based on measured gravity data. A MEC–BP–AdaBoost network-based gravity compensation algorithm used in the training process to establish the prediction model takes the carrier position (longitude and latitude) provided by INS as the input data and the gravity disturbance as the output data, and then compensates the obtained gravity disturbance into the INS’s error equations to restrain the position error propagation. The MEC–BP–AdaBoost algorithm can not only effectively avoid BP neural networks being trapped in local extrema, but also perfectly solve the nonlinearity between the input and output data that cannot be solved by traditional interpolation methods, such as least-square collocation (LSC) interpolation. The accuracy and feasibility of the proposed interpolation method are verified through numerical tests. A comparison of several other compensation methods applied in field experiments, including LSC interpolation and traditional BP interpolation, highlights the superior performance of the proposed method. The field experiment results show that the maximum value of the position error can reduce by 28% with the proposed gravity compensation method. (paper)

16. Variational principles for Ginzburg-Landau equation by He's semi-inverse method

Liu, W.Y.; Yu, Y.J.; Chen, L.D.

2007-01-01

Via the semi-inverse method of establishing variational principles proposed by He, a generalized variational principle is established for Ginzburg-Landau equation. The present theory provides a quite straightforward tool to the search for various variational principles for physical problems. This paper aims at providing a more complete theoretical basis for applications using finite element and other direct variational methods

17. Simplified solutions of the Cox-Thompson inverse scattering method at fixed energy

Palmai, Tamas; Apagyi, Barnabas; Horvath, Miklos

2008-01-01

Simplified solutions of the Cox-Thompson inverse quantum scattering method at fixed energy are derived if a finite number of partial waves with only even or odd angular momenta contribute to the scattering process. Based on new formulae various approximate methods are introduced which also prove applicable to the generic scattering events

18. Inversion methods for fast-ion velocity-space tomography in fusion plasmas

Jacobsen, Asger Schou; Stagner, L.; Salewski, Mirko

2016-01-01

Velocity-space tomography has been used to infer 2D fast-ion velocity distribution functions. Here we compare the performance of five different tomographic inversion methods: truncated singular value decomposition, maximum entropy, minimum Fisher information and zeroth and first-order Tikhonov...... regularization. The inversion methods are applied to fast-ion Dα measurements taken just before and just after a sawtooth crash in the ASDEX Upgrade tokamak as well as to synthetic measurements from different test distributions. We find that the methods regularizing by penalizing steep gradients or maximizing...... entropy perform best. We assess the uncertainty of the calculated inversions taking into account photon noise, uncertainties in the forward model as well as uncertainties introduced by the regularization which allows us to distinguish regions of high and low confidence in the tomographies. In high...

19. The θ-term, CPN-1 model and the inversion approach in the imaginary θ method

Imachi, Masahiro; Kambayashi, Hitoshi; Shinno, Yasuhiko; Yoneyama, Hiroshi

2006-01-01

The weak coupling region of CP N-1 lattice field theory with the θ-term is investigated. Both the usual real theta method can the imaginary theta method are studied. The latter was first proposed by Bhanot and David. Azcoiti et al. proposed an inversion approach based on the imaginary theta method. The role of the inversion approach is investigated in this paper. A wide range of values of h=-Imθ is studied, where θ denotes the magnitude of the topological term. Step-like behavior in the x-h relation (where x=Q/V, Q is the topological charge, and V is the two-dimensional volume) is found in the weak coupling region. The physical meaning of the position of the step-like behavior is discussed. The inversion approach is applied to weak coupling regions. (author)

20. Inverse method for determining radon diffusion coefficient and free radon production rate of fragmented uranium ore

Ye, Yong-jun; Wang, Li-heng; Ding, De-xin; Zhao, Ya-li; Fan, Nan-bin

2014-01-01

1. A general method for closed-loop inverse simulation of helicopter maneuver flight

Wei WU

2017-12-01

Full Text Available Maneuverability is a key factor to determine whether a helicopter could finish certain flight missions successfully or not. Inverse simulation is commonly used to calculate the pilot controls of a helicopter to complete a certain kind of maneuver flight and to assess its maneuverability. A general method for inverse simulation of maneuver flight for helicopters with the flight control system online is developed in this paper. A general mathematical describing function is established to provide mathematical descriptions of different kinds of maneuvers. A comprehensive control solver based on the optimal linear quadratic regulator theory is developed to calculate the pilot controls of different maneuvers. The coupling problem between pilot controls and flight control system outputs is well solved by taking the flight control system model into the control solver. Inverse simulation of three different kinds of maneuvers with different agility requirements defined in the ADS-33E-PRF is implemented based on the developed method for a UH-60 helicopter. The results show that the method developed in this paper can solve the closed-loop inverse simulation problem of helicopter maneuver flight with high reliability as well as efficiency. Keywords: Closed-loop, Flying quality, Helicopters, Inverse simulation, Maneuver flight

2. Two numerical methods for an inverse problem for the 2-D Helmholtz equation

Gryazin, Y A; Lucas, T R

2003-01-01

Two solution methods for the inverse problem for the 2-D Helmholtz equation are developed, tested, and compared. The proposed approaches are based on a marching finite-difference scheme which requires the solution of an overdetermined system at each step. The preconditioned conjugate gradient method is used for rapid solutions of these systems and an efficient preconditioner has been developed for this class of problems. Underlying target applications include the imaging of land mines, unexploded ordinance, and pollutant plumes in environmental cleanup sites, each formulated as an inverse problem for a 2-D Helmholtz equation. The images represent the electromagnetic properties of the respective underground regions. Extensive numerical results are presented.

3. Incompressible Navier-Stokes inverse design method based on adaptive unstructured meshes

Rahmati, M.T.; Charlesworth, D.; Zangeneh, M.

2005-01-01

An inverse method for blade design based on Navier-Stokes equations on adaptive unstructured meshes has been developed. In the method, unlike the method based on inviscid equations, the effect of viscosity is directly taken into account. In the method, the pressure (or pressure loading) is prescribed. The design method then computes the blade shape that would accomplish the target prescribed pressure distribution. The method is implemented using a cell-centered finite volume method, which solves the incompressible Navier-Stokes equations on unstructured meshes. An adaptive unstructured mesh method based on grid subdivision and local adaptive mesh method is utilized for increasing the accuracy. (author)

4. Phonon spectrum of YBCO obtained by specific heat inversion method for real data

Tao Wen; Dai Xian Xi; Dai Ji Xin; Evenson, W E

2003-01-01

In this paper, the phonon spectrum of YBCO is obtained from experimental specific heat data by an exact inversion formula with a parameter for eliminating divergences. The results can be compared to those of neutron inelastic scattering, which can only be carried out in a few laboratories. Some key points of specific heat-phonon spectrum inversion (SPI) theory and a method of asymptotic behaviour control are discussed. An improved unique existence theorem is presented, and a universal function set for numerical calculation of SPI is calculated with high accuracy, which makes the inversion method applicable and convenient in practice. This is the first time specific heat-phonon SPI has been realized for a concrete system.

5. Solutions of the Schrödinger equation with inversely quadratic Hellmann plus inversely quadratic potential using Nikiforov-Uvarov method

Ita, B. I.; Ehi-Eromosele, C. O.; Edobor-Osoh, A.; Ikeuba, A. I.

2014-01-01

By using the Nikiforov-Uvarov (NU) method, the Schrödinger equation has been solved for the interaction of inversely quadratic Hellmann (IQHP) and inversely quadratic potential (IQP) for any angular momentum quantum number, l. The energy eigenvalues and their corresponding eigenfunctions have been obtained in terms of Laguerre polynomials. Special cases of the sum of these potentials have been considered and their energy eigenvalues also obtained

6. An inverse method for the design of energy absorbers in the frontend of passenger cars; Eine inverse Methode zur Auslegung von Energieabsorbern im Frontend von Personenkraftwagen

Goetze, Dirk

2011-07-01

Mobility is one of the key factors of our society. The consequences for the environment and mankind can be seen every day. For example in 2009, about 35,500 people involved in traffic accidents in Europe died. The ambitious objective of the European Union, the reduction of the total number of road casualties in 2010, to 27,000 which is half of the road casualties in 2001, was not obtained. The enormous number of fatalities shows, that road safety will be an important issue in the future. Upcoming initiatives of the European Union will focus on accidents outside the city limits where about 60% of all road fatalities occur but also on vulnerable road users (such as children, pedestrians, cyclists and the elderly). The automotive industry has to assure that the vehicle structures are able to reduce the severity of injuries not only for vehicle occupants but also for the other people who are involved in an accident. This can be reached with active and passive safety systems. In this work an alternative design process for passive safety structures is introduced, which is based on the vehicle requirements. The so-called inverse design method is demonstrated for the design of energy absorbers in frontend systems used for pedestrian protection. It is based on a multi-stage optimization process. Compared to the classic design process, where the crash-pulse is usually based on vehicle stiffness and the deformation length, the inverse method focuses on the structural design based on a desired crash-pulse. Using virtual absorbers, which are not limited by any material behavior or geometry, legform to bumper testes can be simulated. Thus, the desired legform deceleration can be generated. The data obtained is used for the second step of the inverse design method, the generation of a ''real'' absorber. For the design of the ''real'' absorber small drop-tower simulations are sufficient. A parameterized finite element model is used. Both the

7. Testing an inversion method for estimating electron energy fluxes from all-sky camera images

N. Partamies

2004-06-01

Full Text Available An inversion method for reconstructing the precipitating electron energy flux from a set of multi-wavelength digital all-sky camera (ASC images has recently been developed by tomografia. Preliminary tests suggested that the inversion is able to reconstruct the position and energy characteristics of the aurora with reasonable accuracy. This study carries out a thorough testing of the method and a few improvements for its emission physics equations. We compared the precipitating electron energy fluxes as estimated by the inversion method to the energy flux data recorded by the Defense Meteorological Satellite Program (DMSP satellites during four passes over auroral structures. When the aurorae appear very close to the local zenith, the fluxes inverted from the blue (427.8nm filtered ASC images or blue and green line (557.7nm images together give the best agreement with the measured flux values. The fluxes inverted from green line images alone are clearly larger than the measured ones. Closer to the horizon the quality of the inversion results from blue images deteriorate to the level of the ones from green images. In addition to the satellite data, the precipitating electron energy fluxes were estimated from the electron density measurements by the EISCAT Svalbard Radar (ESR. These energy flux values were compared to the ones of the inversion method applied to over 100 ASC images recorded at the nearby ASC station in Longyearbyen. The energy fluxes deduced from these two types of data are in general of the same order of magnitude. In 35% of all of the blue and green image inversions the relative errors were less than 50% and in 90% of the blue and green image inversions less than 100%. This kind of systematic testing of the inversion method is the first step toward using all-sky camera images in the way in which global UV images have recently been used to estimate the energy fluxes. The advantages of ASCs, compared to the space-born imagers, are

8. Performance of some numerical Laplace inversion methods on American put option formula

Octaviano, I.; Yuniar, A. R.; Anisa, L.; Surjanto, S. D.; Putri, E. R. M.

2018-03-01

Numerical inversion approaches of Laplace transform is used to obtain a semianalytic solution. Some of the mathematical inversion methods such as Durbin-Crump, Widder, and Papoulis can be used to calculate American put options through the optimal exercise price in the Laplace space. The comparison of methods on some simple functions is aimed to know the accuracy and parameters which used in the calculation of American put options. The result obtained is the performance of each method regarding accuracy and computational speed. The Durbin-Crump method has an average error relative of 2.006e-004 with computational speed of 0.04871 seconds, the Widder method has an average error relative of 0.0048 with computational speed of 3.100181 seconds, and the Papoulis method has an average error relative of 9.8558e-004 with computational speed of 0.020793 seconds.

9. Testing a Novel Method to Approximate Wood Specific Gravity of Trees

Michael C. Wiemann; G. Bruce. Williamson

2012-01-01

Wood specific gravity (SG) has long been used by foresters as an index for wood properties. More recently, SG has been widely used by ecologists as a plant functional trait and as a key variable in estimates of biomass. However, sampling wood to determine SG can be problematic; at present, the most common method is sampling with an increment borer to extract a bark-to-...

10. Study of Tip-loss Using an Inverse 3D Navier-Stokes Method

Mikkelsen, Robert; Sørensen, Jens Nørkær; Shen, Wen Zhong

2003-01-01

the 3D Navier-Stokes equations combined with the actuator line technique where blade loading is applied using an inverse method. The numerical simulations shows that the method captures the tip-correction when comparing with the theories of Prandtl and Goldstein, however, the accuracy of the obtained...... results reveal that further refinements still is needed. Keywords: Tip-loss; Actuator line; 3D Navier-Stokes methods....

11. Integrating the Toda Lattice with Self-Consistent Source via Inverse Scattering Method

Urazboev, Gayrat

2012-01-01

In this work, there is shown that the solutions of Toda lattice with self-consistent source can be found by the inverse scattering method for the discrete Sturm-Liuville operator. For the considered problem the one-soliton solution is obtained.

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

Fang Jinqing; Yao Weiguang

1993-01-01

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

13. Micro-seismic Imaging Using a Source Independent Waveform Inversion Method

Wang, Hanchen

2016-01-01

waveform inversion (FWI) is widely used. The FWI method updates the velocity model by minimizing the misfit between the observed data and the predicted data. Using FWI to locate and image microseismic events allows for an automatic process (free of picking

14. On the method of inverse scattering problem and Baecklund transformations for supersymmetric equations

Chaichian, M.; Kulish, P. P.

1978-04-01

Supersymmetric Liouville and sine-Gordon equations are studied. We write down for these models the system of linear equations for which the method of inverse scattering problem should be applicable. Expressions for an infinite set of conserved currents are explicitly given. Supersymmetric Baecklund transformations and generalized conservation laws are constructed. (author)

15. Inverse scattering transform method and soliton solutions for Davey-Stewartson II equation

Arkadiev, V.A.; Pogrebkov, A.K.; Polivanov, M.C.

1989-01-01

The inverse scattering method for Davey-Stewartson II (DS-II) equation including both soliton and continuous spectrum solutions is developed. The explicit formulae for N-soliton solutions are given. Note that our solitons decrease as |z| -2 with z tending to infinity. (author). 8 refs

16. The black-body radiation inversion problem, its instability and a new universal function set method

Ye, JiPing; Ji, FengMin; Wen, Tao; Dai, Xian-Xi; Dai, Ji-Xin; Evenson, William E.

2006-01-01

The black-body radiation inversion (BRI) problem is ill-posed and requires special techniques to achieve stable solutions. In this Letter, the universal function set method (UFS), is developed in BRI. An improved unique existence theorem is proposed. Asymptotic behavior control (ABC) is introduced. A numerical example shows that practical calculations are possible with UFS

17. An Analytical Method for the Abel Inversion of Asymmetrical Gaussian Profiles

Xu Guosheng; Wan Baonian

2007-01-01

An analytical algorithm for fast calculation of the Abel inversion for density profile measurement in tokamak is developed. Based upon the assumptions that the particle source is negligibly small in the plasma core region, density profiles can be approximated by an asymmetrical Gaussian distribution controlled only by one parameter V 0 /D and V 0 /D is constant along the radial direction, the analytical algorithm is presented and examined against a testing profile. The validity is confirmed by benchmark with the standard Abel inversion method and the theoretical profile. The scope of application as well as the error analysis is also discussed in detail

18. Multiple estimation channel decoupling and optimization method based on inverse system

Wu, Peng; Mu, Rongjun; Zhang, Xin; Deng, Yanpeng

2018-03-01

This paper addressed the intelligent autonomous navigation request of intelligent deformation missile, based on the intelligent deformation missile dynamics and kinematics modeling, navigation subsystem solution method and error modeling, and then focuses on the corresponding data fusion and decision fusion technology, decouples the sensitive channel of the filter input through the inverse system of design dynamics to reduce the influence of sudden change of the measurement information on the filter input. Then carrying out a series of simulation experiments, which verified the feasibility of the inverse system decoupling algorithm effectiveness.

19. A STUDY ON DYNAMIC LOAD HISTORY RECONSTRUCTION USING PSEUDO-INVERSE METHODS

Santos, Ariane Rebelato Silva dos; Marczak, Rogério José

2017-01-01

Considering that the vibratory forces generally cannot be measured directly at the interface of two bodies, an inverse method is studied in the present work to recover the load history in such cases. The proposed technique attempts to reconstruct the dynamic loads history by using a frequency domain analysis and Moore-Penrose pseudo-inverses of the frequency response function (FRF) of the system. The methodology consists in applying discrete dynamic loads on a finite element model in the time...

20. Fractal-Based Methods and Inverse Problems for Differential Equations: Current State of the Art

Herb E. Kunze

2014-01-01

Full Text Available We illustrate, in this short survey, the current state of the art of fractal-based techniques and their application to the solution of inverse problems for ordinary and partial differential equations. We review several methods based on the Collage Theorem and its extensions. We also discuss two innovative applications: the first one is related to a vibrating string model while the second one considers a collage-based approach for solving inverse problems for partial differential equations on a perforated domain.

1. The algebraic method of the scattering inverse problem solution under untraditional statements

Popushnoj, M N

2001-01-01

The algebraic method of the scattering inverse problem solution under untraditional statements is proposed consistently in this review, in the framework of which some quantum theory od scattering charged particles problem were researched afterwards. The inverse problem of scattering theory of charged particles on the complex plane of the Coulomb coupling constant (CCC) is considered. A procedure of interaction potential restoration is established for the case when the energy, orbital moment quadrate and CCC are linearly dependent. The relation between one-parametric problems of the potential scattering of charged particles is investigated

2. Cycle-Based Cluster Variational Method for Direct and Inverse Inference

Furtlehner, Cyril; Decelle, Aurélien

2016-08-01

Large scale inference problems of practical interest can often be addressed with help of Markov random fields. This requires to solve in principle two related problems: the first one is to find offline the parameters of the MRF from empirical data (inverse problem); the second one (direct problem) is to set up the inference algorithm to make it as precise, robust and efficient as possible. In this work we address both the direct and inverse problem with mean-field methods of statistical physics, going beyond the Bethe approximation and associated belief propagation algorithm. We elaborate on the idea that loop corrections to belief propagation can be dealt with in a systematic way on pairwise Markov random fields, by using the elements of a cycle basis to define regions in a generalized belief propagation setting. For the direct problem, the region graph is specified in such a way as to avoid feed-back loops as much as possible by selecting a minimal cycle basis. Following this line we are led to propose a two-level algorithm, where a belief propagation algorithm is run alternatively at the level of each cycle and at the inter-region level. Next we observe that the inverse problem can be addressed region by region independently, with one small inverse problem per region to be solved. It turns out that each elementary inverse problem on the loop geometry can be solved efficiently. In particular in the random Ising context we propose two complementary methods based respectively on fixed point equations and on a one-parameter log likelihood function minimization. Numerical experiments confirm the effectiveness of this approach both for the direct and inverse MRF inference. Heterogeneous problems of size up to 10^5 are addressed in a reasonable computational time, notably with better convergence properties than ordinary belief propagation.

3. Finite-fault source inversion using adjoint methods in 3D heterogeneous media

2018-04-01

Accounting for lateral heterogeneities in the 3D velocity structure of the crust is known to improve earthquake source inversion, compared to results based on 1D velocity models which are routinely assumed to derive finite-fault slip models. The conventional approach to include known 3D heterogeneity in source inversion involves pre-computing 3D Green's functions, which requires a number of 3D wave propagation simulations proportional to the number of stations or to the number of fault cells. The computational cost of such an approach is prohibitive for the dense datasets that could be provided by future earthquake observation systems. Here, we propose an adjoint-based optimization technique to invert for the spatio-temporal evolution of slip velocity. The approach does not require pre-computed Green's functions. The adjoint method provides the gradient of the cost function, which is used to improve the model iteratively employing an iterative gradient-based minimization method. The adjoint approach is shown to be computationally more efficient than the conventional approach based on pre-computed Green's functions in a broad range of situations. We consider data up to 1 Hz from a Haskell source scenario (a steady pulse-like rupture) on a vertical strike-slip fault embedded in an elastic 3D heterogeneous velocity model. The velocity model comprises a uniform background and a 3D stochastic perturbation with the von Karman correlation function. Source inversions based on the 3D velocity model are performed for two different station configurations, a dense and a sparse network with 1 km and 20 km station spacing, respectively. These reference inversions show that our inversion scheme adequately retrieves the rise time when the velocity model is exactly known, and illustrates how dense coverage improves the inference of peak slip velocities. We investigate the effects of uncertainties in the velocity model by performing source inversions based on an incorrect

4. Gravity Search Algorithm hybridized Recursive Least Square method for power system harmonic estimation

Santosh Kumar Singh

2017-06-01

Full Text Available This paper presents a new hybrid method based on Gravity Search Algorithm (GSA and Recursive Least Square (RLS, known as GSA-RLS, to solve the harmonic estimation problems in the case of time varying power signals in presence of different noises. GSA is based on the Newton’s law of gravity and mass interactions. In the proposed method, the searcher agents are a collection of masses that interact with each other using Newton’s laws of gravity and motion. The basic GSA algorithm strategy is combined with RLS algorithm sequentially in an adaptive way to update the unknown parameters (weights of the harmonic signal. Simulation and practical validation are made with the experimentation of the proposed algorithm with real time data obtained from a heavy paper industry. A comparative performance of the proposed algorithm is evaluated with other recently reported algorithms like, Differential Evolution (DE, Particle Swarm Optimization (PSO, Bacteria Foraging Optimization (BFO, Fuzzy-BFO (F-BFO hybridized with Least Square (LS and BFO hybridized with RLS algorithm, which reveals that the proposed GSA-RLS algorithm is the best in terms of accuracy, convergence and computational time.

5. Study of Seulawah Agam’s Geothermal Source Using Gravity Method

Marwan Marwan

2015-04-01

Full Text Available Gravity method was carried out at Seulawah Agam Area to delineate the existence of geothermal source, which is specifically existed in both the geothermal filed of Heutsz’s Crater and.Cempaga’s Crater. The Seulawah Agam is located in Aceh Besar district. Geologically, the area is dominated by volcanic mudflow and Lam Teuba’s rocks having age from Tersier to Resen Period. The equipment used includes Gravimeter CG-5 Autograv, Portable GPS (Global Positioning System, Navigation type (map of the survey area, computer and the other technical supports, such as handy talky, umbrella, watch, pens and observed data notes. This research was conducted by doing two stages.  Firstly, establishing the base station which is a reference point for all gravity data measurements at each point. Secondly, measuring gravity data at each point by repeating three times following looping pattern as pathway of measurement either in Heutsz’s crater whose nine points recording or in Cempaga’s crater whose seventeen points. The data was simply processed using Microsoft Excel that can just plot the Bouguer anomaly and interpreted qualitatively due to preliminary research. The resultof this research has shown that both areas have two kinds of Bougeur anomalies which slightly attract attention who’s high and low anomaly. At Heutsz’s Crater has high and low density existed at F125 FR and B6 point. The Point whose high density means that it was formed mineralization by hydrothermal process through fracture materials, meanwhile the point whose low density indicates that there is existed the fault which is quite related to Seulimum’s Fault based on Aceh map. This result is also same as obtained at Cempaga’s Crater which means also same interpretation. In addition, it can be sum up that fault zones are essentially important in geothermal system that plays vital role in term of fluid circulation. Employing the gravity method in this research effectively can be

6. Inverse problems for ODEs using contraction maps and suboptimality of the 'collage method'

Kunze, H. E.; Hicken, J. E.; Vrscay, E. R.

2004-06-01

Broad classes of inverse problems in differential and integral equations can be cast in the following framework: the optimal approximation of a target x of a suitable metric space X by the fixed point \\bar x of a contraction map T on X. The 'collage method' attempts to solve such inverse problems by finding an operator Tc that maps the target x as close as possible to itself. In the case of ODEs, the appropriate contraction maps are integral Picard operators. In practice, the target solutions possibly arise from an interpolation of experimental data points. In this paper, we investigate the suboptimality of the collage method. A simple inequality that provides upper bounds on the improvement over collage coding is presented and some examples are studied. We conclude that, at worst, the collage method provides an excellent starting point for further optimization, in contrast to more traditional searching methods that must first select a good starting point.

7. Sliding mode control of photoelectric tracking platform based on the inverse system method

Yao Zong Chen

2016-01-01

Full Text Available In order to improve the photoelectric tracking platform tracking performance, an integral sliding mode control strategy based on inverse system decoupling method is proposed. The electromechanical dynamic model is established based on multi-body system theory and Newton-Euler method. The coupled multi-input multi-output (MIMO nonlinear system is transformed into two pseudo-linear single-input single-output (SISO subsystems based on the inverse system method. An integral sliding mode control scheme is designed for the decoupled pseudo-linear system. In order to eliminate system chattering phenomenon caused by traditional sign function in sliding-mode controller, the sign function is replaced by the Sigmoid function. Simulation results show that the proposed decoupling method and the control strategy can restrain the influences of internal coupling and disturbance effectively, and has better robustness and higher tracking accuracy.

8. An inverse method for non linear ablative thermics with experimentation of automatic differentiation

Alestra, S [Simulation Information Technology and Systems Engineering, EADS IW Toulouse (France); Collinet, J [Re-entry Systems and Technologies, EADS ASTRIUM ST, Les Mureaux (France); Dubois, F [Professor of Applied Mathematics, Conservatoire National des Arts et Metiers Paris (France)], E-mail: stephane.alestra@eads.net, E-mail: jean.collinet@astrium.eads.net, E-mail: fdubois@cnam.fr

2008-11-01

Thermal Protection System is a key element for atmospheric re-entry missions of aerospace vehicles. The high level of heat fluxes encountered in such missions has a direct effect on mass balance of the heat shield. Consequently, the identification of heat fluxes is of great industrial interest but is in flight only available by indirect methods based on temperature measurements. This paper is concerned with inverse analyses of highly evolutive heat fluxes. An inverse problem is used to estimate transient surface heat fluxes (convection coefficient), for degradable thermal material (ablation and pyrolysis), by using time domain temperature measurements on thermal protection. The inverse problem is formulated as a minimization problem involving an objective functional, through an optimization loop. An optimal control formulation (Lagrangian, adjoint and gradient steepest descent method combined with quasi-Newton method computations) is then developed and applied, using Monopyro, a transient one-dimensional thermal model with one moving boundary (ablative surface) that has been developed since many years by ASTRIUM-ST. To compute numerically the adjoint and gradient quantities, for the inverse problem in heat convection coefficient, we have used both an analytical manual differentiation and an Automatic Differentiation (AD) engine tool, Tapenade, developed at INRIA Sophia-Antipolis by the TROPICS team. Several validation test cases, using synthetic temperature measurements are carried out, by applying the results of the inverse method with minimization algorithm. Accurate results of identification on high fluxes test cases, and good agreement for temperatures restitutions, are obtained, without and with ablation and pyrolysis, using bad fluxes initial guesses. First encouraging results with an automatic differentiation procedure are also presented in this paper.

9. Origin and effective reduction of inversion domains in aluminum nitride grown by a sublimation method

Shigetoh, Keisuke; Horibuchi, Kayo; Nakamura, Daisuke

2017-11-01

Owing to the large differences in the chemical properties between Al and N polarities in aluminum nitride (AlN), the choice of the polar direction for crystal growth strongly affects not only the quality but also the shape (facet formation) of the grown crystal. In particular, N-polar (0 0 0 -1) has been considered to be a more preferable direction than Al-polar (0 0 0 1) for sublimation growth because compared to Al-polar (0 0 0 1), N-polar (0 0 0 -1) exhibits better stability at high growth rate (high supersaturation) conditions and enables easier lateral enlargement of the crystal. However, some critical growth conditions induce polarity inversion and hinder stable N-polar growth. Furthermore, the origin of the polarity inversion in AlN growth by the sublimation method is still unclear. To ensure stable N-polar growth without polarity inversion, the formation mechanism of the inversion domain during AlN sublimation growth must be elucidated. Therefore, herein, we demonstrate homoepitaxial growth on an N-polar seed and carefully investigate the obtained crystal that shows polarity inversion. Annular bright-field scanning transmission electron microscopy reveals that polarity is completely converted to the Al polarity via the formation of a 30 nm thick mixed polar layer (MPL) just above the seed. Moreover, three-dimensional atom probe tomography shows the segregation of the oxygen impurities in the MPL with a high concentration of about 3 atom%. Finally, by avoiding the incorporation of oxygen impurity into the crystal at the initial stage of the growth, we demonstrate an effective reduction (seven orders of magnitude) of the inversion domain boundary formation.

10. Advanced Multivariate Inversion Techniques for High Resolution 3D Geophysical Modeling

2011-09-01

2005). We implemented a method to increase the usefulness of gravity data by filtering the Bouguer anomaly map. Though commonly applied 40 km 30 35...remove the long-wavelength components from the Bouguer gravity map we follow Tessema and Antoine (2004), who use an upward continuation method and...inversion of group velocities and gravity. (a) Top: Group velocities from a representative cell in the model. Bottom: Filtered Bouguer anomalies. (b

11. Image Reconstruction Based on Homotopy Perturbation Inversion Method for Electrical Impedance Tomography

Jing Wang

2013-01-01

Full Text Available The image reconstruction for electrical impedance tomography (EIT mathematically is a typed nonlinear ill-posed inverse problem. In this paper, a novel iteration regularization scheme based on the homotopy perturbation technique, namely, homotopy perturbation inversion method, is applied to investigate the EIT image reconstruction problem. To verify the feasibility and effectiveness, simulations of image reconstruction have been performed in terms of considering different locations, sizes, and numbers of the inclusions, as well as robustness to data noise. Numerical results indicate that this method can overcome the numerical instability and is robust to data noise in the EIT image reconstruction. Moreover, compared with the classical Landweber iteration method, our approach improves the convergence rate. The results are promising.

12. Clinical Utility of Noninvasive Method to Measure Specific Gravity in the Pediatric Population.

Hall, Jeanine E; Huynh, Pauline P; Mody, Ameer P; Wang, Vincent J

2018-04-01

Clinicians rely on any combination of signs and symptoms, clinical scores, or invasive procedures to assess the hydration status in children. Noninvasive tests to evaluate for dehydration in the pediatric population are appealing. The objective of our study is to assess the utility of measuring specific gravity of tears compared to specific gravity of urine and the clinical assessment of dehydration. We conducted a prospective cohort convenience sample study, in a pediatric emergency department at a tertiary care children's hospital. We approached parents/guardians of children aged 6 months to 4 years undergoing transurethral catheterization for evaluation of urinary tract infection for enrollment. We collected tears and urine for measurement of tear specific gravity (TSG) and urine specific gravity (USG), respectively. Treating physicians completed dehydration assessment forms to assess for hydration status. Among the 60 participants included, the mean TSG was 1.0183 (SD = 0.007); the mean USG was 1.0186 (SD = 0.0083). TSG and USG were positively correlated with each other (Pearson Correlation = 0.423, p = 0.001). Clinical dehydration scores ranged from 0 to 3, with 87% assigned a score of 0, by physician assessment. Mean number of episodes of vomiting and diarrhea in a 24-hour period were 2.2 (SD = 3.9) and 1.5 (SD = 3.2), respectively. Sixty-two percent of parents reported decreased oral intake. TSG measurements yielded similar results compared with USG. Further studies are needed to determine if TSG can be used as a noninvasive method of dehydration assessment in children. Copyright © 2017 Elsevier Inc. All rights reserved.

13. Mercury Pollution from Small-Scale Gold Mining Can Be Stopped by Implementing the Gravity-Borax Method

Køster-Rasmussen, Rasmus; Westergaard, Maria L; Brasholt, Marie

2016-01-01

Mercury is used globally to extract gold in artisanal and small-scale gold mining. The mercury-free gravity-borax method for gold extraction was introduced in two mining communities using mercury in the provinces Kalinga and Camarines Norte. This article describes project activities...... organization facilitated the shift in Kalinga. In conclusion, the gravity-borax method is a doable alternative to mercury use in artisanal and small-scale gold mining, but support from the civil society is needed....

14. Parallelized Three-Dimensional Resistivity Inversion Using Finite Elements And Adjoint State Methods

Schaa, Ralf; Gross, Lutz; Du Plessis, Jaco

2015-04-01

The resistivity method is one of the oldest geophysical exploration methods, which employs one pair of electrodes to inject current into the ground and one or more pairs of electrodes to measure the electrical potential difference. The potential difference is a non-linear function of the subsurface resistivity distribution described by an elliptic partial differential equation (PDE) of the Poisson type. Inversion of measured potentials solves for the subsurface resistivity represented by PDE coefficients. With increasing advances in multichannel resistivity acquisition systems (systems with more than 60 channels and full waveform recording are now emerging), inversion software require efficient storage and solver algorithms. We developed the finite element solver Escript, which provides a user-friendly programming environment in Python to solve large-scale PDE-based problems (see https://launchpad.net/escript-finley). Using finite elements, highly irregular shaped geology and topography can readily be taken into account. For the 3D resistivity problem, we have implemented the secondary potential approach, where the PDE is decomposed into a primary potential caused by the source current and the secondary potential caused by changes in subsurface resistivity. The primary potential is calculated analytically, and the boundary value problem for the secondary potential is solved using nodal finite elements. This approach removes the singularity caused by the source currents and provides more accurate 3D resistivity models. To solve the inversion problem we apply a 'first optimize then discretize' approach using the quasi-Newton scheme in form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method (see Gross & Kemp 2013). The evaluation of the cost function requires the solution of the secondary potential PDE for each source current and the solution of the corresponding adjoint-state PDE for the cost function gradients with respect to the subsurface

15. A case study of forward calculations of the gravity anomaly by spectral method for a three-dimensional parameterised fault model

Xu, Weimin; Chen, Shi

2018-02-01

Spectral methods provide many advantages for calculating gravity anomalies. In this paper, we derive a kernel function for a three-dimensional (3D) fault model in the wave number domain, and present the full Fortran source code developed for the forward computation of the gravity anomalies and related derivatives obtained from the model. The numerical error and computing speed obtained using the proposed spectral method are compared with those obtained using a 3D rectangular prism model solved in the space domain. The error obtained using the spectral method is shown to be dependent on the sequence length employed in the fast Fourier transform. The spectral method is applied to some examples of 3D fault models, and is demonstrated to be a straightforward and alternative computational approach to enhance computational speed and simplify the procedures for solving many gravitational potential forward problems involving complicated geological models. The proposed method can generate a great number of feasible geophysical interpretations based on a 3D model with only a few variables, and can thereby improve the efficiency of inversion.

16. A fast inverse consistent deformable image registration method based on symmetric optical flow computation

Yang Deshan; Li Hua; Low, Daniel A; Deasy, Joseph O; Naqa, Issam El

2008-01-01

Deformable image registration is widely used in various radiation therapy applications including daily treatment planning adaptation to map planned tissue or dose to changing anatomy. In this work, a simple and efficient inverse consistency deformable registration method is proposed with aims of higher registration accuracy and faster convergence speed. Instead of registering image I to a second image J, the two images are symmetrically deformed toward one another in multiple passes, until both deformed images are matched and correct registration is therefore achieved. In each pass, a delta motion field is computed by minimizing a symmetric optical flow system cost function using modified optical flow algorithms. The images are then further deformed with the delta motion field in the positive and negative directions respectively, and then used for the next pass. The magnitude of the delta motion field is forced to be less than 0.4 voxel for every pass in order to guarantee smoothness and invertibility for the two overall motion fields that are accumulating the delta motion fields in both positive and negative directions, respectively. The final motion fields to register the original images I and J, in either direction, are calculated by inverting one overall motion field and combining the inversion result with the other overall motion field. The final motion fields are inversely consistent and this is ensured by the symmetric way that registration is carried out. The proposed method is demonstrated with phantom images, artificially deformed patient images and 4D-CT images. Our results suggest that the proposed method is able to improve the overall accuracy (reducing registration error by 30% or more, compared to the original and inversely inconsistent optical flow algorithms), reduce the inverse consistency error (by 95% or more) and increase the convergence rate (by 100% or more). The overall computation speed may slightly decrease, or increase in most cases

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

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

2016-05-01

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

18. 3D DC Resistivity Inversion with Topography Based on Regularized Conjugate Gradient Method

Jian-ke Qiang

2013-01-01

Full Text Available During the past decades, we observed a strong interest in 3D DC resistivity inversion and imaging with complex topography. In this paper, we implemented 3D DC resistivity inversion based on regularized conjugate gradient method with FEM. The Fréchet derivative is assembled with the electric potential in order to speed up the inversion process based on the reciprocity theorem. In this study, we also analyzed the sensitivity of the electric potential on the earth’s surface to the conductivity in each cell underground and introduced an optimized weighting function to produce new sensitivity matrix. The synthetic model study shows that this optimized weighting function is helpful to improve the resolution of deep anomaly. By incorporating topography into inversion, the artificial anomaly which is actually caused by topography can be eliminated. As a result, this algorithm potentially can be applied to process the DC resistivity data collected in mountain area. Our synthetic model study also shows that the convergence and computation speed are very stable and fast.

19. Inverse kinematics research using obstacle avoidance geometry method for EAST Articulated Maintenance Arm (EAMA)

Wang, Kun, E-mail: wangkun@ipp.ac.cn [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei (China); Lappeenranta University of Technology, Lappeenranta (Finland); University of Science and Technology of China, Hefei (China); Song, Yuntao [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei (China); University of Science and Technology of China, Hefei (China); Wu, Huapeng [Lappeenranta University of Technology, Lappeenranta (Finland); Wei, Xiaoyang; Khan, Shahab Ud-Din; Cheng, Yong [Institute of Plasma Physics, Chinese Academy of Sciences, Hefei (China)

2017-06-15

Highlights: • An Obstacle Topology Partition Projection (OTPP) method of tokamak-like vessel for collision detection. • Median values preferentially of depth-first search algorithm for solving redundant inverse kinematics based on OTPP. • Application of RIK in grasping target objects. - Abstract: This paper proposed a new method for solving inverse kinematics (IK) of a redundant manipulator called EAST Articulated Maintenance Arm (EAMA), which is applied in the fusion reactor EAST (Experimental Advanced Superconducting Tokamak) and used to complete some maintenance tasks in the complex areas. However, it is difficult to realize remote control due to its redundancy, coupling structure and the complex operational environment. The IK research of the robot played a vital role to the manipulator’s motion control algorithm of remote handling (RH) technology. An Obstacle Topology Partition Projection (OTPP) approach integrated with Modified Inverse Depth First Search (MIDFS) method was presented. This is a kind of new geometric algorithm in order to solve the problem of IK for a high-redundancy manipulator. It can also be used to find a solution satisfying collision avoidance with optimal safety distance between the manipulator and obstacles. Simulations and experiments were conducted to demonstrate the efficiency and accuracy of the proposed method.

20. Inverse kinematics research using obstacle avoidance geometry method for EAST Articulated Maintenance Arm (EAMA)

Wang, Kun; Song, Yuntao; Wu, Huapeng; Wei, Xiaoyang; Khan, Shahab Ud-Din; Cheng, Yong

2017-01-01

Highlights: • An Obstacle Topology Partition Projection (OTPP) method of tokamak-like vessel for collision detection. • Median values preferentially of depth-first search algorithm for solving redundant inverse kinematics based on OTPP. • Application of RIK in grasping target objects. - Abstract: This paper proposed a new method for solving inverse kinematics (IK) of a redundant manipulator called EAST Articulated Maintenance Arm (EAMA), which is applied in the fusion reactor EAST (Experimental Advanced Superconducting Tokamak) and used to complete some maintenance tasks in the complex areas. However, it is difficult to realize remote control due to its redundancy, coupling structure and the complex operational environment. The IK research of the robot played a vital role to the manipulator’s motion control algorithm of remote handling (RH) technology. An Obstacle Topology Partition Projection (OTPP) approach integrated with Modified Inverse Depth First Search (MIDFS) method was presented. This is a kind of new geometric algorithm in order to solve the problem of IK for a high-redundancy manipulator. It can also be used to find a solution satisfying collision avoidance with optimal safety distance between the manipulator and obstacles. Simulations and experiments were conducted to demonstrate the efficiency and accuracy of the proposed method.

1. A method for climate and vegetation reconstruction through the inversion of a dynamic vegetation model

Garreta, Vincent; Guiot, Joel; Hely, Christelle [CEREGE, UMR 6635, CNRS, Universite Aix-Marseille, Europole de l' Arbois, Aix-en-Provence (France); Miller, Paul A.; Sykes, Martin T. [Lund University, Department of Physical Geography and Ecosystems Analysis, Geobiosphere Science Centre, Lund (Sweden); Brewer, Simon [Universite de Liege, Institut d' Astrophysique et de Geophysique, Liege (Belgium); Litt, Thomas [University of Bonn, Paleontological Institute, Bonn (Germany)

2010-08-15

Climate reconstructions from data sensitive to past climates provide estimates of what these climates were like. Comparing these reconstructions with simulations from climate models allows to validate the models used for future climate prediction. It has been shown that for fossil pollen data, gaining estimates by inverting a vegetation model allows inclusion of past changes in carbon dioxide values. As a new generation of dynamic vegetation model is available we have developed an inversion method for one model, LPJ-GUESS. When this novel method is used with high-resolution sediment it allows us to bypass the classic assumptions of (1) climate and pollen independence between samples and (2) equilibrium between the vegetation, represented as pollen, and climate. Our dynamic inversion method is based on a statistical model to describe the links among climate, simulated vegetation and pollen samples. The inversion is realised thanks to a particle filter algorithm. We perform a validation on 30 modern European sites and then apply the method to the sediment core of Meerfelder Maar (Germany), which covers the Holocene at a temporal resolution of approximately one sample per 30 years. We demonstrate that reconstructed temperatures are constrained. The reconstructed precipitation is less well constrained, due to the dimension considered (one precipitation by season), and the low sensitivity of LPJ-GUESS to precipitation changes. (orig.)

2. The generalised Marchenko equation and the canonical structure of the A.K.N.S.-Z.S. inverse method

Dodd, R.K.; Bullough, R.K.

1979-01-01

A generalised Marchenko equation is derived for a 2 X 2 matrix inverse method and it is used to show that, for the subset of equations solvable by the method which can be constructed as defining the flows of Hamiltonians, the inverse transform is a canonical (homogeneous contact) transformation. Baecklund transformations are re-examined from this point of view. (Auth.)

3. Measurement of Critical Heat Flux Using the Transient Inverse Heat Conduction Method in Spray cooling

Kim, Yeung Chan

2016-01-01

A study on the measurement of critical heat flux using the transient inverse heat conduction method in spray cooling was performed. The inverse heat conduction method estimates the surface heat flux or temperature using a measured interior temperature history. The effects of the measuring time interval and location of temperature measurement on the measurement of critical heat flux were primarily investigated. The following results were obtained. The estimated critical heat flux decreased as the time interval of temperature measurement increased. Meanwhile, the effect of measurement location on critical heat flux was not significant. It was also found, from the experimental results, that the critical superheat increased as the measurement location of thermocouple neared the heat transfer surface.

4. Measurement of Critical Heat Flux Using the Transient Inverse Heat Conduction Method in Spray cooling

Kim, Yeung Chan [Andong Nat’l Univ., Andong (Korea, Republic of)

2016-10-15

A study on the measurement of critical heat flux using the transient inverse heat conduction method in spray cooling was performed. The inverse heat conduction method estimates the surface heat flux or temperature using a measured interior temperature history. The effects of the measuring time interval and location of temperature measurement on the measurement of critical heat flux were primarily investigated. The following results were obtained. The estimated critical heat flux decreased as the time interval of temperature measurement increased. Meanwhile, the effect of measurement location on critical heat flux was not significant. It was also found, from the experimental results, that the critical superheat increased as the measurement location of thermocouple neared the heat transfer surface.

5. Detection of Cavities by Inverse Heat Conduction Boundary Element Method Using Minimal Energy Technique

Choi, C. Y.

1997-01-01

A geometrical inverse heat conduction problem is solved for the infrared scanning cavity detection by the boundary element method using minimal energy technique. By minimizing the kinetic energy of temperature field, boundary element equations are converted to the quadratic programming problem. A hypothetical inner boundary is defined such that the actual cavity is located interior to the domain. Temperatures at hypothetical inner boundary are determined to meet the constraints of measurement error of surface temperature obtained by infrared scanning, and then boundary element analysis is performed for the position of an unknown boundary (cavity). Cavity detection algorithm is provided, and the effects of minimal energy technique on the inverse solution method are investigated by means of numerical analysis

6. A domain derivative-based method for solving elastodynamic inverse obstacle scattering problems

Le Louër, Frédérique

2015-01-01

The present work is concerned with the shape reconstruction problem of isotropic elastic inclusions from far-field data obtained by the scattering of a finite number of time-harmonic incident plane waves. This paper aims at completing the theoretical framework which is necessary for the application of geometric optimization tools to the inverse transmission problem in elastodynamics. The forward problem is reduced to systems of boundary integral equations following the direct and indirect methods initially developed for solving acoustic transmission problems. We establish the Fréchet differentiability of the boundary to far-field operator and give a characterization of the first Fréchet derivative and its adjoint operator. Using these results we propose an inverse scattering algorithm based on the iteratively regularized Gauß–Newton method and show numerical experiments in the special case of star-shaped obstacles. (paper)

7. Inverse method for temperature and stress monitoring in complex-shaped bodies

Duda, Piotr; Taler, Jan E- mail: aler@ss5.mech.pk.edu.pl; Roos, Eberhard

2004-01-01

The purpose of this work is to formulate a space marching method, which an be used to solve inverse multidimensional heat conduction problems. The method is designed to reconstruct the transient temperature distribution in a hole construction element based on measured temperatures taken at selected points on the outer surface of the construction element. Next, the Finite element Method is used to calculate thermal stresses and stresses caused by other loads such as, for instance, internal pressure. The developed method or solving temperature and total stress distribution is tested using the measured temperatures generated from a direct solution. Transient temperature nd total stress distributions obtained from the method presented below are compared with the values obtained from the direct solution. Finally, the resented method is experimentally verified during the cooling of a hick-walled cylindrical element. The model of a pressure vessel was reheated at 300 deg.C and then cooled by cold water injection. The comparison of results obtained from the inverse method with experimental data hows the high accuracy of the developed method. The presented method allows o optimize the power block's start-up and shut-down operations, contributes o the reduction of heat loss during these operations and to the extension of power block's life. The fatigue and creep usage factor can be computed in an n-line mode. The presented method herein can be applied to monitoring systems that work in conventional as well as in nuclear power plants

8. The Solution of Two-Phase Inverse Stefan Problem Based on a Hybrid Method with Optimization

Yang Yu

2015-01-01

Full Text Available The two-phase Stefan problem is widely used in industrial field. This paper focuses on solving the two-phase inverse Stefan problem when the interface moving is unknown, which is more realistic from the practical point of view. With the help of optimization method, the paper presents a hybrid method which combines the homotopy perturbation method with the improved Adomian decomposition method to solve this problem. Simulation experiment demonstrates the validity of this method. Optimization method plays a very important role in this paper, so we propose a modified spectral DY conjugate gradient method. And the convergence of this method is given. Simulation experiment illustrates the effectiveness of this modified spectral DY conjugate gradient method.

9. An improved method of inverse kinematics calculation for a six-link manipulator

Sasaki, Shinobu

1987-07-01

As one method of solving the inverse problem related to a six-link manipulator, an improvement was made of previously proposed calculation algorithm based on a solution of an algebraic equation of the 24-th order. In this paper, the same type of a polynomial was derived in the form of the equation of 16-th order, i.e., the order reduced by 8, as compared to previous algorithm. The accuracy of solutions was identified to be much refined. (author)

10. Heat flux estimation in an infrared experimental furnace using an inverse method

Le Bideau, P.; Ploteau, J.P.; Glouannec, P.

2009-01-01

Infrared emitters are widely used in industrial furnaces for thermal treatment. In these processes, the knowledge of the incident heat flux on the surface of the product is a primary step to optimise the command emitters and for maintenance shift. For these reasons, it is necessary to develop autonomous flux meters that could provide an answer to these requirements. These sensors must give an in-line distribution of infrared irradiation in the tunnel furnace and must be able to measure high heat flux in severe thermal environments. In this paper we present a method for in-line assessments solving an inverse heat conduction problem. A metallic mass is instrumented by thermocouples and an inverse method allows the incident heat flux to be estimated. In the first part, attention is focused on a new design tool, which is a numerical code, for the evaluation of potential options during captor conception. In the second part we present the realization and the test of this 'indirect' flux meter and its associated inverse problem. 'Direct' detectors based on thermoelectric devices are compared with this new flux meter in the same conditions in the same furnace. Results prove that this technique is a reliable method, appropriate for high temperature ambiances. This technique can be applied to furnaces where the heat flux is inaccessible to 'direct' measurements.

11. An efficient Bayesian inference approach to inverse problems based on an adaptive sparse grid collocation method

Ma Xiang; Zabaras, Nicholas

2009-01-01

A new approach to modeling inverse problems using a Bayesian inference method is introduced. The Bayesian approach considers the unknown parameters as random variables and seeks the probabilistic distribution of the unknowns. By introducing the concept of the stochastic prior state space to the Bayesian formulation, we reformulate the deterministic forward problem as a stochastic one. The adaptive hierarchical sparse grid collocation (ASGC) method is used for constructing an interpolant to the solution of the forward model in this prior space which is large enough to capture all the variability/uncertainty in the posterior distribution of the unknown parameters. This solution can be considered as a function of the random unknowns and serves as a stochastic surrogate model for the likelihood calculation. Hierarchical Bayesian formulation is used to derive the posterior probability density function (PPDF). The spatial model is represented as a convolution of a smooth kernel and a Markov random field. The state space of the PPDF is explored using Markov chain Monte Carlo algorithms to obtain statistics of the unknowns. The likelihood calculation is performed by directly sampling the approximate stochastic solution obtained through the ASGC method. The technique is assessed on two nonlinear inverse problems: source inversion and permeability estimation in flow through porous media

12. Optical coherence tomography signal analysis: LIDAR like equation and inverse methods

Amaral, Marcello Magri

2012-01-01

Optical Coherence Tomography (OCT) is based on the media backscattering properties in order to obtain tomographic images. In a similar way, LIDAR (Light Detection and Range) technique uses these properties to determine atmospheric characteristics, specially the signal extinction coefficient. Exploring this similarity allowed the application of signal inversion methods to the OCT images, allowing to construct images based in the extinction coefficient, original result until now. The goal of this work was to study, propose, develop and implement algorithms based on OCT signal inversion methodologies with the aim of determine the extinction coefficient as a function of depth. Three inversion methods were used and implemented in LABView R : slope, boundary point and optical depth. Associated errors were studied and real samples (homogeneous and stratified) were used for two and three dimension analysis. The extinction coefficient images obtained from the optical depth method were capable to differentiate air from the sample. The images were studied applying PCA and cluster analysis that established the methodology strength in determining the sample's extinction coefficient value. Moreover, the optical depth methodology was applied to study the hypothesis that there is some correlation between signal extinction coefficient and the enamel teeth demineralization during a cariogenic process. By applying this methodology, it was possible to observe the variation of the extinction coefficient as depth function and its correlation with microhardness variation, showing that in deeper layers its values tends to a healthy tooth values, behaving as the same way that the microhardness. (author)

13. Iterative solution of the inverse Cauchy problem for an elliptic equation by the conjugate gradient method

Vasil'ev, V. I.; Kardashevsky, A. M.; Popov, V. V.; Prokopev, G. A.

2017-10-01

This article presents results of computational experiment carried out using a finite-difference method for solving the inverse Cauchy problem for a two-dimensional elliptic equation. The computational algorithm involves an iterative determination of the missing boundary condition from the override condition using the conjugate gradient method. The results of calculations are carried out on the examples with exact solutions as well as at specifying an additional condition with random errors are presented. Results showed a high efficiency of the iterative method of conjugate gradients for numerical solution

14. Determination of the thermal conductivity and specific heat capacity of neem seeds by inverse problem method

S.N. Nnamchi

2010-01-01

Full Text Available Determination of the thermal conductivity and the specific heat capacity of neem seeds (Azadirachta indica A. Juss usingthe inverse method is the main subject of this work. One-dimensional formulation of heat conduction problem in a spherewas used. Finite difference method was adopted for the solution of the heat conduction problem. The thermal conductivityand the specific heat capacity were determined by least square method in conjunction with Levenberg-Marquardt algorithm.The results obtained compare favourably with those obtained experimentally. These results are useful in the analysis ofneem seeds drying and leaching processes.

15. 3D CSEM data inversion using Newton and Halley class methods

Amaya, M.; Hansen, K. R.; Morten, J. P.

2016-05-01

For the first time in 3D controlled source electromagnetic data inversion, we explore the use of the Newton and the Halley optimization methods, which may show their potential when the cost function has a complex topology. The inversion is formulated as a constrained nonlinear least-squares problem which is solved by iterative optimization. These methods require the derivatives up to second order of the residuals with respect to model parameters. We show how Green's functions determine the high-order derivatives, and develop a diagrammatical representation of the residual derivatives. The Green's functions are efficiently calculated on-the-fly, making use of a finite-difference frequency-domain forward modelling code based on a multi-frontal sparse direct solver. This allow us to build the second-order derivatives of the residuals keeping the memory cost in the same order as in a Gauss-Newton (GN) scheme. Model updates are computed with a trust-region based conjugate-gradient solver which does not require the computation of a stabilizer. We present inversion results for a synthetic survey and compare the GN, Newton, and super-Halley optimization schemes, and consider two different approaches to set the initial trust-region radius. Our analysis shows that the Newton and super-Halley schemes, using the same regularization configuration, add significant information to the inversion so that the convergence is reached by different paths. In our simple resistivity model examples, the convergence speed of the Newton and the super-Halley schemes are either similar or slightly superior with respect to the convergence speed of the GN scheme, close to the minimum of the cost function. Due to the current noise levels and other measurement inaccuracies in geophysical investigations, this advantageous behaviour is at present of low consequence, but may, with the further improvement of geophysical data acquisition, be an argument for more accurate higher-order methods like those

16. Inverse transformation algorithm of transient electromagnetic field and its high-resolution continuous imaging interpretation method

Qi, Zhipeng; Li, Xiu; Lu, Xushan; Zhang, Yingying; Yao, Weihua

2015-01-01

We introduce a new and potentially useful method for wave field inverse transformation and its application in transient electromagnetic method (TEM) 3D interpretation. The diffusive EM field is known to have a unique integral representation in terms of a fictitious wave field that satisfies a wave equation. The continuous imaging of TEM can be accomplished using the imaging methods in seismic interpretation after the diffusion equation is transformed into a fictitious wave equation. The interpretation method based on the imaging of a fictitious wave field could be used as a fast 3D inversion method. Moreover, the fictitious wave field possesses some wave field features making it possible for the application of a wave field interpretation method in TEM to improve the prospecting resolution.Wave field transformation is a key issue in the migration imaging of a fictitious wave field. The equation in the wave field transformation belongs to the first class Fredholm integration equation, which is a typical ill-posed equation. Additionally, TEM has a large dynamic time range, which also facilitates the weakness of this ill-posed problem. The wave field transformation is implemented by using pre-conditioned regularized conjugate gradient method. The continuous imaging of a fictitious wave field is implemented by using Kirchhoff integration. A synthetic aperture and deconvolution algorithm is also introduced to improve the interpretation resolution. We interpreted field data by the method proposed in this paper, and obtained a satisfying interpretation result. (paper)

17. Application of numerical inverse method in calculation of composition-dependent interdiffusion coefficients in finite diffusion couples

Liu, Yuanrong; Chen, Weimin; Zhong, Jing

2017-01-01

The previously developed numerical inverse method was applied to determine the composition-dependent interdiffusion coefficients in single-phase finite diffusion couples. The numerical inverse method was first validated in a fictitious binary finite diffusion couple by pre-assuming four standard...... sets of interdiffusion coefficients. After that, the numerical inverse method was then adopted in a ternary Al-Cu-Ni finite diffusion couple. Based on the measured composition profiles, the ternary interdiffusion coefficients along the entire diffusion path of the target ternary diffusion couple were...... obtained by using the numerical inverse approach. The comprehensive comparisons between the computations and the experiments indicate that the numerical inverse method is also applicable to high-throughput determination of the composition-dependent interdiffusion coefficients in finite diffusion couples....

18. Estimation of oil reservoir thermal properties through temperature log data using inversion method

Cheng, Wen-Long; Nian, Yong-Le; Li, Tong-Tong; Wang, Chang-Long

2013-01-01

Oil reservoir thermal properties not only play an important role in steam injection well heat transfer, but also are the basic parameters for evaluating the oil saturation in reservoir. In this study, for estimating reservoir thermal properties, a novel heat and mass transfer model of steam injection well was established at first, this model made full analysis on the wellbore-reservoir heat and mass transfer as well as the wellbore-formation, and the simulated results by the model were quite consistent with the log data. Then this study presented an effective inversion method for estimating the reservoir thermal properties through temperature log data. This method is based on the heat transfer model in steam injection wells, and can be used to predict the thermal properties as a stochastic approximation method. The inversion method was applied to estimate the reservoir thermal properties of two steam injection wells, it was found that the relative error of thermal conductivity for the two wells were 2.9% and 6.5%, and the relative error of volumetric specific heat capacity were 6.7% and 7.0%,which demonstrated the feasibility of the proposed method for estimating the reservoir thermal properties. - Highlights: • An effective inversion method for predicting the oil reservoir thermal properties was presented. • A novel model for steam injection well made full study on the wellbore-reservoir heat and mass transfer. • The wellbore temperature field and steam parameters can be simulated by the model efficiently. • Both reservoirs and formation thermal properties could be estimated simultaneously by the proposed method. • The estimated steam temperature was quite consistent with the field data

19. Direct inversion of circulation and mixing from tracer measurements – Part 1: Method

T. von Clarmann

2016-11-01

Full Text Available From a series of zonal mean global stratospheric tracer measurements sampled in altitude vs. latitude, circulation and mixing patterns are inferred by the inverse solution of the continuity equation. As a first step, the continuity equation is written as a tendency equation, which is numerically integrated over time to predict a later atmospheric state, i.e., mixing ratio and air density. The integration is formally performed by the multiplication of the initially measured atmospheric state vector by a linear prediction operator. Further, the derivative of the predicted atmospheric state with respect to the wind vector components and mixing coefficients is used to find the most likely wind vector components and mixing coefficients which minimize the residual between the predicted atmospheric state and the later measurement of the atmospheric state. Unless multiple tracers are used, this inversion problem is under-determined, and dispersive behavior of the prediction further destabilizes the inversion. Both these problems are addressed by regularization. For this purpose, a first-order smoothness constraint has been chosen. The usefulness of this method is demonstrated by application to various tracer measurements recorded with the Michelson Interferometer for Passive Atmospheric Sounding (MIPAS. This method aims at a diagnosis of the Brewer–Dobson circulation without involving the concept of the mean age of stratospheric air, and related problems like the stratospheric tape recorder, or intrusions of mesospheric air into the stratosphere.

20. A method to estimate the height of temperature inversion layer and the effective mixing depht

Nicolli, D.

1978-05-01

A review of the concept PBL or turbulent boundary layer is made as it is understood in meteorology. Some features of the PBL parameterization are also discussed, as well as the methods used to estimate the temperature inversion heights during morning and afternoon hours. The study bases on the assumption of the dry adiabatic lapse rate in the mixing layer that is, water vapor and airborne material are supposed to be homogeneously mixed below the inversion layer or in the effective mixing depth. The mean mixing heights over Rio de Janeiro area respectively about 500m and 1000m at morning and afternoon hours. For Sao Paulo these values are respectively 400m and 1300m at morning and afternoon hours [pt

1. Calculation method of water injection forward modeling and inversion process in oilfield water injection network

Liu, Long; Liu, Wei

2018-04-01

A forward modeling and inversion algorithm is adopted in order to determine the water injection plan in the oilfield water injection network. The main idea of the algorithm is shown as follows: firstly, the oilfield water injection network is inversely calculated. The pumping station demand flow is calculated. Then, forward modeling calculation is carried out for judging whether all water injection wells meet the requirements of injection allocation or not. If all water injection wells meet the requirements of injection allocation, calculation is stopped, otherwise the demand injection allocation flow rate of certain step size is reduced aiming at water injection wells which do not meet requirements, and next iterative operation is started. It is not necessary to list the algorithm into water injection network system algorithm, which can be realized easily. Iterative method is used, which is suitable for computer programming. Experimental result shows that the algorithm is fast and accurate.

2. Application of homotopy analysis method and inverse solution of a rectangular wet fin

Panda, Srikumar; Bhowmik, Arka; Das, Ranjan; Repaka, Ramjee; Martha, Subash C.

2014-01-01

Highlights: • Solution of a wet fin with is obtained by homotopy analysis method (HAM). • Present HAM results have been well-validated with literature results. • Inverse analysis is done using genetic algorithm. • Measurement error of ±10–12% (approx.) is found to yield satisfactory reconstructions. - Abstract: This paper presents the analytical solution of a rectangular fin under the simultaneous heat and mass transfer across the fin surface and the fin tip, and estimates the unknown thermal and geometrical configurations of the fin using inverse heat transfer analysis. The local temperature field is obtained by using homotopy analysis method for insulated and convective fin tip boundary conditions. Using genetic algorithm, the thermal and geometrical parameters, viz., thermal conductivity of the material, surface heat transfer coefficient and dimensions of the fin have been simultaneously estimated for the prescribed temperature field. Earlier inverse studies on wet fin have been restricted to the analysis of nonlinear governing equation with either insulated tip condition or finite tip temperature only. The present study developed a closed-form solution with the consideration of nonlinearity effects in both governing equation and boundary condition. The study on inverse optimization leads to many feasible combination of fin materials, thermal conditions and fin dimensions. Thus allows the flexibility for designing a fin under wet conditions, based on multiple combinations of fin materials, fin dimensions and thermal configurations to achieve the required heat transfer duty. It is further determined that the allowable measurement error should be limited to ±10–12% in order to achieve satisfactory reconstruction

3. Total variation regularization for seismic waveform inversion using an adaptive primal dual hybrid gradient method

Yong, Peng; Liao, Wenyuan; Huang, Jianping; Li, Zhenchuan

2018-04-01

Full waveform inversion is an effective tool for recovering the properties of the Earth from seismograms. However, it suffers from local minima caused mainly by the limited accuracy of the starting model and the lack of a low-frequency component in the seismic data. Because of the high velocity contrast between salt and sediment, the relation between the waveform and velocity perturbation is strongly nonlinear. Therefore, salt inversion can easily get trapped in the local minima. Since the velocity of salt is nearly constant, we can make the most of this characteristic with total variation regularization to mitigate the local minima. In this paper, we develop an adaptive primal dual hybrid gradient method to implement total variation regularization by projecting the solution onto a total variation norm constrained convex set, through which the total variation norm constraint is satisfied at every model iteration. The smooth background velocities are first inverted and the perturbations are gradually obtained by successively relaxing the total variation norm constraints. Numerical experiment of the projection of the BP model onto the intersection of the total variation norm and box constraints has demonstrated the accuracy and efficiency of our adaptive primal dual hybrid gradient method. A workflow is designed to recover complex salt structures in the BP 2004 model and the 2D SEG/EAGE salt model, starting from a linear gradient model without using low-frequency data below 3 Hz. The salt inversion processes demonstrate that wavefield reconstruction inversion with a total variation norm and box constraints is able to overcome local minima and inverts the complex salt velocity layer by layer.

4. Methods and Algorithms for Solving Inverse Problems for Fractional Advection-Dispersion Equations

Aldoghaither, Abeer

2015-11-12

Fractional calculus has been introduced as an e cient tool for modeling physical phenomena, thanks to its memory and hereditary properties. For example, fractional models have been successfully used to describe anomalous di↵usion processes such as contaminant transport in soil, oil flow in porous media, and groundwater flow. These models capture important features of particle transport such as particles with velocity variations and long-rest periods. Mathematical modeling of physical phenomena requires the identification of pa- rameters and variables from available measurements. This is referred to as an inverse problem. In this work, we are interested in studying theoretically and numerically inverse problems for space Fractional Advection-Dispersion Equation (FADE), which is used to model solute transport in porous media. Identifying parameters for such an equa- tion is important to understand how chemical or biological contaminants are trans- ported throughout surface aquifer systems. For instance, an estimate of the di↵eren- tiation order in groundwater contaminant transport model can provide information about soil properties, such as the heterogeneity of the medium. Our main contribution is to propose a novel e cient algorithm based on modulat-ing functions to estimate the coe cients and the di↵erentiation order for space FADE, which can be extended to general fractional Partial Di↵erential Equation (PDE). We also show how the method can be applied to the source inverse problem. This work is divided into two parts: In part I, the proposed method is described and studied through an extensive numerical analysis. The local convergence of the proposed two-stage algorithm is proven for 1D space FADE. The properties of this method are studied along with its limitations. Then, the algorithm is generalized to the 2D FADE. In part II, we analyze direct and inverse source problems for a space FADE. The problem consists of recovering the source term using final

5. Inversion of real and complex phase shifts to potentials by the generalized Cox-Thompson inverse scattering method at fixed energy

Melchert, O; Scheid, W; Apagyi, B

2006-01-01

The Cox-Thompson inverse scattering method at fixed energy has been generalized to treat complex phase shifts derived from experiments. New formulae for relating phase shifts to shifted angular momenta are derived. The method is applied to phase shifts of known potentials in order to test its quality and stability and, further, it is used to invert experimental n-α and n- 12 C phase shifts

6. Iterative and range test methods for an inverse source problem for acoustic waves

Alves, Carlos; Kress, Rainer; Serranho, Pedro

2009-01-01

We propose two methods for solving an inverse source problem for time-harmonic acoustic waves. Based on the reciprocity gap principle a nonlinear equation is presented for the locations and intensities of the point sources that can be solved via Newton iterations. To provide an initial guess for this iteration we suggest a range test algorithm for approximating the source locations. We give a mathematical foundation for the range test and exhibit its feasibility in connection with the iteration method by some numerical examples

7. Remarks on a financial inverse problem by means of Monte Carlo Methods

Cuomo, Salvatore; Di Somma, Vittorio; Sica, Federica

2017-10-01

Estimating the price of a barrier option is a typical inverse problem. In this paper we present a numerical and statistical framework for a market with risk-free interest rate and a risk asset, described by a Geometric Brownian Motion (GBM). After approximating the risk asset with a numerical method, we find the final option price by following an approach based on sequential Monte Carlo methods. All theoretical results are applied to the case of an option whose underlying is a real stock.

8. Solution methods for compartment models of transport through the environment using numerical inversion of Laplace transforms

Garratt, T.J.

1989-05-01

Compartment models for the transport of radionuclides in the biosphere are conventionally solved using a numerical time-stepping procedure. This report examines an alternative method based on the numerical inversion of Laplace transforms, which is potentially more efficient and accurate for some classes of problem. The central problem considered is the most efficient and robust technique for solving the Laplace-transformed rate equations. The conclusion is that Gaussian elimination is the most efficient and robust solution method. A general compartment model has been implemented on a personal computer and used to solve a realistic case including radionuclide decay chains. (author)

9. A comparison of inverse boundary element method and near-field acoustical holography

Schuhmacher, Andreas; Hald, Jørgen; Saemann, E.-U.

1999-01-01

An inverse boundary element method (IBEM) is used to estimate the surface velocity of a rolling tyre from measurements of the near-field pressure. Subsequently, the sound pressure is calculated over a finite plane surface next to the tyre from the reconstructed velocity field on the tyre surface........ In order to verify the reconstruction process, part of the measurement data is used together with Near-Field Acoustical Holography (NAH). Estimated distributions of sound pressure and particle velocity over a plane surface obtained from the two methods are compared....

10. The Inverse System Method Applied to the Derivation of Power System Non—linear Control Laws

DonghaiLI; XuezhiJIANG; 等

1997-01-01

The differential geometric method has been applied to a series of power system non-linear control problems effectively.However a set of differential equations must be solved for obtaining the required diffeomorphic transformation.Therefore the derivation of control laws is very complicated.In fact because of the specificity of power system models the required diffeomorphic transformation may be obtained directly,so it is unnecessary to solve a set of differential equations.In addition inverse system method is equivalent to differential geometric method in reality and not limited to affine nonlinear systems,Its physical meaning is able to be viewed directly and its deduction needs only algebraic operation and derivation,so control laws can be obtained easily and the application to engineering is very convenient.Authors of this paper take steam valving control of power system as a typical case to be studied.It is demonstrated that the control law deduced by inverse system method is just the same as one by differential geometric method.The conclusion will simplify the control law derivations of steam valving,excitation,converter and static var compensator by differential geometric method and may be suited to similar control problems in other areas.

11. A Hybrid Optimization Method for Solving Bayesian Inverse Problems under Uncertainty.

Kai Zhang

Full Text Available In this paper, we investigate the application of a new method, the Finite Difference and Stochastic Gradient (Hybrid method, for history matching in reservoir models. History matching is one of the processes of solving an inverse problem by calibrating reservoir models to dynamic behaviour of the reservoir in which an objective function is formulated based on a Bayesian approach for optimization. The goal of history matching is to identify the minimum value of an objective function that expresses the misfit between the predicted and measured data of a reservoir. To address the optimization problem, we present a novel application using a combination of the stochastic gradient and finite difference methods for solving inverse problems. The optimization is constrained by a linear equation that contains the reservoir parameters. We reformulate the reservoir model's parameters and dynamic data by operating the objective function, the approximate gradient of which can guarantee convergence. At each iteration step, we obtain the relatively 'important' elements of the gradient, which are subsequently substituted by the values from the Finite Difference method through comparing the magnitude of the components of the stochastic gradient, which forms a new gradient, and we subsequently iterate with the new gradient. Through the application of the Hybrid method, we efficiently and accurately optimize the objective function. We present a number numerical simulations in this paper that show that the method is accurate and computationally efficient.

12. Experimental Verification of a Simple Method for Accurate Center of Gravity Determination of Small Satellite Platforms

Dario Modenini

2018-01-01

Full Text Available We propose a simple and relatively inexpensive method for determining the center of gravity (CoG of a small spacecraft. This method, which can be ascribed to the class of suspension techniques, is based on dual-axis inclinometer readings. By performing two consecutive suspensions from two different points, the CoG is determined, ideally, as the intersection between two lines which are uniquely defined by the respective rotations. We performed an experimental campaign to verify the method and assess its accuracy. Thanks to a quantitative error budget, we obtained an error distribution with simulations, which we verified through experimental tests. The retrieved experimental error distribution agrees well with the results predicted through simulations, which in turn lead to a CoG error norm smaller than 2 mm with 95% confidence level.

13. A New Method for Optimal Regularization Parameter Determination in the Inverse Problem of Load Identification

Wei Gao

2016-01-01

Full Text Available According to the regularization method in the inverse problem of load identification, a new method for determining the optimal regularization parameter is proposed. Firstly, quotient function (QF is defined by utilizing the regularization parameter as a variable based on the least squares solution of the minimization problem. Secondly, the quotient function method (QFM is proposed to select the optimal regularization parameter based on the quadratic programming theory. For employing the QFM, the characteristics of the values of QF with respect to the different regularization parameters are taken into consideration. Finally, numerical and experimental examples are utilized to validate the performance of the QFM. Furthermore, the Generalized Cross-Validation (GCV method and the L-curve method are taken as the comparison methods. The results indicate that the proposed QFM is adaptive to different measuring points, noise levels, and types of dynamic load.

14. Practical use of control rod calibration system with the inverse kinetics method

Yamanaka, Haruhiko; Hayashi, Kazuhiko; Motohashi, Jun; Kawashima, Kazuhito; Ichimura, Toshiyuki; Tamai, Kazuo; Takeuti, Mitsuo

2002-01-01

The control rod calibration results in the JRR-3 are used as a reactivity standard to measure and manage the reactivity change in the core. The total travel of all six control rods has been calibrated by an inverse kinetics method (IK method) during an annual maintenance period. The IK method has the great merit in saving measuring time compared with the conventional positive period method (PP method). The JRR-3 control rod calibration system was renovated and put into practical use in order to improve reliability and function by accumulating 10-year experience with the IK method in the JRR-3. The report shows the function, the performance and results of verification of the JRR-3 control rod calibration system. (author)

15. 6th International Workshop on New Computational Methods for Inverse Problems

2016-01-01

Foreword This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 6 th International Workshop on New Computational Methods for Inverse Problems, NCMIP 2016 (http://complement.farman.ens-cachan.fr/NCMIP 2016.html). This workshop took place at Ecole Normale Supérieure de Cachan, on May 20, 2016. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of ValueTools Conference, in May 2011, and secondly at the initiative of Institut Farman, in May 2012, May 2013, May 2014 and May 2015. The New Computational Methods for Inverse Problems (NCMIP) workshop focused on recent advances in the resolution of inverse problems. Indeed, inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists in estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one- day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, Kernel

16. Inverse airfoil design method for low-speed straight-bladed Darrieus-type VAWT applications

Saeed, F. [King Fahd Univ. of Petroleum and Minerals, Dhahran (Saudi Arabia); Paraschivoiu, I.; Trifu, O. [Ecole Polytechnique, Montreal, PQ (Canada); Hess, M.; Gabrys, C. [Mariah Power Inc., Reno, NV (United States)

2008-07-01

Inverse airfoil design of a low-speed straight-bladed Darrieus-type vertical axis wind turbine (VAWT) can help improve aerodynamic performance and power output by eliminating undesirable flow field characteristics at very low Reynolds number. This study used an interactive inverse airfoil design method (PROFOIL) that allows specification of velocity and boundary-layer characteristics over different segments of the airfoil subject to constraints on the geometry (closure) and the flow field (far field boundary). Additional constraints were also considered to address pitching moment coefficient, thickness and the power output for a given tip-speed ratio. Performance analyses of the airfoil and the VAWT were carried out using state-of-the-art analyses codes XFOIL and CARDAAV, respectively. XFOIL is a panel method with a coupled boundary-layer scheme and is used to obtain the aerodynamic characteristics of resulting airfoil shapes. The final airfoil geometry is obtained through a multi-dimensional Newton iteration. The study showed that the strength of the method lies in the inverse design methodology whereas its weaknesses is in reliably predicting aerodynamic characteristics of airfoils at low Reynolds numbers and high angles of attack. A 10-15 per cent increase in the relative performance of the VAWT was achieved with this method. Although the results of the study showed that the method has great application potential for VAWTs in general, there is much room for improvement in flow analysis capabilities for low Re flows in reliably predicting post-stall aerodynamic characteristics. In the absence of such analysis capabilities, the authors suggested that the results should be viewed qualitatively and not quantitatively. 36 refs., 1 tab., 4 figs.

17. Application of decomposition method and inverse prediction of parameters in a moving fin

Singla, Rohit K.; Das, Ranjan

2014-01-01

18. Multi-parameter Analysis and Inversion for Anisotropic Media Using the Scattering Integral Method

Djebbi, Ramzi

2017-10-24

The main goal in seismic exploration is to identify locations of hydrocarbons reservoirs and give insights on where to drill new wells. Therefore, estimating an Earth model that represents the right physics of the Earth\\'s subsurface is crucial in identifying these targets. Recent seismic data, with long offsets and wide azimuth features, are more sensitive to anisotropy. Accordingly, multiple anisotropic parameters need to be extracted from the recorded data on the surface to properly describe the model. I study the prospect of applying a scattering integral approach for multi-parameter inversion for a transversely isotropic model with a vertical axis of symmetry. I mainly analyze the sensitivity kernels to understand the sensitivity of seismic data to anisotropy parameters. Then, I use a frequency domain scattering integral approach to invert for the optimal parameterization. The scattering integral approach is based on the explicit computation of the sensitivity kernels. I present a new method to compute the traveltime sensitivity kernels for wave equation tomography using the unwrapped phase. I show that the new kernels are a better alternative to conventional cross-correlation/Rytov kernels. I also derive and analyze the sensitivity kernels for a transversely isotropic model with a vertical axis of symmetry. The kernels structure, for various opening/scattering angles, highlights the trade-off regions between the parameters. For a surface recorded data, I show that the normal move-out velocity vn, ƞ and δ parameterization is suitable for a simultaneous inversion of diving waves and reflections. Moreover, when seismic data is inverted hierarchically, the horizontal velocity vh, ƞ and ϵ is the parameterization with the least trade-off. In the frequency domain, the hierarchical inversion approach is naturally implemented using frequency continuation, which makes vh, ƞ and ϵ parameterization attractive. I formulate the multi-parameter inversion using the

19. Method for the disposal of laundry drain by inverse osmosis method

Sugimoto, Yoshikazu; Yusa, Hideo; Kamiya, Kunio; Ebara, Katsuya.

1976-01-01

Purpose: To effectively obtain clean water of high purity from laundry waste from work clothes or the like worn in the atomic power plant and to increase the concentration factor of the impurities. Constitution: The laundry drain is supplied to a forestage condensation tank through a supply pipe, via a control valve controlled by a level gage so as to always maintain the liquid level constant, and the liquid within the tank is increased in pressure by the fore-stage high pressure pump and supplied to the fore-stage inverse osmosis module. There occurs a phenomenon of inverse osmosis so that water in disposed liquid is urged through a film and discharged from a osmosed water discharge pipe. In this case, the concentration of a surface active agent in the disposed liquid is detected by a flow meter depending on the quantity of osmosed water, and when the concentration exceeds a predetermined level to decrease the quantity of osmosed water, the opening of the control valve is increased and the liquid is discharged from the discharge pipe into the final tank for disposal in substantially similar manner. (Yoshihara, H.)

20. Inverse methods for 3D quantitative optical coherence elasticity imaging (Conference Presentation)

Dong, Li; Wijesinghe, Philip; Hugenberg, Nicholas; Sampson, David D.; Munro, Peter R. T.; Kennedy, Brendan F.; Oberai, Assad A.

2017-02-01

In elastography, quantitative elastograms are desirable as they are system and operator independent. Such quantification also facilitates more accurate diagnosis, longitudinal studies and studies performed across multiple sites. In optical elastography (compression, surface-wave or shear-wave), quantitative elastograms are typically obtained by assuming some form of homogeneity. This simplifies data processing at the expense of smearing sharp transitions in elastic properties, and/or introducing artifacts in these regions. Recently, we proposed an inverse problem-based approach to compression OCE that does not assume homogeneity, and overcomes the drawbacks described above. In this approach, the difference between the measured and predicted displacement field is minimized by seeking the optimal distribution of elastic parameters. The predicted displacements and recovered elastic parameters together satisfy the constraint of the equations of equilibrium. This approach, which has been applied in two spatial dimensions assuming plane strain, has yielded accurate material property distributions. Here, we describe the extension of the inverse problem approach to three dimensions. In addition to the advantage of visualizing elastic properties in three dimensions, this extension eliminates the plane strain assumption and is therefore closer to the true physical state. It does, however, incur greater computational costs. We address this challenge through a modified adjoint problem, spatially adaptive grid resolution, and three-dimensional decomposition techniques. Through these techniques the inverse problem is solved on a typical desktop machine within a wall clock time of 20 hours. We present the details of the method and quantitative elasticity images of phantoms and tissue samples.

1. Superconducting gravity gradiometer for sensitive gravity measurements. II. Experiment

Chan, H.A.; Moody, M.V.; Paik, H.J.

1987-01-01

A sensitive superconducting gravity gradiometer has been constructed and tested. Coupling to gravity signals is obtained by having two superconducting proof masses modulate magnetic fields produced by persistent currents. The induced electrical currents are differenced by a passive superconducting circuit coupled to a superconducting quantum interference device. The experimental behavior of this device has been shown to follow the theoretical model closely in both signal transfer and noise characteristics. While its intrinsic noise level is shown to be 0.07 E Hz/sup -1/2/ (1 Eequivalent10/sup -9/ sec/sup -2/), the actual performance of the gravity gradiometer on a passive platform has been limited to 0.3--0.7 E Hz/sup -1/2/ due to its coupling to the environmental noise. The detailed structure of this excess noise is understood in terms of an analytical error model of the instrument. The calibration of the gradiometer has been obtained by two independent methods: by applying a linear acceleration and a gravity signal in two different operational modes of the instrument. This device has been successfully operated as a detector in a new null experiment for the gravitational inverse-square law. In this paper we report the design, fabrication, and detailed test results of the superconducting gravity gradiometer. We also present additional theoretical analyses which predict the specific dynamic behavior of the gradiometer and of the test

2. Numerical method in reproducing kernel space for an inverse source problem for the fractional diffusion equation

Wang, Wenyan; Han, Bo; Yamamoto, Masahiro

2013-01-01

We propose a new numerical method for reproducing kernel Hilbert space to solve an inverse source problem for a two-dimensional fractional diffusion equation, where we are required to determine an x-dependent function in a source term by data at the final time. The exact solution is represented in the form of a series and the approximation solution is obtained by truncating the series. Furthermore, a technique is proposed to improve some of the existing methods. We prove that the numerical method is convergent under an a priori assumption of the regularity of solutions. The method is simple to implement. Our numerical result shows that our method is effective and that it is robust against noise in L 2 -space in reconstructing a source function. (paper)

3. A Novel Inversion Method of Manufacturing Flaws in the Packaging of Conformal Load-Bearing Antenna Structure

P. Li

2015-01-01

Full Text Available Composite material is widely used in the conformal load-bearing antenna structure (CLAS, and the manufacturing flaws in the packaging process of the CLAS will lead to the degradation of its wave-transparent property. For this problem, a novel inverse method of the flaw’s dimension by antenna-radome system’s far field data has been proposed. Two steps are included in the inversion: the first one is the inversion from the far filed data to the transmission coefficient of the CLAS’s radome; the second one is the inversion from the transmission coefficient to the flaw’s dimension. The inversion also has a good potential for the separable multilayer composite material radome. A 12.5 GHz CLAS with microstrip antenna array is used in the simulation, which indicates the effectiveness of the novel inversion method. Finally, the error analysis of the inversion method is presented by numerical simulation; the results is that the inversed error could be less than 10%, if the measurement error of far field data is less than 0.45 dB in amplitude and ±5° in phase.

4. Simple estimating method of damages of concrete gravity dam based on linear dynamic analysis

Sasaki, T.; Kanenawa, K.; Yamaguchi, Y. [Public Works Research Institute, Tsukuba, Ibaraki (Japan). Hydraulic Engineering Research Group

2004-07-01

Due to the occurrence of large earthquakes like the Kobe Earthquake in 1995, there is a strong need to verify seismic resistance of dams against much larger earthquake motions than those considered in the present design standard in Japan. Problems exist in using nonlinear analysis to evaluate the safety of dams including: that the influence which the set material properties have on the results of nonlinear analysis is large, and that the results of nonlinear analysis differ greatly according to the damage estimation models or analysis programs. This paper reports the evaluation indices based on a linear dynamic analysis method and the characteristics of the progress of cracks in concrete gravity dams with different shapes using a nonlinear dynamic analysis method. The study concludes that if simple linear dynamic analysis is appropriately conducted to estimate tensile stress at potential locations of initiating cracks, the damage due to cracks would be predicted roughly. 4 refs., 1 tab., 13 figs.

5. Isaac Newton's scientific method turning data into evidence about gravity and cosmology

Harper, William L.

2014-01-01

Isaac Newton's Scientific Method examines Newton's argument for universal gravity and his application of it to resolve the problem of deciding between geocentric and heliocentric world systems by measuring masses of the sun and planets. William L. Harper suggests that Newton's inferences from phenomena realize an ideal of empirical success that is richer than prediction. Any theory that can achieve this rich sort of empirical success must not only be able to predict the phenomena it purports to explain, but also have those phenomena accurately measure the parameters which explain them. Harper explores the ways in which Newton's method aims to turn theoretical questions into ones which can be answered empirically by measurement from phenomena, and to establish that propositions inferred from phenomena are provisionally accepted as guides to further research. This methodology, guided by its rich ideal of empirical success, supports a conception of scientific progress that does not require construing it as progr...

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

Avdyushev, Victor A.

2017-12-01

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

7. A matrix-inversion method for gamma-source mapping from gamma-count data - 59082

Bull, Richard K.; Adsley, Ian; Burgess, Claire

2012-01-01

Gamma ray counting is often used to survey the distribution of active waste material in various locations. Ideally the output from such surveys would be a map of the activity of the waste. In this paper a simple matrix-inversion method is presented. This allows an array of gamma-count data to be converted to an array of source activities. For each survey area the response matrix is computed using the gamma-shielding code Microshield [1]. This matrix links the activity array to the count array. The activity array is then obtained via matrix inversion. The method was tested on artificially-created arrays of count-data onto which statistical noise had been added. The method was able to reproduce, quite faithfully, the original activity distribution used to generate the dataset. The method has been applied to a number of practical cases, including the distribution of activated objects in a hot cell and to activated Nimonic springs amongst fuel-element debris in vaults at a nuclear plant. (authors)

8. Indirect Inverse Substructuring Method for Multibody Product Transport System with Rigid and Flexible Coupling

Jun Wang

2015-01-01

Full Text Available The aim of this paper is to develop a new frequency response function- (FRF- based indirect inverse substructuring method without measuring system-level FRFs in the coupling DOFs for the analysis of the dynamic characteristics of a three-substructure coupled product transport system with rigid and flexible coupling. By enforcing the dynamic equilibrium conditions at the coupling coordinates and the displacement compatibility conditions, a closed-form analytical solution to inverse substructuring analysis of multisubstructure coupled product transport system is derived based on the relationship of easy-to-monitor component-level FRFs and the system-level FRFs at the coupling coordinates. The proposed method is validated by a lumped mass-spring-damper model, and the predicted coupling dynamic stiffness is compared with the direct computation, showing exact agreement. The method developed offers an approach to predict the unknown coupling dynamic stiffness from measured FRFs purely. The suggested method may help to obtain the main controlling factors and contributions from the various structure-borne paths for product transport system.

9. FOREWORD: 2nd International Workshop on New Computational Methods for Inverse Problems (NCMIP 2012)

Blanc-Féraud, Laure; Joubert, Pierre-Yves

2012-09-01

Conference logo This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 2nd International Workshop on New Computational Methods for Inverse Problems, (NCMIP 2012). This workshop took place at Ecole Normale Supérieure de Cachan, in Cachan, France, on 15 May 2012, at the initiative of Institut Farman. The first edition of NCMIP also took place in Cachan, France, within the scope of the ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/). The NCMIP Workshop focused on recent advances in the resolution of inverse problems. Indeed inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finance. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational aspects of inversion, Bayesian estimation, kernel methods, learning methods, convex optimization, free discontinuity problems, metamodels, proper orthogonal decomposition

10. FOREWORD: 3rd International Workshop on New Computational Methods for Inverse Problems (NCMIP 2013)

Blanc-Féraud, Laure; Joubert, Pierre-Yves

2013-10-01

Conference logo This volume of Journal of Physics: Conference Series is dedicated to the scientific contributions presented during the 3rd International Workshop on New Computational Methods for Inverse Problems, NCMIP 2013 (http://www.farman.ens-cachan.fr/NCMIP_2013.html). This workshop took place at Ecole Normale Supérieure de Cachan, in Cachan, France, on 22 May 2013, at the initiative of Institut Farman. The prior editions of NCMIP also took place in Cachan, France, firstly within the scope of the ValueTools Conference, in May 2011 (http://www.ncmip.org/2011/), and secondly at the initiative of Institut Farman, in May 2012 (http://www.farman.ens-cachan.fr/NCMIP_2012.html). The NCMIP Workshop focused on recent advances in the resolution of inverse problems. Indeed inverse problems appear in numerous scientific areas such as geophysics, biological and medical imaging, material and structure characterization, electrical, mechanical and civil engineering, and finances. The resolution of inverse problems consists of estimating the parameters of the observed system or structure from data collected by an instrumental sensing or imaging device. Its success firstly requires the collection of relevant observation data. It also requires accurate models describing the physical interactions between the instrumental device and the observed system, as well as the intrinsic properties of the solution itself. Finally, it requires the design of robust, accurate and efficient inversion algorithms. Advanced sensor arrays and imaging devices provide high rate and high volume data; in this context, the efficient resolution of the inverse problem requires the joint development of new models and inversion methods, taking computational and implementation aspects into account. During this one-day workshop, researchers had the opportunity to bring to light and share new techniques and results in the field of inverse problems. The topics of the workshop were: algorithms and computational

11. Micro-seismic imaging using a source function independent full waveform inversion method

Wang, Hanchen; Alkhalifah, Tariq

2018-03-01

At the heart of micro-seismic event measurements is the task to estimate the location of the source micro-seismic events, as well as their ignition times. The accuracy of locating the sources is highly dependent on the velocity model. On the other hand, the conventional micro-seismic source locating methods require, in many cases manual picking of traveltime arrivals, which do not only lead to manual effort and human interaction, but also prone to errors. Using full waveform inversion (FWI) to locate and image micro-seismic events allows for an automatic process (free of picking) that utilizes the full wavefield. However, full waveform inversion of micro-seismic events faces incredible nonlinearity due to the unknown source locations (space) and functions (time). We developed a source function independent full waveform inversion of micro-seismic events to invert for the source image, source function and the velocity model. It is based on convolving reference traces with these observed and modeled to mitigate the effect of an unknown source ignition time. The adjoint-state method is used to derive the gradient for the source image, source function and velocity updates. The extended image for the source wavelet in Z axis is extracted to check the accuracy of the inverted source image and velocity model. Also, angle gathers is calculated to assess the quality of the long wavelength component of the velocity model. By inverting for the source image, source wavelet and the velocity model simultaneously, the proposed method produces good estimates of the source location, ignition time and the background velocity for synthetic examples used here, like those corresponding to the Marmousi model and the SEG/EAGE overthrust model.

12. Micro-seismic imaging using a source function independent full waveform inversion method

Wang, Hanchen

2018-03-26

At the heart of micro-seismic event measurements is the task to estimate the location of the source micro-seismic events, as well as their ignition times. The accuracy of locating the sources is highly dependent on the velocity model. On the other hand, the conventional micro-seismic source locating methods require, in many cases manual picking of traveltime arrivals, which do not only lead to manual effort and human interaction, but also prone to errors. Using full waveform inversion (FWI) to locate and image micro-seismic events allows for an automatic process (free of picking) that utilizes the full wavefield. However, full waveform inversion of micro-seismic events faces incredible nonlinearity due to the unknown source locations (space) and functions (time). We developed a source function independent full waveform inversion of micro-seismic events to invert for the source image, source function and the velocity model. It is based on convolving reference traces with these observed and modeled to mitigate the effect of an unknown source ignition time. The adjoint-state method is used to derive the gradient for the source image, source function and velocity updates. The extended image for the source wavelet in Z axis is extracted to check the accuracy of the inverted source image and velocity model. Also, angle gathers is calculated to assess the quality of the long wavelength component of the velocity model. By inverting for the source image, source wavelet and the velocity model simultaneously, the proposed method produces good estimates of the source location, ignition time and the background velocity for synthetic examples used here, like those corresponding to the Marmousi model and the SEG/EAGE overthrust model.

13. Solution to Two-Dimensional Steady Inverse Heat Transfer Problems with Interior Heat Source Based on the Conjugate Gradient Method

Shoubin Wang

2017-01-01

Full Text Available The compound variable inverse problem which comprises boundary temperature distribution and surface convective heat conduction coefficient of two-dimensional steady heat transfer system with inner heat source is studied in this paper applying the conjugate gradient method. The introduction of complex variable to solve the gradient matrix of the objective function obtains more precise inversion results. This paper applies boundary element method to solve the temperature calculation of discrete points in forward problems. The factors of measuring error and the number of measuring points zero error which impact the measurement result are discussed and compared with L-MM method in inverse problems. Instance calculation and analysis prove that the method applied in this paper still has good effectiveness and accuracy even if measurement error exists and the boundary measurement points’ number is reduced. The comparison indicates that the influence of error on the inversion solution can be minimized effectively using this method.

14. Preconditioned alternating direction method of multipliers for inverse problems with constraints

Jiao, Yuling; Jin, Qinian; Lu, Xiliang; Wang, Weijie

2017-01-01

We propose a preconditioned alternating direction method of multipliers (ADMM) to solve linear inverse problems in Hilbert spaces with constraints, where the feature of the sought solution under a linear transformation is captured by a possibly non-smooth convex function. During each iteration step, our method avoids solving large linear systems by choosing a suitable preconditioning operator. In case the data is given exactly, we prove the convergence of our preconditioned ADMM without assuming the existence of a Lagrange multiplier. In case the data is corrupted by noise, we propose a stopping rule using information on noise level and show that our preconditioned ADMM is a regularization method; we also propose a heuristic rule when the information on noise level is unavailable or unreliable and give its detailed analysis. Numerical examples are presented to test the performance of the proposed method. (paper)

15. Demonstration of improved seismic source inversion method of tele-seismic body wave

Yagi, Y.; Okuwaki, R.

2017-12-01

Seismic rupture inversion of tele-seismic body wave has been widely applied to studies of large earthquakes. In general, tele-seismic body wave contains information of overall rupture process of large earthquake, while the tele-seismic body wave is inappropriate for analyzing a detailed rupture process of M6 7 class earthquake. Recently, the quality and quantity of tele-seismic data and the inversion method has been greatly improved. Improved data and method enable us to study a detailed rupture process of M6 7 class earthquake even if we use only tele-seismic body wave. In this study, we demonstrate the ability of the improved data and method through analyses of the 2016 Rieti, Italy earthquake (Mw 6.2) and the 2016 Kumamoto, Japan earthquake (Mw 7.0) that have been well investigated by using the InSAR data set and the field observations. We assumed the rupture occurring on a single fault plane model inferred from the moment tensor solutions and the aftershock distribution. We constructed spatiotemporal discretized slip-rate functions with patches arranged as closely as possible. We performed inversions using several fault models and found that the spatiotemporal location of large slip-rate area was robust. In the 2016 Kumamoto, Japan earthquake, the slip-rate distribution shows that the rupture propagated to southwest during the first 5 s. At 5 s after the origin time, the main rupture started to propagate toward northeast. First episode and second episode correspond to rupture propagation along the Hinagu fault and the Futagawa fault, respectively. In the 2016 Rieti, Italy earthquake, the slip-rate distribution shows that the rupture propagated to up-dip direction during the first 2 s, and then rupture propagated toward northwest. From both analyses, we propose that the spatiotemporal slip-rate distribution estimated by improved inversion method of tele-seismic body wave has enough information to study a detailed rupture process of M6 7 class earthquake.

16. Non-local currents in 2D QFT: an alternative To - the quantum inverse scattering method

Bernard, D.; Leclair, A.; Cornell Univ., Ithaca, NY

1990-01-01

The formalism based on non-local charges that we propose provides an alternative to the quantum inverse scattering method for solving integrable quantum field theories in 2D. The content of the paper is: 1. Introduction: historical background. 2. The NLC approach to 2D QFT: a summary. 3 Exchange algebras and on-shell conservation laws: why non-local charges are useful. 4. The lattice construction: the geometrical origin of non-local conserved currents. 5. The continuum construction: how to deal with non-local conserved currents. 6. Examples: Yangian and quantum group currents. 7 Conclusions: open problems. 22 refs., 4 figs

17. A NEW METHOD OF CHANNEL FRICTION INVERSION BASED ON KALMAN FILTER WITH UNKNOWN PARAMETER VECTOR

CHENG Wei-ping; MAO Gen-hai; LIU Guo-hua

2005-01-01

Channel friction is an important parameter in hydraulic analysis.A channel friction parameter inversion method based on Kalman Filter with unknown parameter vector is proposed.Numerical simulations indicate that when the number of monitoring stations exceeds a critical value, the solution is hardly affected.In addition, Kalman Filter with unknown parameter vector is effective only at unsteady state.For the nonlinear equations, computations of sensitivity matrices are time-costly.Two simplified measures can reduce computing time, but not influence the results.One is to reduce sensitivity matrix analysis time, the other is to substitute for sensitivity matrix.

18. Inverse Heat Conduction Methods in the CHAR Code for Aerothermal Flight Data Reconstruction

Oliver, A. Brandon; Amar, Adam J.

2016-01-01

Reconstruction of flight aerothermal environments often requires the solution of an inverse heat transfer problem, which is an ill-posed problem of determining boundary conditions from discrete measurements in the interior of the domain. This paper will present the algorithms implemented in the CHAR code for use in reconstruction of EFT-1 flight data and future testing activities. Implementation details will be discussed, and alternative hybrid-methods that are permitted by the implementation will be described. Results will be presented for a number of problems.

19. Design of a new urban wind turbine airfoil using a pressure-load inverse method

Henriques, J.C.C.; Gato, L.M.C. [IDMEC, Instituto Superior Tecnico, Universidade Tecnica de Lisboa, Av. Rovisco Pais, 1049-001 Lisboa (Portugal); Marques da Silva, F. [LNEC - Laboratorio Nacional de Engenharia Civil, Av. Brasil, 101, 1700-066 Lisboa (Portugal); Estanqueiro, A.I. [INETI - Instituto Nacional de Engenharia, Tecnologia e Inovacao Estrada do Paco do Lumiar, 1649-038 Lisboa (Portugal)

2009-12-15

This paper presents the design methodology of a new wind turbine airfoil that achieves high performance in urban environment by increasing the maximum lift. For this purpose, an inverse method was applied to obtain a new wind turbine blade section with constant pressure-load along the chord, at the design inlet angle. In comparison with conventional blade section designs, the new airfoil has increased maximum lift, reduced leading edge suction peak and controlled soft-stall behaviour, due to a reduction of the adverse pressure gradient on the suction side. Wind tunnel experimental results confirmed the computational results. (author)

20. A comparison of two methods for earthquake source inversion using strong motion seismograms

G. C. Beroza

1994-06-01

Full Text Available In this paper we compare two time-domain inversion methods that have been widely applied to the problem of modeling earthquake rupture using strong-motion seismograms. In the multi-window method, each point on the fault is allowed to rupture multiple times. This allows flexibility in the rupture time and hence the rupture velocity. Variations in the slip-velocity function are accommodated by variations in the slip amplitude in each time-window. The single-window method assumes that each point on the fault ruptures only once, when the rupture front passes. Variations in slip amplitude are allowed and variations in rupture velocity are accommodated by allowing the rupture time to vary. Because the multi-window method allows greater flexibility, it has the potential to describe a wider range of faulting behavior; however, with this increased flexibility comes an increase in the degrees of freedom and the solutions are comparatively less stable. We demonstrate this effect using synthetic data for a test model of the Mw 7.3 1992 Landers, California earthquake, and then apply both inversion methods to the actual recordings. The two approaches yield similar fits to the strong-motion data with different seismic moments indicating that the moment is not well constrained by strong-motion data alone. The slip amplitude distribution is similar using either approach, but important differences exist in the rupture propagation models. The single-window method does a better job of recovering the true seismic moment and the average rupture velocity. The multi-window method is preferable when rise time is strongly variable, but tends to overestimate the seismic moment. Both methods work well when the rise time is constant or short compared to the periods modeled. Neither approach can recover the temporal details of rupture propagation unless the distribution of slip amplitude is constrained by independent data.

1. Forward and Inverse Modeling of Self-potential. A Tomography of Groundwater Flow and Comparison Between Deterministic and Stochastic Inversion Methods

Quintero-Chavarria, E.; Ochoa Gutierrez, L. H.

2016-12-01

Applications of the Self-potential Method in the fields of Hydrogeology and Environmental Sciences have had significant developments during the last two decades with a strong use on groundwater flows identification. Although only few authors deal with the forward problem's solution -especially in geophysics literature- different inversion procedures are currently being developed but in most cases they are compared with unconventional groundwater velocity fields and restricted to structured meshes. This research solves the forward problem based on the finite element method using the St. Venant's Principle to transform a point dipole, which is the field generated by a single vector, into a distribution of electrical monopoles. Then, two simple aquifer models were generated with specific boundary conditions and head potentials, velocity fields and electric potentials in the medium were computed. With the model's surface electric potential, the inverse problem is solved to retrieve the source of electric potential (vector field associated to groundwater flow) using deterministic and stochastic approaches. The first approach was carried out by implementing a Tikhonov regularization with a stabilized operator adapted to the finite element mesh while for the second a hierarchical Bayesian model based on Markov chain Monte Carlo (McMC) and Markov Random Fields (MRF) was constructed. For all implemented methods, the result between the direct and inverse models was contrasted in two ways: 1) shape and distribution of the vector field, and 2) magnitude's histogram. Finally, it was concluded that inversion procedures are improved when the velocity field's behavior is considered, thus, the deterministic method is more suitable for unconfined aquifers than confined ones. McMC has restricted applications and requires a lot of information (particularly in potentials fields) while MRF has a remarkable response especially when dealing with confined aquifers.

2. A penalty method for PDE-constrained optimization in inverse problems

Leeuwen, T van; Herrmann, F J

2016-01-01

Many inverse and parameter estimation problems can be written as PDE-constrained optimization problems. The goal is to infer the parameters, typically coefficients of the PDE, from partial measurements of the solutions of the PDE for several right-hand sides. Such PDE-constrained problems can be solved by finding a stationary point of the Lagrangian, which entails simultaneously updating the parameters and the (adjoint) state variables. For large-scale problems, such an all-at-once approach is not feasible as it requires storing all the state variables. In this case one usually resorts to a reduced approach where the constraints are explicitly eliminated (at each iteration) by solving the PDEs. These two approaches, and variations thereof, are the main workhorses for solving PDE-constrained optimization problems arising from inverse problems. In this paper, we present an alternative method that aims to combine the advantages of both approaches. Our method is based on a quadratic penalty formulation of the constrained optimization problem. By eliminating the state variable, we develop an efficient algorithm that has roughly the same computational complexity as the conventional reduced approach while exploiting a larger search space. Numerical results show that this method indeed reduces some of the nonlinearity of the problem and is less sensitive to the initial iterate. (paper)

3. Imaging disturbance zones ahead of a tunnel by elastic full-waveform inversion: Adjoint gradient based inversion vs. parameter space reduction using a level-set method

Andre Lamert

2018-03-01

Full Text Available We present and compare two flexible and effective methodologies to predict disturbance zones ahead of underground tunnels by using elastic full-waveform inversion. One methodology uses a linearized, iterative approach based on misfit gradients computed with the adjoint method while the other uses iterative, gradient-free unscented Kalman filtering in conjunction with a level-set representation. Whereas the former does not involve a priori assumptions on the distribution of elastic properties ahead of the tunnel, the latter introduces a massive reduction in the number of explicit model parameters to be inverted for by focusing on the geometric form of potential disturbances and their average elastic properties. Both imaging methodologies are validated through successful reconstructions of simple disturbances. As an application, we consider an elastic multiple disturbance scenario. By using identical synthetic time-domain seismograms as test data, we obtain satisfactory, albeit different, reconstruction results from the two inversion methodologies. The computational costs of both approaches are of the same order of magnitude, with the gradient-based approach showing a slight advantage. The model parameter space reduction approach compensates for this by additionally providing a posteriori estimates of model parameter uncertainty. Keywords: Tunnel seismics, Full waveform inversion, Seismic waves, Level-set method, Adjoint method, Kalman filter

4. Distribution functions of magnetic nanoparticles determined by a numerical inversion method

Bender, P; Balceris, C; Ludwig, F; Posth, O; Bogart, L K; Szczerba, W; Castro, A; Nilsson, L; Costo, R; Gavilán, H; González-Alonso, D; Pedro, I de; Barquín, L Fernández; Johansson, C

2017-01-01

In the present study, we applied a regularized inversion method to extract the particle size, magnetic moment and relaxation-time distribution of magnetic nanoparticles from small-angle x-ray scattering (SAXS), DC magnetization (DCM) and AC susceptibility (ACS) measurements. For the measurements the particles were colloidally dispersed in water. At first approximation the particles could be assumed to be spherically shaped and homogeneously magnetized single-domain particles. As model functions for the inversion, we used the particle form factor of a sphere (SAXS), the Langevin function (DCM) and the Debye model (ACS). The extracted distributions exhibited features/peaks that could be distinctly attributed to the individually dispersed and non-interacting nanoparticles. Further analysis of these peaks enabled, in combination with a prior characterization of the particle ensemble by electron microscopy and dynamic light scattering, a detailed structural and magnetic characterization of the particles. Additionally, all three extracted distributions featured peaks, which indicated deviations of the scattering (SAXS), magnetization (DCM) or relaxation (ACS) behavior from the one expected for individually dispersed, homogeneously magnetized nanoparticles. These deviations could be mainly attributed to partial agglomeration (SAXS, DCM, ACS), uncorrelated surface spins (DCM) and/or intra-well relaxation processes (ACS). The main advantage of the numerical inversion method is that no ad hoc assumptions regarding the line shape of the extracted distribution functions are required, which enabled the detection of these contributions. We highlighted this by comparing the results with the results obtained by standard model fits, where the functional form of the distributions was a priori assumed to be log-normal shaped. (paper)

5. Inverse design-momentum, a method for the preliminary design of horizontal axis wind turbines

Battisti, L; Soraperra, G; Fedrizzi, R; Zanne, L

2007-01-01

6. Objective mapping of temperature field by stochastic inverse method using acoustic tomography experimental data of eastern Arabian Sea

Murty, T.V.R.; Rao, M.M.M.; Sadhuram, Y.

. The data are revisited for objective mapping of the temperature fields using Stochastic Inverse Method. Hourly reciprocal transmissions were carried with time lag of 30 minutes between each direction. From the multipath arrival patterns, significant peaks...

7. Obtaining source current density related to irregularly structured electromagnetic target field inside human body using hybrid inverse/FDTD method.

Han, Jijun; Yang, Deqiang; Sun, Houjun; Xin, Sherman Xuegang

2017-01-01

Inverse method is inherently suitable for calculating the distribution of source current density related with an irregularly structured electromagnetic target field. However, the present form of inverse method cannot calculate complex field-tissue interactions. A novel hybrid inverse/finite-difference time domain (FDTD) method that can calculate the complex field-tissue interactions for the inverse design of source current density related with an irregularly structured electromagnetic target field is proposed. A Huygens' equivalent surface is established as a bridge to combine the inverse and FDTD method. Distribution of the radiofrequency (RF) magnetic field on the Huygens' equivalent surface is obtained using the FDTD method by considering the complex field-tissue interactions within the human body model. The obtained magnetic field distributed on the Huygens' equivalent surface is regarded as the next target. The current density on the designated source surface is derived using the inverse method. The homogeneity of target magnetic field and specific energy absorption rate are calculated to verify the proposed method.

8. SCIENTIFIC AND METHODICAL ASPECTS OF FORMATION OF SUBJECT CONTENT OF TRAINING COURSESFOR INVERSE PROBLEMS FOR DIFFERENTIAL EQUATIONS

В С Корнилов

2016-12-01

Full Text Available The article presents scientific and methodical aspects of forming the content of education inverse problems for differential equations for students of higher educational institutions of physical, mathematical and natural science training areas. The goals are formulated and the principles of training are the content of learning inverse problems for differential equations. Attention is drawn to the particular issues of teaching courses inverse problems. Describes the classification criteria and target modules that play the role of tools to create and analyze the model and curriculum, forming learning content inverse problems for differential equations. The content classification features and target modules. Formulate conclusions that learning the inverse problems for differential equations has scientific, educational and humanitarian potential of students and as a result of this training they gain the fundamental knowledge in the applied and computational mathematics, and also develop scientific worldview, applied, environmental, information thinking.

9. Invisibility problem in acoustics, electromagnetism and heat transfer. Inverse design method

Alekseev, G.; Tokhtina, A.; Soboleva, O.

2017-10-01

Two approaches (direct design and inverse design methods) for solving problems of designing devices providing invisibility of material bodies of detection using different physical fields - electromagnetic, acoustic and static are discussed. The second method is applied for solving problems of designing cloaking devices for the 3D stationary thermal scattering model. Based on this method the design problems under study are reduced to respective control problems. The material parameters (radial and tangential heat conductivities) of the inhomogeneous anisotropic medium filling the thermal cloak and the density of auxiliary heat sources play the role of controls. A unique solvability of direct thermal scattering problem in the Sobolev space is proved and the new estimates of solutions are established. Using these results, the solvability of control problem is proved and the optimality system is derived. Based on analysis of optimality system, the stability estimates of optimal solutions are established and numerical algorithms for solving particular thermal cloaking problem are proposed.

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

Fang Jinqing; Yao Weiguang

1993-01-01

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

11. Subspace-based optimization method for inverse scattering problems with an inhomogeneous background medium

Chen, Xudong

2010-01-01

This paper proposes a version of the subspace-based optimization method to solve the inverse scattering problem with an inhomogeneous background medium where the known inhomogeneities are bounded in a finite domain. Although the background Green's function at each discrete point in the computational domain is not directly available in an inhomogeneous background scenario, the paper uses the finite element method to simultaneously obtain the Green's function at all discrete points. The essence of the subspace-based optimization method is that part of the contrast source is determined from the spectrum analysis without using any optimization, whereas the orthogonally complementary part is determined by solving a lower dimension optimization problem. This feature significantly speeds up the convergence of the algorithm and at the same time makes it robust against noise. Numerical simulations illustrate the efficacy of the proposed algorithm. The algorithm presented in this paper finds wide applications in nondestructive evaluation, such as through-wall imaging

12. An analytical method for the inverse Cauchy problem of Lame equation in a rectangle

Grigor’ev, Yu

2018-04-01

In this paper, we present an analytical computational method for the inverse Cauchy problem of Lame equation in the elasticity theory. A rectangular domain is frequently used in engineering structures and we only consider the analytical solution in a two-dimensional rectangle, wherein a missing boundary condition is recovered from the full measurement of stresses and displacements on an accessible boundary. The essence of the method consists in solving three independent Cauchy problems for the Laplace and Poisson equations. For each of them, the Fourier series is used to formulate a first-kind Fredholm integral equation for the unknown function of data. Then, we use a Lavrentiev regularization method, and the termwise separable property of kernel function allows us to obtain a closed-form regularized solution. As a result, for the displacement components, we obtain solutions in the form of a sum of series with three regularization parameters. The uniform convergence and error estimation of the regularized solutions are proved.

13. Proximal methods for the resolution of inverse problems: application to positron emission tomography

Pustelnik, N.

2010-12-01

The objective of this work is to propose reliable, efficient and fast methods for minimizing convex criteria, that are found in inverse problems for imagery. We focus on restoration/reconstruction problems when data is degraded with both a linear operator and noise, where the latter is not assumed to be necessarily additive.The reliability of the method is ensured through the use of proximal algorithms, the convergence of which is guaranteed when a convex criterion is considered. Efficiency is sought through the choice of criteria adapted to the noise characteristics, the linear operators and the image specificities. Of particular interest are regularization terms based on total variation and/or sparsity of signal frame coefficients. As a consequence of the use of frames, two approaches are investigated, depending on whether the analysis or the synthesis formulation is chosen. Fast processing requirements lead us to consider proximal algorithms with a parallel structure. Theoretical results are illustrated on several large size inverse problems arising in image restoration, stereoscopy, multi-spectral imagery and decomposition into texture and geometry components. We focus on a particular application, namely Positron Emission Tomography (PET), which is particularly difficult because of the presence of a projection operator combined with Poisson noise, leading to highly corrupted data. To optimize the quality of the reconstruction, we make use of the spatio-temporal characteristics of brain tissue activity. (author)

14. An inverse method for crack characterization from ultrasonic B-Scan images

Faur, M.; Roy, O.; Benoist, PH.; Morisseau, PH.

1996-01-01

Concern has been expressed about the capabilities of performing non destructive evaluation (NDE) of flaws located near to the outer surface in nuclear pressurized water reactor (PWR) vessels. The ultrasonic examination of PWR is accomplished from the inside with ultrasonic focused transducers working in the pulse echo mode. By recording the echoes as a function of time, the Ascan representation may be obtained. Many ultrasonic flaw detectors used for NDE are based on the simple Ascan concept involving measuring a time interval called 'time of flight'. By combining the Ascan concept synchronized transducer scanning, one can produce Bscan images that are two dimensional descriptions of the flaw interaction with the ultrasonic field. In the following, the flaw is assumed to be an axially oriented crack (the most serious flaw to be found in a pressurized component). In the case of the outer surface cracks (OSC's), analyzing and interpreting ultrasonic Ascan images become difficult because of the various reflections of the ultrasonic beam on the crack and on the outer surface (the so-called corner effect). Methods for automatic interpretation of ultrasonic experimental data are currently under investigation. In this paper, we present an inverse method for determining the geometrical characteristics of OSC's from ultrasonic Bscan images. The direct model used for the inversion procedure predicts synthetic Bscan images of ultrasonic examination of blocks containing planar defects interrogated by focused probes. (authors)

15. Microseismic imaging using a source-independent full-waveform inversion method

Wang, Hanchen

2016-09-06

Using full waveform inversion (FWI) to locate microseismic and image microseismic events allows for an automatic process (free of picking) that utilizes the full wavefield. However, waveform inversion of microseismic events faces incredible nonlinearity due to the unknown source location (space) and function (time). We develop a source independent FWI of microseismic events to invert for the source image, source function and the velocity model. It is based on convolving reference traces with the observed and modeled data to mitigate the effect of an unknown source ignition time. The adjoint-state method is used to derive the gradient for the source image, source function and velocity updates. The extended image for source wavelet in z axis is extracted to check the accuracy of the inverted source image and velocity model. Also the angle gather is calculated to see if the velocity model is correct. By inverting for all the source image, source wavelet and the velocity model, the proposed method produces good estimates of the source location, ignition time and the background velocity for part of the SEG overthrust model.

16. Microseismic imaging using a source-independent full-waveform inversion method

Wang, Hanchen

2016-01-01

Using full waveform inversion (FWI) to locate microseismic and image microseismic events allows for an automatic process (free of picking) that utilizes the full wavefield. However, waveform inversion of microseismic events faces incredible nonlinearity due to the unknown source location (space) and function (time). We develop a source independent FWI of microseismic events to invert for the source image, source function and the velocity model. It is based on convolving reference traces with the observed and modeled data to mitigate the effect of an unknown source ignition time. The adjoint-state method is used to derive the gradient for the source image, source function and velocity updates. The extended image for source wavelet in z axis is extracted to check the accuracy of the inverted source image and velocity model. Also the angle gather is calculated to see if the velocity model is correct. By inverting for all the source image, source wavelet and the velocity model, the proposed method produces good estimates of the source location, ignition time and the background velocity for part of the SEG overthrust model.

17. Spatial and Temporal Antarctic Ice Sheet Mass Trends, Glacio-Isostatic Adjustment, and Surface Processes from a Joint Inversion of Satellite Altimeter, Gravity, and GPS Data

Martin-Espanol, Alba; Zammit-Mangion, Andrew; Clarke, Peter J.; Flament, Thomas; Helm, Veit; King, Matt A.; Luthcke, Scott B.; Petrie, Elizabeth; Remy, Frederique; Schon, Nana;

2016-01-01

We present spatiotemporal mass balance trends for the Antarctic Ice Sheet from a statistical inversion of satellite altimetry, gravimetry, and elastic-corrected GPS data for the period 2003-2013. Our method simultaneously determines annual trends in ice dynamics, surface mass balance anomalies, and a time-invariant solution for glacio-isostatic adjustment while remaining largely independent of forward models. We establish that over the period 2003-2013, Antarctica has been losing mass at a rateof -84 +/- 22 Gt per yr, with a sustained negative mean trend of dynamic imbalance of -111 +/- 13 Gt per yr. West Antarctica is the largest contributor with -112 +/- 10 Gt per yr, mainly triggered by high thinning rates of glaciers draining into the Amundsen Sea Embayment. The Antarctic Peninsula has experienced a dramatic increase in mass loss in the last decade, with a mean rate of -28 +/- 7 Gt per yr and significantly higher values for the most recent years following the destabilization of the Southern Antarctic Peninsula around 2010. The total mass loss is partly compensated by a significant mass gain of 56 +/- 18 Gt per yr in East Antarctica due to a positive trend of surface mass balance anomalies.

18. M. Sybis

2016-04-01

Full Text Available Purpose. The development of a wide construction market and a desire to design innovative architectural building constructions has resulted in the need to create complex numerical models of objects having increasingly higher computational complexity. The purpose of this work is to show that choosing a proper method for solving the set of equations can improve the calculation time (reduce the complexity by a few levels of magnitude. Methodology. The article presents an analysis of the impact of matrix inversion algorithm on the deflection calculation in the beam, using the finite element method (FEM. Based on the literature analysis, common methods of calculating set of equations were determined. From the found solutions the Gaussian elimination, LU and Cholesky decomposition methods have been implemented to determine the effect of the matrix inversion algorithm used for solving the equations set on the number of computational operations performed. In addition, each of the implemented method has been further optimized thereby reducing the number of necessary arithmetic operations. Findings. These optimizations have been performed on the use of certain properties of the matrix, such as symmetry or significant number of zero elements in the matrix. The results of the analysis are presented for the division of the beam to 5, 50, 100 and 200 nodes, for which the deflection has been calculated. Originality. The main achievement of this work is that it shows the impact of the used methodology on the complexity of solving the problem (or equivalently, time needed to obtain results. Practical value. The difference between the best (the less complex and the worst (the most complex is in the row of few orders of magnitude. This result shows that choosing wrong methodology may enlarge time needed to perform calculation significantly.

19. Inverse methods for estimating primary input signals from time-averaged isotope profiles

Passey, Benjamin H.; Cerling, Thure E.; Schuster, Gerard T.; Robinson, Todd F.; Roeder, Beverly L.; Krueger, Stephen K.

2005-08-01

Mammalian teeth are invaluable archives of ancient seasonality because they record along their growth axes an isotopic record of temporal change in environment, plant diet, and animal behavior. A major problem with the intra-tooth method is that intra-tooth isotope profiles can be extremely time-averaged compared to the actual pattern of isotopic variation experienced by the animal during tooth formation. This time-averaging is a result of the temporal and spatial characteristics of amelogenesis (tooth enamel formation), and also results from laboratory sampling. This paper develops and evaluates an inverse method for reconstructing original input signals from time-averaged intra-tooth isotope profiles. The method requires that the temporal and spatial patterns of amelogenesis are known for the specific tooth and uses a minimum length solution of the linear system Am = d, where d is the measured isotopic profile, A is a matrix describing temporal and spatial averaging during amelogenesis and sampling, and m is the input vector that is sought. Accuracy is dependent on several factors, including the total measurement error and the isotopic structure of the measured profile. The method is shown to accurately reconstruct known input signals for synthetic tooth enamel profiles and the known input signal for a rabbit that underwent controlled dietary changes. Application to carbon isotope profiles of modern hippopotamus canines reveals detailed dietary histories that are not apparent from the measured data alone. Inverse methods show promise as an effective means of dealing with the time-averaging problem in studies of intra-tooth isotopic variation.

20. The boundary element method for the solution of the multidimensional inverse heat conduction problem

Lagier, Guy-Laurent

1999-01-01

This work focuses on the solution of the inverse heat conduction problem (IHCP), which consists in the determination of boundary conditions from a given set of internal temperature measurements. This problem is difficult to solve due to its ill-posedness and high sensitivity to measurement error. As a consequence, numerical regularization procedures are required to solve this problem. However, most of these methods depend on the dimension and the nature, stationary or transient, of the problem. Furthermore, these methods introduce parameters, called hyper-parameters, which have to be chosen optimally, but can not be determined a priori. So, a new general method is proposed for solving the IHCP. This method is based on a Boundary Element Method formulation, and the use of the Singular Values Decomposition as a regularization procedure. Thanks to this method, it's possible to identify and eliminate the directions of the solution where the measurement error plays the major role. This algorithm is first validated on two-dimensional stationary and one-dimensional transient problems. Some criteria are presented in order to choose the hyper-parameters. Then, the methodology is applied to two-dimensional and three-dimensional, theoretical or experimental, problems. The results are compared with those obtained by a standard method and show the accuracy of the method, its generality, and the validity of the proposed criteria. (author) [fr

1. Inverse method for stress monitoring in pressure components of steam generators

Duda, P.

2003-01-01

The purpose of this work is to formulate a space marching method, which can be used to solve inverse multidimensional heat conduction problems. The method is designed to reconstruct the transient temperature distribution in a whole construction element based on measured temperatures taken at selected points inside or on the outer surface of the construction element. Next, the Finite Element Method is used to calculate thermal stresses and stresses caused by other loads such as, for instance, internal pressure. The developed method for solving temperature and total stress distribution will be tested using the measured temperatures generated from a direct solution. Transient temperature and total stress distribution obtained from method presented below will be compared with the values obtained from the direct solution. Finally, the presented method will be applied in order to monitor temperature and stress distribution in an outlet header using the real measured temperature values at seven points on the header's outer surface during the power boiler's shut down operation. The presented method allows to optimize the power block's start-up and shut-down operations, contributes to the reduction of heat loss during these operations and to the extension of power block's life. The fatigue and creep usage factor can be computed in an on-line mode. The presented method herein can be applied to monitoring systems that work in conventional as well as in nuclear power plants. (author)

2. Theoretical comparison of performance using transfer functions for reactivity meters based on inverse kinetic method and simple feedback method

Shimazu, Yoichiro; Tashiro, Shoichi; Tojo, Masayuki

2017-01-01

The performance of two digital reactivity meters, one based on the conventional inverse kinetic method and the other one based on simple feedback theory, are compared analytically using their respective transfer functions. The latter one is proposed by one of the authors. It has been shown that the performance of the two reactivity meters become almost identical when proper system parameters are selected for each reactivity meter. A new correlation between the system parameters of the two reactivity meters is found. With this correlation, filter designers can easily determine the system parameters for the respective reactivity meters to obtain identical performance. (author)

3. Talbot's method for the numerical inversion of Laplace transforms: an implementation for personal computers

Garratt, T.J.

1989-05-01

Safety assessments of radioactive waste disposal require efficient computer models for the important processes. The present paper is based on an efficient computational technique which can be used to solve a wide variety of safety assessment models. It involves the numerical inversion of analytical solutions to the Laplace-transformed differential equations using a method proposed by Talbot. This method has been implemented on a personal computer in a user-friendly manner. The steps required to implement a particular transform and run the program are outlined. Four examples are described which illustrate the flexibility, accuracy and efficiency of the program. The improvements in computational efficiency described in this paper have application to the probabilistic safety assessment codes ESCORT and MASCOT which are currently under development. Also, it is hoped that the present work will form the basis of software for personal computers which could be used to demonstrate safety assessment procedures to a wide audience. (author)

4. Thermophysical properties estimation of paraffin/graphite composite phase change material using an inverse method

Lachheb, Mohamed; Karkri, Mustapha; Albouchi, Fethi; Mzali, Foued; Nasrallah, Sassi Ben

2014-01-01

Highlights: • Preparation of paraffin/graphite composites by uni-axial compression technique. • Measurement of thermophysical properties of paraffin/graphite using the periodic method. • Measurement of the experimental densities of paraffin/graphite composites. • Prediction of the effective thermal conductivity using analytical models. - Abstract: In this paper, two types of graphite were combined with paraffin in an attempt to improve thermal conductivity of paraffin phase change material (PCM): Synthetic graphite (Timrex SFG75) and graphite waste obtained from damaged Tubular graphite Heat Exchangers. These paraffin/graphite phase change material (PCM) composites are prepared by the cold uniaxial compression technique and the thermophysical properties were estimated using a periodic temperature method and an inverse technique. Results showed that the thermal conductivity and thermal diffusivity are greatly influenced by the graphite addition

5. Geometric shapes inversion method of space targets by ISAR image segmentation

Huo, Chao-ying; Xing, Xiao-yu; Yin, Hong-cheng; Li, Chen-guang; Zeng, Xiang-yun; Xu, Gao-gui

2017-11-01

The geometric shape of target is an effective characteristic in the process of space targets recognition. This paper proposed a method of shape inversion of space target based on components segmentation from ISAR image. The Radon transformation, Hough transformation, K-means clustering, triangulation will be introduced into ISAR image processing. Firstly, we use Radon transformation and edge detection to extract space target's main body spindle and solar panel spindle from ISAR image. Then the targets' main body, solar panel, rectangular and circular antenna are segmented from ISAR image based on image detection theory. Finally, the sizes of every structural component are computed. The effectiveness of this method is verified using typical targets' simulation data.

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

Haber, E; Horesh, L; Tenorio, L

2010-01-01

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

7. Identification of strain-rate and thermal sensitive material model with an inverse method

Peroni, L; Peroni, M

2010-01-01

This paper describes a numerical inverse method to extract material strength parameters from the experimental data obtained via mechanical tests at different strain-rates and temperatures. It will be shown that this procedure is particularly useful to analyse experimental results when the stress-strain fields in the specimen cannot be correctly described via analytical models. This commonly happens in specimens with no regular shape, in specimens with a regular shape when some instability phenomena occur (for example the necking phenomena in tensile tests that create a strongly heterogeneous stress-strain fields) or in dynamic tests (where the strain-rate field is not constant due to wave propagation phenomena). Furthermore the developed procedure is useful to take into account thermal phenomena generally affecting high strain-rate tests due to the adiabatic overheating related to the conversion of plastic work. The method presented requires strong effort both from experimental and numerical point of view, an...

8. GRAPHIC-ANALYTICAL METHODS FOR CALCULATING THE GRAVITY CENTER OF A MODEL AIRPLANE

DIACONESCU Olivian

2012-01-01

This paper presents a stage of the realization of an airplane capable to work with low capacity motors between 2.5 cmc and 4 cmc, as it presents the gravity center calculation. Firstly for an airplane to fly properly we must calculate the gravity center, the top speed which is necessary for picking the servomotors that equip the airplane.

9. Joining direct and indirect inverse calibration methods to characterize karst, coastal aquifers

De Filippis, Giovanna; Foglia, Laura; Giudici, Mauro; Mehl, Steffen; Margiotta, Stefano; Negri, Sergio

2016-04-01

Parameter estimation is extremely relevant for accurate simulation of groundwater flow. Parameter values for models of large-scale catchments are usually derived from a limited set of field observations, which can rarely be obtained in a straightforward way from field tests or laboratory measurements on samples, due to a number of factors, including measurement errors and inadequate sampling density. Indeed, a wide gap exists between the local scale, at which most of the observations are taken, and the regional or basin scale, at which the planning and management decisions are usually made. For this reason, the use of geologic information and field data is generally made by zoning the parameter fields. However, pure zoning does not perform well in the case of fairly complex aquifers and this is particularly true for karst aquifers. In fact, the support of the hydraulic conductivity measured in the field is normally much smaller than the cell size of the numerical model, so it should be upscaled to a scale consistent with that of the numerical model discretization. Automatic inverse calibration is a valuable procedure to identify model parameter values by conditioning on observed, available data, limiting the subjective evaluations introduced with the trial-and-error technique. Many approaches have been proposed to solve the inverse problem. Generally speaking, inverse methods fall into two groups: direct and indirect methods. Direct methods allow determination of hydraulic conductivities from the groundwater flow equations which relate the conductivity and head fields. Indirect methods, instead, can handle any type of parameters, independently from the mathematical equations that govern the process, and condition parameter values and model construction on measurements of model output quantities, compared with the available observation data, through the minimization of an objective function. Both approaches have pros and cons, depending also on model complexity. For

10. Compositional modeling of three-phase flow with gravity using higher-order finite element methods

Moortgat, Joachim

2011-05-11

A wide range of applications in subsurface flow involve water, a nonaqueous phase liquid (NAPL) or oil, and a gas phase, such as air or CO2. The numerical simulation of such processes is computationally challenging and requires accurate compositional modeling of three-phase flow in porous media. In this work, we simulate for the first time three-phase compositional flow using higher-order finite element methods. Gravity poses complications in modeling multiphase processes because it drives countercurrent flow among phases. To resolve this issue, we propose a new method for the upwinding of three-phase mobilities. Numerical examples, related to enhanced oil recovery and carbon sequestration, are presented to illustrate the capabilities of the proposed algorithm. We pay special attention to challenges associated with gravitational instabilities and take into account compressibility and various phase behavior effects, including swelling, viscosity changes, and vaporization. We find that the proposed higher-order method can capture sharp solution discontinuities, yielding accurate predictions of phase boundaries arising in computational three-phase flow. This work sets the stage for a broad extension of the higher-order methods for numerical simulation of three-phase flow for complex geometries and processes.

11. 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.

12. An inverse method to estimate the flow through a levee breach

D'Oria, Marco; Mignosa, Paolo; Tanda, Maria Giovanna

2015-08-01

We propose a procedure to estimate the flow through a levee breach based on water levels recorded in river stations downstream and/or upstream of the failure site. The inverse problem is solved using a Bayesian approach and requires the execution of several forward unsteady flow simulations. For this purpose, we have used the well-known 1-D HEC-RAS model, but any unsteady flow model could be adopted in the same way. The procedure has been tested using four synthetic examples. Levee breaches with different characteristics (free flow, flow with tailwater effects, etc.) have been simulated to collect the synthetic level data used at a later stage in the inverse procedure. The method was able to accurately reproduce the flow through the breach in all cases. The practicability of the procedure was then confirmed applying it to the inundation of the Polesine Region (Northern Italy) which occurred in 1951 and was caused by three contiguous and almost simultaneous breaches on the left embankment of the Po River.

13. Characterization of a Method for Inverse Heat Conduction Using Real and Simulated Thermocouple Data

Pizzo, Michelle E.; Glass, David E.

2017-01-01

It is often impractical to instrument the external surface of high-speed vehicles due to the aerothermodynamic heating. Temperatures can instead be measured internal to the structure using embedded thermocouples, and direct and inverse methods can then be used to estimate temperature and heat flux on the external surface. Two thermocouples embedded at different depths are required to solve direct and inverse problems, and filtering schemes are used to reduce noise in the measured data. Accuracy in the estimated surface temperature and heat flux is dependent on several factors. Factors include the thermocouple location through the thickness of a material, the sensitivity of the surface solution to the error in the specified location of the embedded thermocouples, and the sensitivity to the error in thermocouple data. The effect of these factors on solution accuracy is studied using the methodology discussed in the work of Pizzo, et. al.1 A numerical study is performed to determine if there is an optimal depth at which to embed one thermocouple through the thickness of a material assuming that a second thermocouple is installed on the back face. Solution accuracy will be discussed for a range of embedded thermocouple depths. Moreover, the sensitivity of the surface solution to (a) the error in the specified location of the embedded thermocouple and to (b) the error in the thermocouple data are quantified using numerical simulation, and the results are discussed.

14. Global Scale Exploration Seismics: Mapping Mantle Discontinuities with Inverse Scattering Methods and Millions of Seismograms

van der Hilst, R. D.; de Hoop, M. V.; Shim, S. H.; Shang, X.; Wang, P.; Cao, Q.

2012-04-01

Over the past three decades, tremendous progress has been made with the mapping of mantle heterogeneity and with the understanding of these structures in terms of, for instance, the evolution of Earth's crust, continental lithosphere, and thermo-chemical mantle convection. Converted wave imaging (e.g., receiver functions) and reflection seismology (e.g. SS stacks) have helped constrain interfaces in crust and mantle; surface wave dispersion (from earthquake or ambient noise signals) characterizes wavespeed variations in continental and oceanic lithosphere, and body wave and multi-mode surface wave data have been used to map trajectories of mantle convection and delineate mantle regions of anomalous elastic properties. Collectively, these studies have revealed substantial ocean-continent differences and suggest that convective flow is strongly influenced by but permitted to cross the upper mantle transition zone. Many questions have remained unanswered, however, and further advances in understanding require more accurate depictions of Earth's heterogeneity at a wider range of length scales. To meet this challenge we need new observations—more, better, and different types of data—and methods that help us extract and interpret more information from the rapidly growing volumes of broadband data. The huge data volumes and the desire to extract more signal from them means that we have to go beyond 'business as usual' (that is, simplified theory, manual inspection of seismograms, …). Indeed, it inspires the development of automated full wave methods, both for tomographic delineation of smooth wavespeed variations and the imaging (for instance through inverse scattering) of medium contrasts. Adjoint tomography and reverse time migration, which are closely related wave equation methods, have begun to revolutionize seismic inversion of global and regional waveform data. In this presentation we will illustrate this development - and its promise - drawing from our work

15. An efficient inverse radiotherapy planning method for VMAT using quadratic programming optimization.

Hoegele, W; Loeschel, R; Merkle, N; Zygmanski, P

2012-01-01

The purpose of this study is to investigate the feasibility of an inverse planning optimization approach for the Volumetric Modulated Arc Therapy (VMAT) based on quadratic programming and the projection method. The performance of this method is evaluated against a reference commercial planning system (eclipse(TM) for rapidarc(TM)) for clinically relevant cases. The inverse problem is posed in terms of a linear combination of basis functions representing arclet dose contributions and their respective linear coefficients as degrees of freedom. MLC motion is decomposed into basic motion patterns in an intuitive manner leading to a system of equations with a relatively small number of equations and unknowns. These equations are solved using quadratic programming under certain limiting physical conditions for the solution, such as the avoidance of negative dose during optimization and Monitor Unit reduction. The modeling by the projection method assures a unique treatment plan with beneficial properties, such as the explicit relation between organ weightings and the final dose distribution. Clinical cases studied include prostate and spine treatments. The optimized plans are evaluated by comparing isodose lines, DVH profiles for target and normal organs, and Monitor Units to those obtained by the clinical treatment planning system eclipse(TM). The resulting dose distributions for a prostate (with rectum and bladder as organs at risk), and for a spine case (with kidneys, liver, lung and heart as organs at risk) are presented. Overall, the results indicate that similar plan qualities for quadratic programming (QP) and rapidarc(TM) could be achieved at significantly more efficient computational and planning effort using QP. Additionally, results for the quasimodo phantom [Bohsung et al., "IMRT treatment planning: A comparative inter-system and inter-centre planning exercise of the estro quasimodo group," Radiother. Oncol. 76(3), 354-361 (2005)] are presented as an example

16. High-gravity combustion synthesis and in situ melt infiltration: A new method for preparing cemented carbides

Liu, Guanghua; Li, Jiangtao; Yang, Zengchao; Guo, Shibin; Chen, Yixiang

2013-01-01

A new method of high-gravity combustion synthesis and in situ melt infiltration is reported for preparing cemented carbides, where hot nickel melt is in situ synthesized from a highly exothermic combustion reaction and then infiltrated into tungsten carbide powder compacts. The as-prepared sample showed a homogeneous microstructure, and its relative density, hardness and flexural strength were 94.4%, 84 HRA and 1.49 GPa, respectively. Compared with conventional powder metallurgy approaches, high-gravity combustion synthesis offers a fast and furnace-free way to produce cemented carbides

17. Inverse probability weighting in STI/HIV prevention research: methods for evaluating social and community interventions

Lippman, Sheri A.; Shade, Starley B.; Hubbard, Alan E.

2011-01-01

Background Intervention effects estimated from non-randomized intervention studies are plagued by biases, yet social or structural intervention studies are rarely randomized. There are underutilized statistical methods available to mitigate biases due to self-selection, missing data, and confounding in longitudinal, observational data permitting estimation of causal effects. We demonstrate the use of Inverse Probability Weighting (IPW) to evaluate the effect of participating in a combined clinical and social STI/HIV prevention intervention on reduction of incident chlamydia and gonorrhea infections among sex workers in Brazil. Methods We demonstrate the step-by-step use of IPW, including presentation of the theoretical background, data set up, model selection for weighting, application of weights, estimation of effects using varied modeling procedures, and discussion of assumptions for use of IPW. Results 420 sex workers contributed data on 840 incident chlamydia and gonorrhea infections. Participators were compared to non-participators following application of inverse probability weights to correct for differences in covariate patterns between exposed and unexposed participants and between those who remained in the intervention and those who were lost-to-follow-up. Estimators using four model selection procedures provided estimates of intervention effect between odds ratio (OR) .43 (95% CI:.22-.85) and .53 (95% CI:.26-1.1). Conclusions After correcting for selection bias, loss-to-follow-up, and confounding, our analysis suggests a protective effect of participating in the Encontros intervention. Evaluations of behavioral, social, and multi-level interventions to prevent STI can benefit by introduction of weighting methods such as IPW. PMID:20375927

18. Influence of inverse dynamics methods on the calculation of inter-segmental moments in vertical jumping and weightlifting

Cleather Daniel J

2010-11-01

Full Text Available Abstract Background A vast number of biomechanical studies have employed inverse dynamics methods to calculate inter-segmental moments during movement. Although all inverse dynamics methods are rooted in classical mechanics and thus theoretically the same, there exist a number of distinct computational methods. Recent research has demonstrated a key influence of the dynamics computation of the inverse dynamics method on the calculated moments, despite the theoretical equivalence of the methods. The purpose of this study was therefore to explore the influence of the choice of inverse dynamics on the calculation of inter-segmental moments. Methods An inverse dynamics analysis was performed to analyse vertical jumping and weightlifting movements using two distinct methods. The first method was the traditional inverse dynamics approach, in this study characterized as the 3 step method, where inter-segmental moments were calculated in the local coordinate system of each segment, thus requiring multiple coordinate system transformations. The second method (the 1 step method was the recently proposed approach based on wrench notation that allows all calculations to be performed in the global coordinate system. In order to best compare the effect of the inverse dynamics computation a number of the key assumptions and methods were harmonized, in particular unit quaternions were used to parameterize rotation in both methods in order to standardize the kinematics. Results Mean peak inter-segmental moments calculated by the two methods were found to agree to 2 decimal places in all cases and were not significantly different (p > 0.05. Equally the normalized dispersions of the two methods were small. Conclusions In contrast to previously documented research the difference between the two methods was found to be negligible. This study demonstrates that the 1 and 3 step method are computationally equivalent and can thus be used interchangeably in

19. Application of the inverse estimation method of current distribution from magnetic fields using genetic algorithm to beam profile measurement

Kishimoto, M.; Sakasai, K.; Ara, K.

1994-01-01

In this paper, the new type of non-invasive beam profile monitor for intense ion accelerator using high-temperature superconductor. We regard the inverse estimation problem of beam profile as the optimum allocation problem of the currents into the cross-section of the beam vacuum pipe and applied genetic algorithm to solve this optimization problem. And we carried out the computer simulation to verify the effectiveness of this inverse estimation method of beam profile. (author)

20. Multilayer densities using a wavelet-based gravity method and their tectonic implications beneath the Tibetan Plateau

Xu, Chuang; Luo, Zhicai; Sun, Rong; Zhou, Hao; Wu, Yihao

2018-06-01

Determining density structure of the Tibetan Plateau is helpful in better understanding of tectonic structure and development. Seismic method, as traditional approach obtaining a large number of achievements of density structure in the Tibetan Plateau except in the centre and west, is primarily inhibited by the poor seismic station coverage. As the implementation of satellite gravity missions, gravity method is more competitive because of global homogeneous gravity coverage. In this paper, a novel wavelet-based gravity method with high computation efficiency and excellent local identification capability is developed to determine multilayer densities beneath the Tibetan Plateau. The inverted six-layer densities from 0 to 150 km depth can reveal rich tectonic structure and development of study area: (1) The densities present a clockwise pattern, nearly east-west high-low alternating pattern in the west and nearly south-north high-low alternating pattern in the east, which is almost perpendicular to surface movement direction relative to the stable Eurasia from the Global Positioning System velocity field; (2) Apparent fold structure approximately from 10 to 110 km depth can be inferred from the multilayer densities, the deformational direction of which is nearly south-north in the west and east-west in the east; (3) Possible channel flows approximately from 30 to 110 km depth can also be observed clearly during the multilayer densities. Moreover, the inverted multilayer densities are in agreement with previous studies, which verify the correctness and effectiveness of our method.

1. Multilayer Densities Using a Wavelet-based Gravity Method and Their Tectonic Implications beneath the Tibetan Plateau

Xu, Chuang; Luo, Zhicai; Sun, Rong; Zhou, Hao; Wu, Yihao

2018-03-01

Determining density structure of the Tibetan Plateau is helpful in better understanding tectonic structure and development. Seismic method, as traditional approach obtaining a large number of achievements of density structure in the Tibetan Plateau except in the center and west, is primarily inhibited by the poor seismic station coverage. As the implementation of satellite gravity missions, gravity method is more competitive because of global homogeneous gravity coverage. In this paper, a novel wavelet-based gravity method with high computation efficiency and excellent local identification capability is developed to determine multilayer densities beneath the Tibetan Plateau. The inverted 6-layer densities from 0 km to 150 km depth can reveal rich tectonic structure and development of study area: (1) The densities present a clockwise pattern, nearly east-west high-low alternating pattern in the west and nearly south-north high-low alternating pattern in the east, which is almost perpendicular to surface movement direction relative to the stable Eurasia from the Global Positioning System velocity field; (2) Apparent fold structure approximately from 10 km to 110 km depth can be inferred from the multilayer densities, the deformational direction of which is nearly south-north in the west and east-west in the east; (3) Possible channel flows approximately from 30 km to 110 km depth can be also observed clearly during the multilayer densities. Moreover, the inverted multilayer densities are in agreement with previous studies, which verify the correctness and effectiveness of our method.

2. Inverse problems of geophysics

Yanovskaya, T.B.

2003-07-01

This report gives an overview and the mathematical formulation of geophysical inverse problems. General principles of statistical estimation are explained. The maximum likelihood and least square fit methods, the Backus-Gilbert method and general approaches for solving inverse problems are discussed. General formulations of linearized inverse problems, singular value decomposition and properties of pseudo-inverse solutions are given

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

Fymat, A. L.

1976-01-01

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

4. Simulation by the method of inverse cumulative distribution function applied in optimising of foundry plant production

J. Szymszal

2009-01-01

Full Text Available The study discusses application of computer simulation based on the method of inverse cumulative distribution function. The simulationrefers to an elementary static case, which can also be solved by physical experiment, consisting mainly in observations of foundryproduction in a selected foundry plant. For the simulation and forecasting of foundry production quality in selected cast iron grade, arandom number generator of Excel calculation sheet was chosen. Very wide potentials of this type of simulation when applied to theevaluation of foundry production quality were demonstrated, using a number generator of even distribution for generation of a variable ofan arbitrary distribution, especially of a preset empirical distribution, without any need of adjusting to this variable the smooth theoreticaldistributions.

5. An alternative 3D inversion method for magnetic anomalies with depth resolution

M. Chiappini

2006-06-01

Full Text Available This paper presents a new method to invert magnetic anomaly data in a variety of non-complex contexts when a priori information about the sources is not available. The region containing magnetic sources is discretized into a set of homogeneously magnetized rectangular prisms, polarized along a common direction. The magnetization distribution is calculated by solving an underdetermined linear system, and is accomplished through the simultaneous minimization of the norm of the solution and the misfit between the observed and the calculated field. Our algorithm makes use of a dipolar approximation to compute the magnetic field of the rectangular blocks. We show how this approximation, in conjunction with other correction factors, presents numerous advantages in terms of computing speed and depth resolution, and does not affect significantly the success of the inversion. The algorithm is tested on both synthetic and real magnetic datasets.

6. Nuclear lifetime measurements with the DSA coincidence method in inverse reactions

Hermans, J.A.J.

1977-01-01

This thesis describes lifetime measurements with the DSA coincidence method in inverse reactions. Bombardment of 2 H and 3 H targets with heavy ions of energies up to 50 MeV produces nuclei recoiling at initial velocities of v(0) approximately equal to 0.05 c. Heavy-ion beams of 11 B, 12 C, 14 N, 16 O, 18 O, 19 F, 27 A1, 28 Si, 30 Si, 31 P, 32 S, 35 Cl and 37 Cl are at present available from the Utrecht 6 MV EN tandem accelerator. The recoil nuclei are slowed down in Mg, Al, Cu, Ag or Au and the γ-ray Doppler pattern is observed with a large Ge(Li) detector in coincidence with protons

7. Variational methods for direct/inverse problems of atmospheric dynamics and chemistry

Penenko, Vladimir; Penenko, Alexey; Tsvetova, Elena

2013-04-01

We present a variational approach for solving direct and inverse problems of atmospheric hydrodynamics and chemistry. It is important that the accurate matching of numerical schemes has to be provided in the chain of objects: direct/adjoint problems - sensitivity relations - inverse problems, including assimilation of all available measurement data. To solve the problems we have developed a new enhanced set of cost-effective algorithms. The matched description of the multi-scale processes is provided by a specific choice of the variational principle functionals for the whole set of integrated models. Then all functionals of variational principle are approximated in space and time by splitting and decomposition methods. Such approach allows us to separately consider, for example, the space-time problems of atmospheric chemistry in the frames of decomposition schemes for the integral identity sum analogs of the variational principle at each time step and in each of 3D finite-volumes. To enhance the realization efficiency, the set of chemical reactions is divided on the subsets related to the operators of production and destruction. Then the idea of the Euler's integrating factors is applied in the frames of the local adjoint problem technique [1]-[3]. The analytical solutions of such adjoint problems play the role of integrating factors for differential equations describing atmospheric chemistry. With their help, the system of differential equations is transformed to the equivalent system of integral equations. As a result we avoid the construction and inversion of preconditioning operators containing the Jacobi matrixes which arise in traditional implicit schemes for ODE solution. This is the main advantage of our schemes. At the same time step but on the different stages of the "global" splitting scheme, the system of atmospheric dynamic equations is solved. For convection - diffusion equations for all state functions in the integrated models we have developed the

8. Thermo-mechanical model identification of a strengthened copper with an inverse method

Peroni, M; Dallocchio, A

2009-01-01

This paper describes a numerical inverse method to extract material strength parameters from the experimental data obtained via mechanical tests at different strain-rates. It will be shown that this procedure is particularly useful to analyse experimental results when the stress-strain fields in the specimen cannot be correctly described via analytical models. This commonly happens in specimens with no regular shape, in specimens with a regular shape when some instability phenomena occur (for example the necking phenomena in tensile tests that create a strongly heterogeneous stress-strain fields) or in dynamic tests (where the strain-rate field is not constant due to wave propagation phenomena). Furthermore the developed procedure is useful to take into account thermal phenomena generally affecting high strain-rate tests due to the adiabatic overheating related to the conversion of plastic work.

9. Shrinkage-thresholding enhanced born iterative method for solving 2D inverse electromagnetic scattering problem

Desmal, Abdulla

2014-07-01

A numerical framework that incorporates recently developed iterative shrinkage thresholding (IST) algorithms within the Born iterative method (BIM) is proposed for solving the two-dimensional inverse electromagnetic scattering problem. IST algorithms minimize a cost function weighted between measurement-data misfit and a zeroth/first-norm penalty term and therefore promote "sharpness" in the solution. Consequently, when applied to domains with sharp variations, discontinuities, or sparse content, the proposed framework is more efficient and accurate than the "classical" BIM that minimizes a cost function with a second-norm penalty term. Indeed, numerical results demonstrate the superiority of the IST-BIM over the classical BIM when they are applied to sparse domains: Permittivity and conductivity profiles recovered using the IST-BIM are sharper and more accurate and converge faster. © 1963-2012 IEEE.

10. Using Chebyshev polynomials and approximate inverse triangular factorizations for preconditioning the conjugate gradient method

Kaporin, I. E.

2012-02-01

In order to precondition a sparse symmetric positive definite matrix, its approximate inverse is examined, which is represented as the product of two sparse mutually adjoint triangular matrices. In this way, the solution of the corresponding system of linear algebraic equations (SLAE) by applying the preconditioned conjugate gradient method (CGM) is reduced to performing only elementary vector operations and calculating sparse matrix-vector products. A method for constructing the above preconditioner is described and analyzed. The triangular factor has a fixed sparsity pattern and is optimal in the sense that the preconditioned matrix has a minimum K-condition number. The use of polynomial preconditioning based on Chebyshev polynomials makes it possible to considerably reduce the amount of scalar product operations (at the cost of an insignificant increase in the total number of arithmetic operations). The possibility of an efficient massively parallel implementation of the resulting method for solving SLAEs is discussed. For a sequential version of this method, the results obtained by solving 56 test problems from the Florida sparse matrix collection (which are large-scale and ill-conditioned) are presented. These results show that the method is highly reliable and has low computational costs.

11. Comparison of inversion methods in seismic tomography: application to tectonic structures in Northwestern Italy

C. Eva

1994-06-01

Full Text Available In this paper we apply various inversion methods to a set of teleseismic data collected by a network operating along the Ligurian Belt in the transition region between Alps and Apennines. In particular, we consider the regularization method, the truncated singular value decomposition, the Landweber method (with the Related Simultaneous Iterative Reconstruction Technique and the conjugate gradient method. All the methods provide rather similar velocity models which are well approximated by that provided by back-projection (used with an appropriate normalization constant. A drawback of these models seems to be the large discrepancy (of the order of 40% between the observed time residuals and those computed from the model itself. However, for each station of the network, the azimuth dependence of the computed time residuals reproduces rather well the observed one so that it is believable that the most significant information contained in the data has been expIoited. The computed velocity models indicate strong heterogeneities in the first 200 km below the Apennines.

12. An inverse method for identification of a distributed random excitation acting on a vibrating structure flow-induced vibration application

Perotin, L.; Granger, S.

1997-01-01

In order to improve the prediction of wear problems due to flow-induced vibration in PWR components, an inverse method for identifying a distributed random excitation acting on a dynamical system has been developed at EDF. This method, whose applications go far beyond the flow-induced vibration field, has been implemented into the MEIDEE software. This method is presented. (author)

13. 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.

14. A survey of direct inversion methods having possible application to tunnel detection

Mager, R.D.

1985-01-01

Within recent years there has been considerable interest in the development of geophysical methods for the location of hidden underground tunnels and cavities. Consideration of this problem has been motivated by military applications, such as the detection of shallow man-made tunnels and arm caches, as well as civilian applications such as detection of limestone cavities in karst terrain and the mapping of abandoned mine workings. There are also applications for in-situ coal gasification and for the monitoring of nuclear waste disposal sites. The most reliable method presently used to map these underground anomalies has been direct detection by closely spaced drilling. However, the high cost of drilling renders this method impractical except for detailed and localized mapping, and certainly unfeasible for any type of broad-scale reconnaissance activity. Largely motivated by petroleum and mineral exploration needs, however, the seismic industry has seen a virtual revolution in acquisition and processing techniques within the past ten years. Paralleling these developments have been corresponding developments in acoustical imaging and non-destructive testing. Researchers in the field of inverse scattering have produced a number of new methods for target imaging from backscattered reflection data

15. An Augmented Lagrangian Method for a Class of Inverse Quadratic Programming Problems

Zhang Jianzhong; Zhang Liwei

2010-01-01

We consider an inverse quadratic programming (QP) problem in which the parameters in the objective function of a given QP problem are adjusted as little as possible so that a known feasible solution becomes the optimal one. We formulate this problem as a minimization problem with a positive semidefinite cone constraint and its dual is a linearly constrained semismoothly differentiable (SC 1 ) convex programming problem with fewer variables than the original one. We demonstrate the global convergence of the augmented Lagrangian method for the dual problem and prove that the convergence rate of primal iterates, generated by the augmented Lagrange method, is proportional to 1/r, and the rate of multiplier iterates is proportional to 1/√r, where r is the penalty parameter in the augmented Lagrangian. As the objective function of the dual problem is a SC 1 function involving the projection operator onto the cone of symmetrically semi-definite matrices, the analysis requires extensive tools such as the singular value decomposition of matrices, an implicit function theorem for semismooth functions, and properties of the projection operator in the symmetric-matrix space. Furthermore, the semismooth Newton method with Armijo line search is applied to solve the subproblems in the augmented Lagrange approach, which is proven to have global convergence and local quadratic rate. Finally numerical results, implemented by the augmented Lagrangian method, are reported.

16. Inversion of potential field data using the finite element method on parallel computers

Gross, L.; Altinay, C.; Shaw, S.

2015-11-01

In this paper we present a formulation of the joint inversion of potential field anomaly data as an optimization problem with partial differential equation (PDE) constraints. The problem is solved using the iterative Broyden-Fletcher-Goldfarb-Shanno (BFGS) method with the Hessian operator of the regularization and cross-gradient component of the cost function as preconditioner. We will show that each iterative step requires the solution of several PDEs namely for the potential fields, for the adjoint defects and for the application of the preconditioner. In extension to the traditional discrete formulation the BFGS method is applied to continuous descriptions of the unknown physical properties in combination with an appropriate integral form of the dot product. The PDEs can easily be solved using standard conforming finite element methods (FEMs) with potentially different resolutions. For two examples we demonstrate that the number of PDE solutions required to reach a given tolerance in the BFGS iteration is controlled by weighting regularization and cross-gradient but is independent of the resolution of PDE discretization and that as a consequence the method is weakly scalable with the number of cells on parallel computers. We also show a comparison with the UBC-GIF GRAV3D code.

17. 3D Gravity Modeling of Complex Salt Features in the Southern Gulf of Mexico

Mauricio Nava-Flores

2016-01-01

Full Text Available We present a three-dimensional (3D gravity modeling and inversion approach and its application to complex geological settings characterized by several allochthonous salt bodies embedded in terrigenous sediments. Synthetic gravity data were computed for 3D forward modeling of salt bodies interpreted from Prestack Depth Migration (PSDM seismic images. Density contrasts for the salt bodies surrounded by sedimentary units are derived from density-compaction curves for the northern Gulf of Mexico’s oil exploration surveys. By integrating results from different shape- and depth-source estimation algorithms, we built an initial model for the gravity anomaly inversion. We then applied a numerically optimized 3D simulated annealing gravity inversion method. The inverted 3D density model successfully retrieves the synthetic salt body ensemble. Results highlight the significance of integrating high-resolution potential field data for salt and subsalt imaging in oil exploration.

18. A novel variable-gravity simulation method: potential for astronaut training.

Sussingham, J C; Cocks, F H

1995-11-01

Zero gravity conditions for astronaut training have traditionally used neutral buoyancy tanks, and with such tanks hypogravity conditions are produced by the use of supplemental weights. This technique does not allow for the influence of water viscosity on any reduced gravity exercise regime. With a water-foam fluid produced by using a microbubble air flow together with surface active agents to prevent bubble agglomeration, it has been found possible to simulate a range of gravity conditions without the need for supplemental weights and additionally with a substantial reduction in the resulting fluid viscosity. This new technique appears to have application in improving the simulation environment for astronaut training under the reduced gravity conditions to be found on the moon or on Mars, and may have terrestrial applications in patient rehabilitation and exercise as well.

19. Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods.

Gramfort, Alexandre; Kowalski, Matthieu; Hämäläinen, Matti

2012-04-07

Magneto- and electroencephalography (M/EEG) measure the electromagnetic fields produced by the neural electrical currents. Given a conductor model for the head, and the distribution of source currents in the brain, Maxwell's equations allow one to compute the ensuing M/EEG signals. Given the actual M/EEG measurements and the solution of this forward problem, one can localize, in space and in time, the brain regions that have produced the recorded data. However, due to the physics of the problem, the limited number of sensors compared to the number of possible source locations, and measurement noise, this inverse problem is ill-posed. Consequently, additional constraints are needed. Classical inverse solvers, often called minimum norm estimates (MNE), promote source estimates with a small ℓ₂ norm. Here, we consider a more general class of priors based on mixed norms. Such norms have the ability to structure the prior in order to incorporate some additional assumptions about the sources. We refer to such solvers as mixed-norm estimates (MxNE). In the context of M/EEG, MxNE can promote spatially focal sources with smooth temporal estimates with a two-level ℓ₁/ℓ₂ mixed-norm, while a three-level mixed-norm can be used to promote spatially non-overlapping sources between different experimental conditions. In order to efficiently solve the optimization problems of MxNE, we introduce fast first-order iterative schemes that for the ℓ₁/ℓ₂ norm give solutions in a few seconds making such a prior as convenient as the simple MNE. Furthermore, thanks to the convexity of the optimization problem, we can provide optimality conditions that guarantee global convergence. The utility of the methods is demonstrated both with simulations and experimental MEG data.

20. EFFECT OF INVERSION ON TREATMENT OF FENCE SUBJECTED TO SAP DISPLACEMENT METHOD

Juarez Benigno Paes

2014-03-01

Full Text Available http://dx.doi.org/10.5902/1980509813338This work aimed to evaluate the effect of inversion of Prosopis juliflora and Leucaena leucocephala fenceposts, in distribution, penetration and retention of copper chrome borate (CCB solution applied by sapdisplacement method. The Prosopis juliflora was collected in Brazilian Agricultural Research Company(EMBRAPA and the Leucaena leucocephala at the Federal University of Campina Grande in Patos,Paraíba state, Brazil. Trees with DAP from 5.0 to 10.0 cm were employed. Disks of 2.0 cm of thicknesswere retired on the top and on the base of pieces. The external disks were then discarded and the internones were employed to determine the wood characteristics, being the round pieces with 2.0 m. A solutionof 2% of active ingredients of CCB was used to treated woods. A total of 10 pieces of each species weretreated, and five of them remained in the solution for 8 days and the five ones had their tops inverted afterthe sixth day of treatment. The pieces were seasoned; disks of 2.0 cm of thickness were taken in 5 positions along of pieces and the analyses for determination of copper and boron penetration took place. The valuesof wood characteristics indicated that the pieces were homogeneous. The absorption of the solution was of19.9 liters (Prosopis juliflora and of 17.0 liters (Leucaena leucocephala. The nominal retentions of CCBwere 7.72 and 5.34 kg active ingredients (a.i./m3, respectively. In general, the inversion of the pieces inthe preservative solution is recommended, by providing a better distribution, penetration and retention ofCCB on treated pieces.

1. Identification of strain-rate and thermal sensitive material model with an inverse method

Peroni M.

2010-06-01

Full Text Available This paper describes a numerical inverse method to extract material strength parameters from the experimental data obtained via mechanical tests at different strainrates and temperatures. It will be shown that this procedure is particularly useful to analyse experimental results when the stress-strain fields in the specimen cannot be correctly described via analytical models. This commonly happens in specimens with no regular shape, in specimens with a regular shape when some instability phenomena occur (for example the necking phenomena in tensile tests that create a strongly heterogeneous stress-strain fields or in dynamic tests (where the strain-rate field is not constant due to wave propagation phenomena. Furthermore the developed procedure is useful to take into account thermal phenomena generally affecting high strain-rate tests due to the adiabatic overheating related to the conversion of plastic work. The method presented requires strong effort both from experimental and numerical point of view, anyway it allows to precisely identify the parameters of different material models. This could provide great advantages when high reliability of the material behaviour is necessary. Applicability of this method is particularly indicated for special applications in the field of aerospace engineering, ballistic, crashworthiness studies or particle accelerator technologies, where materials could be submitted to strong plastic deformations at high-strain rate in a wide range of temperature. Thermal softening effect has been investigated in a temperature range between 20°C and 1000°C.

2. Technical note: An inverse method to relate organic carbon reactivity to isotope composition from serial oxidation

J. D. Hemingway

2017-11-01

Full Text Available Serial oxidation coupled with stable carbon and radiocarbon analysis of sequentially evolved CO2 is a promising method to characterize the relationship between organic carbon (OC chemical composition, source, and residence time in the environment. However, observed decay profiles depend on experimental conditions and oxidation pathway. It is therefore necessary to properly assess serial oxidation kinetics before utilizing decay profiles as a measure of OC reactivity. We present a regularized inverse method to estimate the distribution of OC activation energy (E, a proxy for bond strength, using serial oxidation. Here, we apply this method to ramped temperature pyrolysis or oxidation (RPO analysis but note that this approach is broadly applicable to any serial oxidation technique. RPO analysis directly compares thermal reactivity to isotope composition by determining the E range for OC decaying within each temperature interval over which CO2 is collected. By analyzing a decarbonated test sample at multiple masses and oven ramp rates, we show that OC decay during RPO analysis follows a superposition of parallel first-order kinetics and that resulting E distributions are independent of experimental conditions. We therefore propose the E distribution as a novel proxy to describe OC thermal reactivity and suggest that E vs. isotope relationships can provide new insight into the compositional controls on OC source and residence time.

3. Technical note: An inverse method to relate organic carbon reactivity to isotope composition from serial oxidation

Hemingway, Jordon D.; Rothman, Daniel H.; Rosengard, Sarah Z.; Galy, Valier V.

2017-11-01

Serial oxidation coupled with stable carbon and radiocarbon analysis of sequentially evolved CO2 is a promising method to characterize the relationship between organic carbon (OC) chemical composition, source, and residence time in the environment. However, observed decay profiles depend on experimental conditions and oxidation pathway. It is therefore necessary to properly assess serial oxidation kinetics before utilizing decay profiles as a measure of OC reactivity. We present a regularized inverse method to estimate the distribution of OC activation energy (E), a proxy for bond strength, using serial oxidation. Here, we apply this method to ramped temperature pyrolysis or oxidation (RPO) analysis but note that this approach is broadly applicable to any serial oxidation technique. RPO analysis directly compares thermal reactivity to isotope composition by determining the E range for OC decaying within each temperature interval over which CO2 is collected. By analyzing a decarbonated test sample at multiple masses and oven ramp rates, we show that OC decay during RPO analysis follows a superposition of parallel first-order kinetics and that resulting E distributions are independent of experimental conditions. We therefore propose the E distribution as a novel proxy to describe OC thermal reactivity and suggest that E vs. isotope relationships can provide new insight into the compositional controls on OC source and residence time.

4. Inverse PCR-based method for isolating novel SINEs from genome.

Han, Yawei; Chen, Liping; Guan, Lihong; He, Shunping

2014-04-01

Short interspersed elements (SINEs) are moderately repetitive DNA sequences in eukaryotic genomes. Although eukaryotic genomes contain numerous SINEs copy, it is very difficult and laborious to isolate and identify them by the reported methods. In this study, the inverse PCR was successfully applied to isolate SINEs from Opsariichthys bidens genome in Eastern Asian Cyprinid. A group of SINEs derived from tRNA(Ala) molecular had been identified, which were named Opsar according to Opsariichthys. SINEs characteristics were exhibited in Opsar, which contained a tRNA(Ala)-derived region at the 5' end, a tRNA-unrelated region, and AT-rich region at the 3' end. The tRNA-derived region of Opsar shared 76 % sequence similarity with tRNA(Ala) gene. This result indicated that Opsar could derive from the inactive or pseudogene of tRNA(Ala). The reliability of method was tested by obtaining C-SINE, Ct-SINE, and M-SINEs from Ctenopharyngodon idellus, Megalobrama amblycephala, and Cyprinus carpio genomes. This method is simpler than the previously reported, which successfully omitted many steps, such as preparation of probes, construction of genomic libraries, and hybridization.

5. The factorization method for inverse acoustic scattering in a layered medium

Bondarenko, Oleksandr; Kirsch, Andreas; Liu, Xiaodong

2013-01-01

In this paper, we consider a problem of inverse acoustic scattering by an impenetrable obstacle embedded in a layered medium. We will show that the factorization method can be applied to recover the embedded obstacle; that is, the equation F-tilde g =φ z is solvable if and only if the sampling point z is in the interior of the unknown obstacle. Here, F-tilde is a self-adjoint operator related to the far field operator and ϕ z is the far field pattern of the Green function with respect to the problem of scattering by the background medium for point z. The validity of the factorization method is proven with the help of a mixed reciprocity principle and an application of the scattering operator. Due to the established mixed reciprocity principle, knowledge of the Green function for the background medium is no longer required, which makes the method attractive from the computational point of view. The paper is only concerned with sound-soft obstacles, but the analysis can be easily extended for sound-hard obstacles, or obstacles with separated sound-soft and sound-hard parts. Finally, we provide an explicit example for a radially symmetric case and present some numerical examples. (paper)

6. Micro-seismic Imaging Using a Source Independent Waveform Inversion Method

Wang, Hanchen

2016-04-18

Micro-seismology is attracting more and more attention in the exploration seismology community. The main goal in micro-seismic imaging is to find the source location and the ignition time in order to track the fracture expansion, which will help engineers monitor the reservoirs. Conventional imaging methods work fine in this field but there are many limitations such as manual picking, incorrect migration velocity and low signal to noise ratio (S/N). In traditional surface survey imaging, full waveform inversion (FWI) is widely used. The FWI method updates the velocity model by minimizing the misfit between the observed data and the predicted data. Using FWI to locate and image microseismic events allows for an automatic process (free of picking) that utilizes the full wavefield. Use the FWI technique, and overcomes the difficulties of manual pickings and incorrect velocity model for migration. However, the technique of waveform inversion of micro-seismic events faces its own problems. There is significant nonlinearity due to the unknown source location (space) and function (time). We have developed a source independent FWI of micro-seismic events to simultaneously invert for the source image, source function and velocity model. It is based on convolving reference traces with the observed and modeled data to mitigate the effect of an unknown source ignition time. The adjoint-state method is used to derive the gradient for the source image, source function and velocity updates. To examine the accuracy of the inverted source image and velocity model the extended image for source wavelet in z-axis is extracted. Also the angle gather is calculated to check the applicability of the migration velocity. By inverting for the source image, source wavelet and the velocity model simultaneously, the proposed method produces good estimates of the source location, ignition time and the background velocity in the synthetic experiments with both parts of the Marmousi and the SEG

7. Study on Fault Diagnostics of a Turboprop Engine Using Inverse Performance Model and Artificial Intelligent Methods

Kong, Changduk; Lim, Semyeong

2011-12-01

Recently, the health monitoring system of major gas path components of gas turbine uses mostly the model based method like the Gas Path Analysis (GPA). This method is to find quantity changes of component performance characteristic parameters such as isentropic efficiency and mass flow parameter by comparing between measured engine performance parameters such as temperatures, pressures, rotational speeds, fuel consumption, etc. and clean engine performance parameters without any engine faults which are calculated by the base engine performance model. Currently, the expert engine diagnostic systems using the artificial intelligent methods such as Neural Networks (NNs), Fuzzy Logic and Genetic Algorithms (GAs) have been studied to improve the model based method. Among them the NNs are mostly used to the engine fault diagnostic system due to its good learning performance, but it has a drawback due to low accuracy and long learning time to build learning data base if there are large amount of learning data. In addition, it has a very complex structure for finding effectively single type faults or multiple type faults of gas path components. This work builds inversely a base performance model of a turboprop engine to be used for a high altitude operation UAV using measured performance data, and proposes a fault diagnostic system using the base engine performance model and the artificial intelligent methods such as Fuzzy logic and Neural Network. The proposed diagnostic system isolates firstly the faulted components using Fuzzy Logic, then quantifies faults of the identified components using the NN leaned by fault learning data base, which are obtained from the developed base performance model. In leaning the NN, the Feed Forward Back Propagation (FFBP) method is used. Finally, it is verified through several test examples that the component faults implanted arbitrarily in the engine are well isolated and quantified by the proposed diagnostic system.

8. Path integral solutions of the master equation. [Lagrangian function, Ehrenfest-type theorem, Cauchy method, inverse functions

Etim, E; Basili, C [Rome Univ. (Italy). Ist. di Matematica

1978-08-21

The lagrangian in the path integral solution of the master equation of a stationary Markov process is derived by application of the Ehrenfest-type theorem of quantum mechanics and the Cauchy method of finding inverse functions. Applied to the non-linear Fokker-Planck equation the authors reproduce the result obtained by integrating over Fourier series coefficients and by other methods.

9. Application of Adjoint Method and Spectral-Element Method to Tomographic Inversion of Regional Seismological Structure Beneath Japanese Islands

Tsuboi, S.; Miyoshi, T.; Obayashi, M.; Tono, Y.; Ando, K.

2014-12-01

Recent progress in large scale computing by using waveform modeling technique and high performance computing facility has demonstrated possibilities to perform full-waveform inversion of three dimensional (3D) seismological structure inside the Earth. We apply the adjoint method (Liu and Tromp, 2006) to obtain 3D structure beneath Japanese Islands. First we implemented Spectral-Element Method to K-computer in Kobe, Japan. We have optimized SPECFEM3D_GLOBE (Komatitsch and Tromp, 2002) by using OpenMP so that the code fits hybrid architecture of K-computer. Now we could use 82,134 nodes of K-computer (657,072 cores) to compute synthetic waveform with about 1 sec accuracy for realistic 3D Earth model and its performance was 1.2 PFLOPS. We use this optimized SPECFEM3D_GLOBE code and take one chunk around Japanese Islands from global mesh and compute synthetic seismograms with accuracy of about 10 second. We use GAP-P2 mantle tomography model (Obayashi et al., 2009) as an initial 3D model and use as many broadband seismic stations available in this region as possible to perform inversion. We then use the time windows for body waves and surface waves to compute adjoint sources and calculate adjoint kernels for seismic structure. We have performed several iteration and obtained improved 3D structure beneath Japanese Islands. The result demonstrates that waveform misfits between observed and theoretical seismograms improves as the iteration proceeds. We now prepare to use much shorter period in our synthetic waveform computation and try to obtain seismic structure for basin scale model, such as Kanto basin, where there are dense seismic network and high seismic activity. Acknowledgements: This research was partly supported by MEXT Strategic Program for Innovative Research. We used F-net seismograms of the National Research Institute for Earth Science and Disaster Prevention.

10. Development of Gravity Acceleration Measurement Using Simple Harmonic Motion Pendulum Method Based on Digital Technology and Photogate Sensor

Yulkifli; Afandi, Zurian; Yohandri

2018-04-01

Development of gravitation acceleration measurement using simple harmonic motion pendulum method, digital technology and photogate sensor has been done. Digital technology is more practical and optimizes the time of experimentation. The pendulum method is a method of calculating the acceleration of gravity using a solid ball that connected to a rope attached to a stative pole. The pendulum is swung at a small angle resulted a simple harmonic motion. The measurement system consists of a power supply, Photogate sensors, Arduino pro mini and seven segments. The Arduino pro mini receives digital data from the photogate sensor and processes the digital data into the timing data of the pendulum oscillation. The calculation result of the pendulum oscillation time is displayed on seven segments. Based on measured data, the accuracy and precision of the experiment system are 98.76% and 99.81%, respectively. Based on experiment data, the system can be operated in physics experiment especially in determination of the gravity acceleration.

11. Rainfall assimilation in RAMS by means of the Kuo parameterisation inversion: method and preliminary results

Orlandi, A.; Ortolani, A.; Meneguzzo, F.; Levizzani, V.; Torricella, F.; Turk, F. J.

2004-03-01

In order to improve high-resolution forecasts, a specific method for assimilating rainfall rates into the Regional Atmospheric Modelling System model has been developed. It is based on the inversion of the Kuo convective parameterisation scheme. A nudging technique is applied to 'gently' increase with time the weight of the estimated precipitation in the assimilation process. A rough but manageable technique is explained to estimate the partition of convective precipitation from stratiform one, without requiring any ancillary measurement. The method is general purpose, but it is tuned for geostationary satellite rainfall estimation assimilation. Preliminary results are presented and discussed, both through totally simulated experiments and through experiments assimilating real satellite-based precipitation observations. For every case study, Rainfall data are computed with a rapid update satellite precipitation estimation algorithm based on IR and MW satellite observations. This research was carried out in the framework of the EURAINSAT project (an EC research project co-funded by the Energy, Environment and Sustainable Development Programme within the topic 'Development of generic Earth observation technologies', Contract number EVG1-2000-00030).

12. Application of random seismic inversion method based on tectonic model in thin sand body research

Dianju, W.; Jianghai, L.; Qingkai, F.

2017-12-01

The oil and gas exploitation at Songliao Basin, Northeast China have already progressed to the period with high water production. The previous detailed reservoir description that based on seismic image, sediment core, borehole logging has great limitations in small scale structural interpretation and thin sand body characterization. Thus, precise guidance for petroleum exploration is badly in need of a more advanced method. To do so, we derived the method of random seismic inversion constrained by tectonic model.It can effectively improve the depicting ability of thin sand bodies, combining numerical simulation techniques, which can credibly reducing the blindness of reservoir analysis from the whole to the local and from the macroscopic to the microscopic. At the same time, this can reduce the limitations of the study under the constraints of different geological conditions of the reservoir, accomplish probably the exact estimation for the effective reservoir. Based on the research, this paper has optimized the regional effective reservoir evaluation and the productive location adjustment of applicability, combined with the practical exploration and development in Aonan oil field.

13. Systematic hierarchical coarse-graining with the inverse Monte Carlo method

Lyubartsev, Alexander P., E-mail: alexander.lyubartsev@mmk.su.se [Division of Physical Chemistry, Arrhenius Laboratory, Stockholm University, S 106 91 Stockholm (Sweden); Naômé, Aymeric, E-mail: aymeric.naome@unamur.be [Division of Physical Chemistry, Arrhenius Laboratory, Stockholm University, S 106 91 Stockholm (Sweden); UCPTS Division, University of Namur, 61 Rue de Bruxelles, B 5000 Namur (Belgium); Vercauteren, Daniel P., E-mail: daniel.vercauteren@unamur.be [UCPTS Division, University of Namur, 61 Rue de Bruxelles, B 5000 Namur (Belgium); Laaksonen, Aatto, E-mail: aatto@mmk.su.se [Division of Physical Chemistry, Arrhenius Laboratory, Stockholm University, S 106 91 Stockholm (Sweden); Science for Life Laboratory, 17121 Solna (Sweden)

2015-12-28

We outline our coarse-graining strategy for linking micro- and mesoscales of soft matter and biological systems. The method is based on effective pairwise interaction potentials obtained in detailed ab initio or classical atomistic Molecular Dynamics (MD) simulations, which can be used in simulations at less accurate level after scaling up the size. The effective potentials are obtained by applying the inverse Monte Carlo (IMC) method [A. P. Lyubartsev and A. Laaksonen, Phys. Rev. E 52(4), 3730–3737 (1995)] on a chosen subset of degrees of freedom described in terms of radial distribution functions. An in-house software package MagiC is developed to obtain the effective potentials for arbitrary molecular systems. In this work we compute effective potentials to model DNA-protein interactions (bacterial LiaR regulator bound to a 26 base pairs DNA fragment) at physiological salt concentration at a coarse-grained (CG) level. Normally the IMC CG pair-potentials are used directly as look-up tables but here we have fitted them to five Gaussians and a repulsive wall. Results show stable association between DNA and the model protein as well as similar position fluctuation profile.

14. Modified Inverse First Order Reliability Method (I-FORM) for Predicting Extreme Sea States.

Eckert-Gallup, Aubrey Celia; Sallaberry, Cedric Jean-Marie; Dallman, Ann Renee; Neary, Vincent Sinclair

2014-09-01

Environmental contours describing extreme sea states are generated as the input for numerical or physical model simulation s as a part of the stand ard current practice for designing marine structure s to survive extreme sea states. Such environmental contours are characterized by combinations of significant wave height ( ) and energy period ( ) values calculated for a given recurrence interval using a set of data based on hindcast simulations or buoy observations over a sufficient period of record. The use of the inverse first - order reliability method (IFORM) i s standard design practice for generating environmental contours. In this paper, the traditional appli cation of the IFORM to generating environmental contours representing extreme sea states is described in detail and its merits and drawbacks are assessed. The application of additional methods for analyzing sea state data including the use of principal component analysis (PCA) to create an uncorrelated representation of the data under consideration is proposed. A reexamination of the components of the IFORM application to the problem at hand including the use of new distribution fitting techniques are shown to contribute to the development of more accurate a nd reasonable representations of extreme sea states for use in survivability analysis for marine struc tures. Keywords: In verse FORM, Principal Component Analysis , Environmental Contours, Extreme Sea State Characteri zation, Wave Energy Converters

15. An inverse method for determining the interaction force between the probe and sample using scanning near-field optical microscopy

Chang, Win-Jin; Fang, Te-Hua

2006-01-01

This study proposes a means for calculating the interaction force during the scanning process using a scanning near-field optical microscope (SNOM) probe. The determination of the interaction force in the scanning system is regarded as an inverse vibration problem. The conjugate gradient method is applied to treat the inverse problem using available displacement measurements. The results show that the conjugate gradient method is less sensitive to measurement errors and prior information on the functional form of quality was not required. Furthermore, the initial guesses for the interaction force can be arbitrarily chosen for the iteration process

16. Semi-analytic equations to the Cox-Thompson inverse scattering method at fixed energy for special cases

Palmai, T.; Apagyi, B.; Horvath, M.

2008-01-01

Solution of the Cox-Thompson inverse scattering problem at fixed energy 1-3 is reformulated resulting in semi-analytic equations. The new set of equations for the normalization constants and the nonphysical (shifted) angular momenta are free of matrix inversion operations. This simplification is a result of treating only the input phase shifts of partial waves of a given parity. Therefore, the proposed method can be applied for identical particle scattering of the bosonic type (or for certain cases of identical fermionic scattering). The new formulae are expected to be numerically more efficient than the previous ones. Based on the semi-analytic equations an approximate method is proposed for the generic inverse scattering problem, when partial waves of arbitrary parity are considered. (author)

17. Design optimization of axial flow hydraulic turbine runner: Part I - an improved Q3D inverse method

Peng, Guoyi; Cao, Shuliang; Ishizuka, Masaru; Hayama, Shinji

2002-06-01

With the aim of constructing a comprehensive design optimization procedure of axial flow hydraulic turbine, an improved quasi-three-dimensional inverse method has been proposed from the viewpoint of system and a set of rotational flow governing equations as well as a blade geometry design equation has been derived. The computation domain is firstly taken from the inlet of guide vane to the far outlet of runner blade in the inverse method and flows in different regions are solved simultaneously. So the influence of wicket gate parameters on the runner blade design can be considered and the difficulty to define the flow condition at the runner blade inlet is surmounted. As a pre-computation of initial blade design on S2m surface is newly adopted, the iteration of S1 and S2m surfaces has been reduced greatly and the convergence of inverse computation has been improved. The present model has been applied to the inverse computation of a Kaplan turbine runner. Experimental results and the direct flow analysis have proved the validation of inverse computation. Numerical investigations show that a proper enlargement of guide vane distribution diameter is advantageous to improve the performance of axial hydraulic turbine runner. Copyright

18. Comparison of various methods to determine bulk specific gravity of cores : an investigation of high values using AASHTO T275 - paraffin-coated method.

2012-07-01

A report from a MoDOT asphalt paving project was that unexpected results were obtained when adhering to the standard for determination of bulk specific gravity of compacted asphalt mixture (Gmb) specimens, AASHTO T 166. The test method requires speci...

19. Kinematic inversion of the 2008 Mw7 Iwate-Miyagi (Japan) earthquake by two independent methods: Sensitivity and resolution analysis

Gallovic, Frantisek; Cirella, Antonella; Plicka, Vladimir; Piatanesi, Alessio

2013-04-01

On 14 June 2008, UTC 23:43, the border of Iwate and Miyagi prefectures was hit by an Mw7 reverse-fault type crustal earthquake. The event is known to have the largest ground acceleration observed to date (~4g), which was recorded at station IWTH25. We analyze observed strong motion data with the objective to image the event rupture process and the associated uncertainties. Two different slip inversion approaches are used, the difference between the two methods being only in the parameterization of the source model. To minimize mismodeling of the propagation effects we use crustal model obtained by full waveform inversion of aftershock records in the frequency range between 0.05-0.3 Hz. In the first method, based on linear formulation, the parameters are represented by samples of slip velocity functions along the (finely discretized) fault in a time window spanning the whole rupture duration. Such a source description is very general with no prior constraint on the nucleation point, rupture velocity, shape of the velocity function. Thus the inversion could resolve very general (unexpected) features of the rupture evolution, such as multiple rupturing, rupture-propagation reversals, etc. On the other hand, due to the relatively large number of model parameters, the inversion result is highly non-unique, with possibility of obtaining a biased solution. The second method is a non-linear global inversion technique, where each point on the fault can slip only once, following a prescribed functional form of the source time function. We invert simultaneously for peak slip velocity, slip angle, rise time and rupture time by allowing a given range of variability for each kinematic model parameter. For this reason, unlike to the linear inversion approach, the rupture process needs a smaller number of parameters to be retrieved, and is more constrained with a proper control on the allowed range of parameter values. In order to test the resolution and reliability of the

20. Models for the dynamics of dust-like matter in the self-gravity field: The method of hydrodynamic substitutions

Zhuravlev, V. M.

2017-09-01

Models for the dynamics of a dust-like medium in the self-gravity field are investigated. Solutions of the corresponding problems are constructed by the method of hydrodynamic substitutions generalizing the Cole-Hopf substitutions. The method is extended to multidimensional ideal and viscous fluid flows with cylindrical and spherical symmetries for which exact solutions are constructed. Solutions for the dynamics of self-gravitating dust with arbitrary initial distributions of both fluid density and velocity are constructed using special coordinate transformations. In particular, the problem of cosmological expansion is considered in terms of Newton's gravity theory. Models of a one-dimensional viscous dust fluid flow and some problems of gas hydrodynamics are considered. Examples of exact solutions and their brief analysis are provided.

1. Inverse modelling of atmospheric tracers: non-Gaussian methods and second-order sensitivity analysis

M. Bocquet

2008-02-01

Full Text Available For a start, recent techniques devoted to the reconstruction of sources of an atmospheric tracer at continental scale are introduced. A first method is based on the principle of maximum entropy on the mean and is briefly reviewed here. A second approach, which has not been applied in this field yet, is based on an exact Bayesian approach, through a maximum a posteriori estimator. The methods share common grounds, and both perform equally well in practice. When specific prior hypotheses on the sources are taken into account such as positivity, or boundedness, both methods lead to purposefully devised cost-functions. These cost-functions are not necessarily quadratic because the underlying assumptions are not Gaussian. As a consequence, several mathematical tools developed in data assimilation on the basis of quadratic cost-functions in order to establish a posteriori analysis, need to be extended to this non-Gaussian framework. Concomitantly, the second-order sensitivity analysis needs to be adapted, as well as the computations of the averaging kernels of the source and the errors obtained in the reconstruction. All of these developments are applied to a real case of tracer dispersion: the European Tracer Experiment [ETEX]. Comparisons are made between a least squares cost function (similar to the so-called 4D-Var approach and a cost-function which is not based on Gaussian hypotheses. Besides, the information content of the observations which is used in the reconstruction is computed and studied on the application case. A connection with the degrees of freedom for signal is also established. As a by-product of these methodological developments, conclusions are drawn on the information content of the ETEX dataset as seen from the inverse modelling point of view.

2. Inverse Modeling Using Markov Chain Monte Carlo Aided by Adaptive Stochastic Collocation Method with Transformation

Zhang, D.; Liao, Q.

2016-12-01

The Bayesian inference provides a convenient framework to solve statistical inverse problems. In this method, the parameters to be identified are treated as random variables. The prior knowledge, the system nonlinearity, and the measurement errors can be directly incorporated in the posterior probability density function (PDF) of the parameters. The Markov chain Monte Carlo (MCMC) method is a powerful tool to generate samples from the posterior PDF. However, since the MCMC usually requires thousands or even millions of forward simulations, it can be a computationally intensive endeavor, particularly when faced with large-scale flow and transport models. To address this issue, we construct a surrogate system for the model responses in the form of polynomials by the stochastic collocation method. In addition, we employ interpolation based on the nested sparse grids and takes into account the different importance of the parameters, under the condition of high random dimensions in the stochastic space. Furthermore, in case of low regularity such as discontinuous or unsmooth relation between the input parameters and the output responses, we introduce an additional transform process to improve the accuracy of the surrogate model. Once we build the surrogate system, we may evaluate the likelihood with very little computational cost. We analyzed the convergence rate of the forward solution and the surrogate posterior by Kullback-Leibler divergence, which quantifies the difference between probability distributions. The fast convergence of the forward solution implies fast convergence of the surrogate posterior to the true posterior. We also tested the proposed algorithm on water-flooding two-phase flow reservoir examples. The posterior PDF calculated from a very long chain with direct forward simulation is assumed to be accurate. The posterior PDF calculated using the surrogate model is in reasonable agreement with the reference, revealing a great improvement in terms of

3. Inverse gas chromatography as a method for determination of surface properties of binding materials

Yu, Jihai; Lu, Xiaolei; Yang, Chunxia; Du, Baoli; Wang, Shuxian; Ye, Zhengmao

2017-09-01

Inverse gas chromatography (IGC) is a promising measurement technique for investigating the surface properties of binding materials, which are the major influence element for the adsorption performance of superplasticizer. In this work, using the IGC method, blast furnace slag (BFS), sulphoaluminate cement (SAC) and portland cement (P·O) are employed to systematically evaluate the corresponding dispersive component (γsd), specific surface free energy (γsab), and acid-base properties. The obtained results show that γsd contributes to a major section of the surface free energy in the three binding materials, suggesting they are of a relatively low polarity. Compared to the two kinds of cements, the BFS possesses the highest dispersive and specific surface free energies (the values are 45.01 mJ/m2 and 11.68 mJ/m2, respectively), and also exhibits a wider distribution range of γsd, indicating their surfaces are heterogeneous. For acid-base properties, the results indicate the surfaces of three samples are basic in nature. In addition, the adsorption investigation shows that per unit surface of BFS adsorbs the most superplasticizer molecules, which indicates the higher surface free energies is beneficial to the superplasticizer adsorption.

4. A proposed through-flow inverse method for the design of mixed-flow pumps

Borges, Joao Eduardo

1991-01-01

A through-flow (hub-to-shroud) truly inverse method is proposed and described. It uses an imposition of mean swirl, i.e., radius times mean tangential velocity, given throughout the meridional section of the turbomachine as an initial design specification. In the present implementation, it is assumed that the fluid is inviscid, incompressible, and irrotational at inlet and that the blades are supposed to have zero thickness. Only blade rows that impart to the fluid a constant work along the space are considered. An application of this procedure to design the rotor of a mixed-flow pump is described in detail. The strategy used to find a suitable mean swirl distribution and the other design inputs is also described. The final blade shape and pressure distributions on the blade surface are presented, showing that it is possible to obtain feasible designs using this technique. Another advantage of this technique is the fact that it does not require large amounts of CPU time.

5. Inverse Problem and Variation Method to Optimize Cascade Heat Exchange Network in Central Heating System

ZHANG Yin; WEI Zhiyuan; ZHANG Yinping; WANG Xin

2017-01-01

Urban heating in northern China accounts for 40％ of total building energy usage.In central heating systems,heat is often transfened from heat source to users by the heat network where several heat exchangers arc installed at heat source,substations and terminals respectively.For given overall heating capacity and heat source temperarure,increasing the terminal fluid temperature is an effective way to improve the thermal performance of such cascade heat exchange network for energy saving.In this paper,the mathematical optimization model of the cascade heat exchange network with three-stage heat exchangers in series is established.Aim at maximizing the cold fluid temperature for given hot fluid temperature and overall heating capacity,the optimal heat exchange area distribution and the medium fluids' flow rates are determined through inverse problem and variation method.The preliminary results show that the heat exchange areas should be distributed equally for each heat exchanger.It also indicates that in order to improve the thernmal performance of the whole system,more heat exchange areas should be allocated to the heat exchanger where flow rate difference between two fluids is relatively small.This work is important for guiding the optimization design of practical cascade heating systems.

6. The Application Research of Inverse Finite Element Method for Frame Deformation Estimation

Yong Zhao

2017-01-01

Full Text Available A frame deformation estimation algorithm is investigated for the purpose of real-time control and health monitoring of flexible lightweight aerospace structures. The inverse finite element method (iFEM for beam deformation estimation was recently proposed by Gherlone and his collaborators. The methodology uses a least squares principle involving section strains of Timoshenko theory for stretching, torsion, bending, and transverse shearing. The proposed methodology is based on stain-displacement relations only, without invoking force equilibrium. Thus, the displacement fields can be reconstructed without the knowledge of structural mode shapes, material properties, and applied loading. In this paper, the number of the locations where the section strains are evaluated in the iFEM is discussed firstly, and the algorithm is subsequently investigated through a simple supplied beam and an experimental aluminum wing-like frame model in the loading case of end-node force. The estimation results from the iFEM are compared with reference displacements from optical measurement and computational analysis, and the accuracy of the algorithm estimation is quantified by the root-mean-square error and percentage difference error.

7. Inverse method for effects characterization from ultrasonic b-scan images

Faur, M.

1999-02-01

In service inspections of French nuclear pressure water reactor vessels are carried out automatically in complete immersion from the inside by means of ultrasonic focused probes working in the pulse echo mode. Concern has been expressed about the capabilities of performing non destructive evaluation of the Outer Surface Defects (OSD), i.e. defects located in the vicinity of the outer surface of the inspected components. OSD are insonified by both a direct field that passes through the inner surface (water/steel) of the component containing the defect and a secondary field reflected from the outer surface. Consequently, the Bscan images, containing the signatures of such defects, are complicated and their interpretation is a difficult task. This work deals with extraction of the maximum available information for characterizing OSD from ultrasonic Bscan images. Our main objectives are to obtain the type of OSD and their geometric parameters by means of two specific inverse methods. The first method is used for the identification of the geometrical parameters of the equivalent planar OSD from segmented Bscan images. Ultrasonic equivalent defect sizing model-based methods may be used to size a defect in a material by obtaining a best-fit simple equivalent shape that matches the ultrasonic observed data. We illustrate the application of such an equivalent sizing OSD method that is based on a simplified direct model. The major drawback of this identification method, as used to date, is that only a part of the useful information contained into original Bscan image, i.e. segmented Bscan image, is used for defect characterization. Moreover, it requires the availability of defect classification information (i.e. if the defect is volumetric or planer, e. g. a crack or a lack of fusion), which, generally, may be as difficult to obtain as the defect parameters themselves. Therefore, we propose a parameter estimation method for extracting complementary information on the defect

8. Multi-parameter Analysis and Inversion for Anisotropic Media Using the Scattering Integral Method

Djebbi, Ramzi

2017-01-01

the model. I study the prospect of applying a scattering integral approach for multi-parameter inversion for a transversely isotropic model with a vertical axis of symmetry. I mainly analyze the sensitivity kernels to understand the sensitivity of seismic

9. Full waveform inversion using oriented time-domain imaging method for vertical transverse isotropic media

Zhang, Zhendong; Alkhalifah, Tariq Ali

2017-01-01

Full waveform inversion for reection events is limited by its linearized update re-quirements given by a process equivalent to migration. Unless the background velocity model is reasonably accurate, the resulting gradient can have an inaccurate

10. Standard Test Method for Water Absorption, Bulk Density, Apparent Porosity, and Apparent Specific Gravity of Fired Whiteware Products

American Society for Testing and Materials. Philadelphia

2006-01-01

1.1 This test method covers procedures for determining water absorption, bulk density, apparent porosity, and apparent specific gravity of fired unglazed whiteware products. 1.2 This standard may involve hazardous materials, operations, and equipment. This standard does not purport to address all of the safety problems associated with its use. It is the responsibility of the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatory limitations prior to use.

11. Non-regularized inversion method from light scattering applied to ferrofluid magnetization curves for magnetic size distribution analysis

Rijssel, Jos van; Kuipers, Bonny W.M.; Erné, Ben H.

2014-01-01

A numerical inversion method known from the analysis of light scattering by colloidal dispersions is now applied to magnetization curves of ferrofluids. The distribution of magnetic particle sizes or dipole moments is determined without assuming that the distribution is unimodal or of a particular shape. The inversion method enforces positive number densities via a non-negative least squares procedure. It is tested successfully on experimental and simulated data for ferrofluid samples with known multimodal size distributions. The created computer program MINORIM is made available on the web. - Highlights: • A method from light scattering is applied to analyze ferrofluid magnetization curves. • A magnetic size distribution is obtained without prior assumption of its shape. • The method is tested successfully on ferrofluids with a known size distribution. • The practical limits of the method are explored with simulated data including noise. • This method is implemented in the program MINORIM, freely available online

12. Gravity-Assist Trajectories to the Ice Giants: An Automated Method to Catalog Mass-or Time-Optimal Solutions

Hughes, Kyle M.; Knittel, Jeremy M.; Englander, Jacob A.

2017-01-01

This work presents an automated method of calculating mass (or time) optimal gravity-assist trajectories without a priori knowledge of the flyby-body combination. Since gravity assists are particularly crucial for reaching the outer Solar System, we use the Ice Giants, Uranus and Neptune, as example destinations for this work. Catalogs are also provided that list the most attractive trajectories found over launch dates ranging from 2024 to 2038. The tool developed to implement this method, called the Python EMTG Automated Trade Study Application (PEATSA), iteratively runs the Evolutionary Mission Trajectory Generator (EMTG), a NASA Goddard Space Flight Center in-house trajectory optimization tool. EMTG finds gravity-assist trajectories with impulsive maneuvers using a multiple-shooting structure along with stochastic methods (such as monotonic basin hopping) and may be run with or without an initial guess provided. PEATSA runs instances of EMTG in parallel over a grid of launch dates. After each set of runs completes, the best results within a neighborhood of launch dates are used to seed all other cases in that neighborhood---allowing the solutions across the range of launch dates to improve over each iteration. The results here are compared against trajectories found using a grid-search technique, and PEATSA is found to outperform the grid-search results for most launch years considered.

13. A new approach to the inverse kinematics of a multi-joint robot manipulator using a minimization method

Sasaki, Shinobu

1987-01-01

This paper proposes a new approach to solve the inverse kinematics of a type of sixlink manipulator. Directing our attention to features of joint structures of the manipulator, the original problem is first formulated by a system of equations with four variables and solved by means of a minimization technique. The remaining two variables are determined from constrained conditions involved. This is the basic idea in the present approach. The results of computer simulation of the present algorithm showed that the accuracies of solutions and convergence speed are much higher and quite satisfactory for practical purposes, as compared with the linearization-iteration method based on the conventional inverse Jacobian matrix. (author)

14. Geological modeling and infiltration pattern of a karstic system based upon crossed geophysical methods and image-guided inversion

Duran, Lea; Jardani, Abderrahim; Fournier, Matthieu; Massei, Nicolas

2015-04-01

Karstic aquifers represent an important part of the water resources worldwide. Though they have been widely studied on many aspects, their geological and hydrogeological modeling is still complex. Geophysical methods can provide useful subsurface information for the characterization and mapping of karstic systems, especially when not accessible by speleology. The site investigated in this study is a sinkhole-spring system, with small diameter conduits that run within a chalk aquifer (Norville, in Upper Normandy, France). This site was investigated using several geophysical methods: electrical tomography, self-potential, mise-à-la-masse methods, and electromagnetic method (EM34). Coupling those results with boreholes data, a 3D geological model of the hydrogeological basin was established, including tectonic features as well as infiltration structures (sinkhole, covered dolines). The direction of the karstic conduits near the main sinkhole could be established, and the major fault was shown to be a hydraulic barrier. Also the average concentration of dolines on the basin could be estimated, as well as their depth. At last, several hypotheses could be made concerning the location of the main conduit network between the sinkhole and the spring, using previous hydrodynamic study of the site along with geophysical data. In order to validate the 3D geological model, an image-guided inversion of the apparent resistivity data was used. With this approach it is possible to use geological cross sections to constrain the inversion of apparent resistivity data, preserving both discontinuities and coherences in the inversion of the resistivity data. This method was used on the major fault, enabling to choose one geological interpretation over another (fault block structure near the fault, rather than important folding). The constrained inversion was also applied on covered dolines, to validate the interpretation of their shape and depth. Key words: Magnetic and electrical

15. Estimation of Slip Distribution of the 2007 Bengkulu Earthquake from GPS Observation Using Least Squares Inversion Method

2012-07-01

Full Text Available Continuous Global Positioning System (GPS observations showed significant crustal displacements as a result of the Bengkulu earthquake occurring on September 12, 2007. A maximum horizontal displacement of 2.11 m was observed at PRKB station, while the vertical component at BSAT station was uplifted with a maximum of 0.73 m, and the vertical component at LAIS station was subsided by -0.97 m. The method of adding more constraint on the inversion for the Bengkulu earthquake slip distribution from GPS observations can help solve a least squares inversion with an under-determined condition. Checkerboard tests were performed to help conduct the weighting for constraining the inversion. The inversion calculation of the Bengkulu earthquake slip distribution yielded in an optimum value of slip distribution by giving a weight of smoothing constraint of 0.001 and a weight of slip value constraint = 0 at the edge of the earthquake rupture area. A maximum coseismic slip of the optimal inversion calculation was 5.12 m at the lower area of PRKB and BSAT stations. The seismic moment calculated from the optimal slip distribution was 7.14 x 1021 Nm, which is equivalent to a magnitude of 8.5.

16. The earth's shape and gravity

Garland, G D; Wilson, J T

2013-01-01

The Earth's Shape and Gravity focuses on the progress of the use of geophysical methods in investigating the interior of the earth and its shape. The publication first offers information on gravity, geophysics, geodesy, and geology and gravity measurements. Discussions focus on gravity measurements and reductions, potential and equipotential surfaces, absolute and relative measurements, and gravity networks. The text then elaborates on the shape of the sea-level surface and reduction of gravity observations. The text takes a look at gravity anomalies and structures in the earth's crust; interp

17. An inverse method for calculation of thermal inertia and heat gain in air conditioning and refrigeration systems

Fayazbakhsh, M.A.; Bagheri, F.; Bahrami, M.

2015-01-01

Highlights: • An inverse method is proposed to calculate thermal inertia in HVAC-R systems. • Real-time thermal loads are estimated using the proposed intelligent algorithm. • Calculation algorithm is validated with on-site measurements. • Freezer duty cycle data are extracted only based on temperature measurements. - Abstract: A new inverse method is proposed for estimation of thermal inertia and heat gain in air conditioning and refrigeration systems using on-site temperature measurements. The method is applied on a walk-in freezer room of a restaurant in Surrey, British Columbia, Canada during one week of its regular operation. The thermal inertia and instantaneous heat gain are calculated and the results are validated using actual information of the materials inside the freezer room. The proposed method can be implemented in intelligent control systems designed for new and existing HVAC-R systems to improve their overall energy efficiency and reduce their environmental impacts

18. Numerical solution to a multi-dimensional linear inverse heat conduction problem by a splitting-based conjugate gradient method

Dinh Nho Hao; Nguyen Trung Thanh; Sahli, Hichem

2008-01-01

In this paper we consider a multi-dimensional inverse heat conduction problem with time-dependent coefficients in a box, which is well-known to be severely ill-posed, by a variational method. The gradient of the functional to be minimized is obtained by aids of an adjoint problem and the conjugate gradient method with a stopping rule is then applied to this ill-posed optimization problem. To enhance the stability and the accuracy of the numerical solution to the problem we apply this scheme to the discretized inverse problem rather than to the continuous one. The difficulties with large dimensions of discretized problems are overcome by a splitting method which only requires the solution of easy-to-solve one-dimensional problems. The numerical results provided by our method are very good and the techniques seem to be very promising.

19. A New Wave Equation Based Source Location Method with Full-waveform Inversion

Wu, Zedong

2017-05-26

Locating the source of a passively recorded seismic event is still a challenging problem, especially when the velocity is unknown. Many imaging approaches to focus the image do not address the velocity issue and result in images plagued with illumination artifacts. We develop a waveform inversion approach with an additional penalty term in the objective function to reward the focusing of the source image. This penalty term is relaxed early to allow for data fitting, and avoid cycle skipping, using an extended source. At the later stages the focusing of the image dominates the inversion allowing for high resolution source and velocity inversion. We also compute the source location explicitly and numerical tests show that we obtain good estimates of the source locations with this approach.

20. On the joint inversion of SGG and SST data from the GOCE mission

P. Ditmar

2003-01-01

Full Text Available The computation of spherical harmonic coefficients of the Earth’s gravity field from satellite-to-satellite tracking (SST data and satellite gravity gradiometry (SGG data is considered. As long as the functional model related to SST data contains nuisance parameters (e.g. unknown initial state vectors, assembling of the corresponding normal matrix must be supplied with the back-substitution operation, so that the nuisance parameters are excluded from consideration. The traditional back-substitution algorithm, however, may result in large round-off errors. Hence an alternative approach, back-substitution at the level of the design matrix, is implemented. Both a stand-alone inversion of either type of data and a joint inversion of both types are considered. The conclusion drawn is that the joint inversion results in a much better model of the Earth’s gravity field than a standalone inversion. Furthermore, two numerical techniques for solving the joint system of normal equations are compared: (i the Cholesky method based on an explicit computation of the normal matrix, and (ii the pre-conditioned conjugate gradient method (PCCG, for which an explicit computation of the entire normal matrix is not needed. The comparison shows that the PCCG method is much faster than the Cholesky method.Key words. Earth’s gravity field, GOCE, satellite-tosatellite tracking, satellite gravity gradiometry, backsubstitution

1. A method to compute the inverse of a complex n-block tridiagonal quasi-hermitian matrix

Godfrin, Elena

1990-01-01

This paper presents a method to compute the inverse of a complex n-block tridiagonal quasi-hermitian matrix using adequate partitions of the complete matrix. This type of matrix is very usual in quantum mechanics and, more specifically, in solid state physics (e.g., interfaces and superlattices), when the tight-binding approximation is used. The efficiency of the method is analyzed comparing the required CPU time and work-area for different usual techniques. (Author)

2. Random fixed point equations and inverse problems using "collage method" for contraction mappings

Kunze, H. E.; La Torre, D.; Vrscay, E. R.

2007-10-01

In this paper we are interested in the direct and inverse problems for the following class of random fixed point equations T(w,x(w))=x(w) where is a given operator, [Omega] is a probability space and X is a Polish metric space. The inverse problem is solved by recourse to the collage theorem for contractive maps. We then consider two applications: (i) random integral equations, and (ii) random iterated function systems with greyscale maps (RIFSM), for which noise is added to the classical IFSM.

3. Estimation of physical properties of laminated composites via the method of inverse vibration problem

Balci, Murat [Dept. of Mechanical Engineering, Bayburt University, Bayburt (Turkmenistan); Gundogdu, Omer [Dept. of Mechanical Engineering, Ataturk University, Erzurum (Turkmenistan)

2017-01-15

In this study, estimation of some physical properties of a laminated composite plate was conducted via the inverse vibration problem. Laminated composite plate was modelled and simulated to obtain vibration responses for different length-to-thickness ratio in ANSYS. Furthermore, a numerical finite element model was developed for the laminated composite utilizing the Kirchhoff plate theory and programmed in MATLAB for simulations. Optimizing the difference between these two vibration responses, inverse vibration problem was solved to obtain some of the physical properties of the laminated composite using genetic algorithms. The estimated parameters are compared with the theoretical results, and a very good correspondence was observed.

4. Estimation of physical properties of laminated composites via the method of inverse vibration problem

Balci, Murat; Gundogdu, Omer

2017-01-01

In this study, estimation of some physical properties of a laminated composite plate was conducted via the inverse vibration problem. Laminated composite plate was modelled and simulated to obtain vibration responses for different length-to-thickness ratio in ANSYS. Furthermore, a numerical finite element model was developed for the laminated composite utilizing the Kirchhoff plate theory and programmed in MATLAB for simulations. Optimizing the difference between these two vibration responses, inverse vibration problem was solved to obtain some of the physical properties of the laminated composite using genetic algorithms. The estimated parameters are compared with the theoretical results, and a very good correspondence was observed

5. Ruthenium determination by the method of inversion voltammetry on graphite electrode

Dominova, I G; Kolpakova, N A; Stromberg, A G [Tomskij Politekhnicheskij Inst. (USSR)

1978-12-01

Optimal conditions for determining ruthenium by inversion voltammetry on a graphite electrode are 0.1 M KCl or KNO/sub 3/, pH 2-3, electrolysis potential - 1.0 V. A linear dependence of ruthenium electrodissolution current on its concentration in the solution makes it possible to use inversion voltammetry for determining 5x10/sup -7/ - 1x10/sup -4/ g-ion Ru/l. Ruthenium can be determined in the presence of a large excess of nickel and copper but commensurable amounts of mercury adn platinum metals interfere.

6. An estimate of the terrestrial carbon budget of Russia using inventory-based, eddy covariance and inversion methods

A. J. Dolman

2012-12-01

Full Text Available We determine the net land to atmosphere flux of carbon in Russia, including Ukraine, Belarus and Kazakhstan, using inventory-based, eddy covariance, and inversion methods. Our high boundary estimate is −342 Tg C yr−1 from the eddy covariance method, and this is close to the upper bounds of the inventory-based Land Ecosystem Assessment and inverse models estimates. A lower boundary estimate is provided at −1350 Tg C yr−1 from the inversion models. The average of the three methods is −613.5 Tg C yr−1. The methane emission is estimated separately at 41.4 Tg C yr−1.

These three methods agree well within their respective error bounds. There is thus good consistency between bottom-up and top-down methods. The forests of Russia primarily cause the net atmosphere to land flux (−692 Tg C yr−1 from the LEA. It remains however remarkable that the three methods provide such close estimates (−615, −662, −554 Tg C yr–1 for net biome production (NBP, given the inherent uncertainties in all of the approaches. The lack of recent forest inventories, the few eddy covariance sites and associated uncertainty with upscaling and undersampling of concentrations for the inversions are among the prime causes of the uncertainty. The dynamic global vegetation models (DGVMs suggest a much lower uptake at −91 Tg C yr−1, and we argue that this is caused by a high estimate of heterotrophic respiration compared to other methods.

7. Field estimates of gravity terrain corrections and Y2K-compatible method to convert from gravity readings with multiple base stations to tide- and long-term drift-corrected observations

Plouff, Donald

2000-01-01

Gravity observations are directly made or are obtained from other sources by the U.S. Geological Survey in order to prepare maps of the anomalous gravity field and consequently to interpret the subsurface distribution of rock densities and associated lithologic or geologic units. Observations are made in the field with gravity meters at new locations and at reoccupations of previously established gravity "stations." This report illustrates an interactively-prompted series of steps needed to convert gravity "readings" to values that are tied to established gravity datums and includes computer programs to implement those steps. Inasmuch as individual gravity readings have small variations, gravity-meter (instrument) drift may not be smoothly variable, and acommodations may be needed for ties to previously established stations, the reduction process is iterative. Decision-making by the program user is prompted by lists of best values and graphical displays. Notes about irregularities of topography, which affect the value of observed gravity but are not shown in sufficient detail on topographic maps, must be recorded in the field. This report illustrates ways to record field notes (distances, heights, and slope angles) and includes computer programs to convert field notes to gravity terrain corrections. This report includes approaches that may serve as models for other applications, for example: portrayal of system flow; style of quality control to document and validate computer applications; lack of dependence on proprietary software except source code compilation; method of file-searching with a dwindling list; interactive prompting; computer code to write directly in the PostScript (Adobe Systems Incorporated) printer language; and high-lighting the four-digit year on the first line of time-dependent data sets for assured Y2K compatibility. Computer source codes provided are written in the Fortran scientific language. In order for the programs to operate, they first

8. Information-entropic method for studying the stability bound of nonrelativistic polytropic stars within modified gravity theories

Wibisono, C.; Sulaksono, A.

We study the stability of nonrelativistic polytropic stars within two modified gravity theories, i.e. beyond Horndeski gravity and Eddington-inspired Born-Infeld theories, using the configuration entropy method. We use the spatially localized bounded function of energy density as solutions from stellar effective equations to construct the corresponding configuration entropy. We use the same argument as the one used by Gleiser and coworkers [M. Gleiser and D. Sowinski, Phys. Lett. B 727 (2013) 272; M. Gleiser and N. Jiang, Phys. Rev. D 92 (2015) 044046] that the stars are stable if there is a peak in configuration entropy as a function of adiabatic index curve. Specifically, the boundary between stable and unstable regions which corresponds to Chandrasekhar stability bound is indicated from the existence of the maximum peak while the most stable polytropic stars are indicated by the minimum peak in the corresponding curve. We have found that the values of critical adiabatic indexes of Chandrasekhar stability bound and the most stable polytropic stars predicted by the nonrelativistic limits of beyond Horndeski gravity and Eddington-inspired Born-Infeld theories are different to those predicted by general relativity where the corresponding differences depend on the free parameters of both theories.

9. Large scale inverse problems computational methods and applications in the earth sciences

Scheichl, Robert; Freitag, Melina A; Kindermann, Stefan

2013-01-01

This book is thesecond volume of three volume series recording the ""Radon Special Semester 2011 on Multiscale Simulation & Analysis in Energy and the Environment"" taking place in Linz, Austria, October 3-7, 2011. The volume addresses the common ground in the mathematical and computational procedures required for large-scale inverse problems and data assimilation in forefront applications.

10. A New Wave Equation Based Source Location Method with Full-waveform Inversion

Wu, Zedong; Alkhalifah, Tariq Ali

2017-01-01

with illumination artifacts. We develop a waveform inversion approach with an additional penalty term in the objective function to reward the focusing of the source image. This penalty term is relaxed early to allow for data fitting, and avoid cycle skipping, using

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

Oh, Geok Lian; Jacobsen, Finn

2013-01-01

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

12. A hybrid finite difference and integral equation method for modeling and inversion of marine CSEM data

Yoon, Daeung; Zhdanov, Michael; Cai, Hongzhu

2015-01-01

One of the major problems in the modeling and inversion of marine controlled source electromagnetic (MCSEM) data is related to the need for accurate representation of very complex geoelectrical models typical for marine environment. At the same time, the corresponding forward modeling algorithms...

13. An inverse analysis of a transient 2-D conduction-radiation problem using the lattice Boltzmann method and the finite volume method coupled with the genetic algorithm

Das, Ranjan; Mishra, Subhash C.; Ajith, M.; Uppaluri, R.

2008-01-01

This article deals with the simultaneous estimation of parameters in a 2-D transient conduction-radiation heat transfer problem. The homogeneous medium is assumed to be absorbing, emitting and scattering. The boundaries of the enclosure are diffuse gray. Three parameters, viz. the scattering albedo, the conduction-radiation parameter and the boundary emissivity, are simultaneously estimated by the inverse method involving the lattice Boltzmann method (LBM) and the finite volume method (FVM) in conjunction with the genetic algorithm (GA). In the direct method, the FVM is used for computing the radiative information while the LBM is used to solve the energy equation. The temperature field obtained in the direct method is used in the inverse method for simultaneous estimation of unknown parameters using the LBM-FVM and the GA. The LBM-FVM-GA combination has been found to accurately predict the unknown parameters

14. Gravity interpretation via EULDPH

2003-01-01

Euler's homogeneity equation for determining the coordinates of the source body especially to estimate the depth (EULDPH) is discussed at this paper. This method is applied to synthetic and high-resolution real data such as gradiometric or microgravity data. Low-quality gravity data especially in the areas with a complex geology structure has rarely been used. The Bouguer gravity anomalies are computed from absolute gravity data after the required corrections. Bouguer anomaly is transferred to residual gravity anomaly. The gravity gradients are estimated from residual anomaly values. Bouguer anomaly is the gravity gradients, using EULDPH. The coordinates of the perturbing body will be determined. Two field examples one in the east of Tehran (Mard Abad) where we would like to determine the location of the anomaly (hydrocarbon) and another in the south-east of Iran close to the border with Afghanistan (Nosrat Abad) where we are exploring chromite are presented

15. Inverse problems for random differential equations using the collage method for random contraction mappings

Kunze, H. E.; La Torre, D.; Vrscay, E. R.

2009-01-01

In this paper we are concerned with differential equations with random coefficients which will be considered as random fixed point equations of the form T([omega],x([omega]))=x([omega]), [omega][set membership, variant][Omega]. Here T:[Omega]×X-->X is a random integral operator, is a probability space and X is a complete metric space. We consider the following inverse problem for such equations: Given a set of realizations of the fixed point of T (possibly the interpolations of different observational data sets), determine the operator T or the mean value of its random components, as appropriate. We solve the inverse problem for this class of equations by using the collage theorem for contraction mappings.

16. Gradient Correlation Method for the Stabilization of Inversion Results of Aerosol Microphysical Properties Retrieved from Profiles of Optical Data

Kolgotin Alexei

2016-01-01

Full Text Available Correlation relationships between aerosol microphysical parameters and optical data are investigated. The results show that surface-area concentrations and extinction coefficients are linearly correlated with a correlation coefficient above 0.99 for arbitrary particle size distribution. The correlation relationships that we obtained can be used as constraints in our inversion of optical lidar data. Simulation studies demonstrate a significant stabilization of aerosol microphysical data products if we apply the gradient correlation method in our traditional regularization technique.

17. Forward and inverse problems for surface acoustic waves in anisotropic media: A Ritz-Rayleigh method based approach

Stoklasová, Pavla; Sedlák, Petr; Seiner, Hanuš; Landa, Michal

2015-01-01

Roč. 56, February 2015 (2015), s. 381-389 ISSN 0041-624X R&D Projects: GA ČR GPP101/12/P428 Institutional support: RVO:61388998 Keywords : surface acoustic waves * anisotropic materials * Ritz-Rayleigh method * inverse problem Subject RIV: BI - Acoustics Impact factor: 1.954, year: 2015 http://www.sciencedirect.com/science/article/pii/S0041624X14002686

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

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

1979-01-01

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

19. Toward an optimal inversion method for synthetic aperture radar wind retrieval

Portabella, M.; Stoffelen, A.; Johannessen, Johnny A.

2002-01-01

In recent years, particular efforts have been made to derive wind fields over the oceans from synthetic aperture radar (SAR) images. In contrast with the scatterometer, the SAR has a higher spatial resolution and therefore has the potential to provide higher resolution wind information. Since there are at least two geophysical parameters (wind speed and wind direction) modulating the single SAR backscatter measurements, the inversion of wind fields from SAR observations has an inherent proble...

20. The optimized gradient method for full waveform inversion and its spectral implementation

Wu, Zedong; Alkhalifah, Tariq Ali

2016-01-01

At the heart of the full waveform inversion (FWI) implementation is wavefield extrapolation, and specifically its accuracy and cost. To obtain accurate, dispersion free wavefields, the extrapolation for modelling is often expensive. Combining an efficient extrapolation with a novel gradient preconditioning can render an FWI implementation that efficiently converges to an accurate model. We, specifically, recast the extrapolation part of the inversion in terms of its spectral components for both data and gradient calculation. This admits dispersion free wavefields even at large extrapolation time steps, which improves the efficiency of the inversion. An alternative spectral representation of the depth axis in terms of sine functions allows us to impose a free surface boundary condition, which reflects our medium boundaries more accurately. Using a newly derived perfectly matched layer formulation for this spectral implementation, we can define a finite model with absorbing boundaries. In order to reduce the nonlinearity in FWI, we propose a multiscale conditioning of the objective function through combining the different directional components of the gradient to optimally update the velocity. Through solving a simple optimization problem, it specifically admits the smoothest approximate update while guaranteeing its ascending direction. An application to the Marmousi model demonstrates the capability of the proposed approach and justifies our assertions with respect to cost and convergence.

1. The optimized gradient method for full waveform inversion and its spectral implementation

Wu, Zedong

2016-03-28

At the heart of the full waveform inversion (FWI) implementation is wavefield extrapolation, and specifically its accuracy and cost. To obtain accurate, dispersion free wavefields, the extrapolation for modelling is often expensive. Combining an efficient extrapolation with a novel gradient preconditioning can render an FWI implementation that efficiently converges to an accurate model. We, specifically, recast the extrapolation part of the inversion in terms of its spectral components for both data and gradient calculation. This admits dispersion free wavefields even at large extrapolation time steps, which improves the efficiency of the inversion. An alternative spectral representation of the depth axis in terms of sine functions allows us to impose a free surface boundary condition, which reflects our medium boundaries more accurately. Using a newly derived perfectly matched layer formulation for this spectral implementation, we can define a finite model with absorbing boundaries. In order to reduce the nonlinearity in FWI, we propose a multiscale conditioning of the objective function through combining the different directional components of the gradient to optimally update the velocity. Through solving a simple optimization problem, it specifically admits the smoothest approximate update while guaranteeing its ascending direction. An application to the Marmousi model demonstrates the capability of the proposed approach and justifies our assertions with respect to cost and convergence.

2. Elastic full waveform inversion based on the homogenization method: theoretical framework and 2-D numerical illustrations

Capdeville, Yann; Métivier, Ludovic

2018-05-01

Seismic imaging is an efficient tool to investigate the Earth interior. Many of the different imaging techniques currently used, including the so-called full waveform inversion (FWI), are based on limited frequency band data. Such data are not sensitive to the true earth model, but to a smooth version of it. This smooth version can be related to the true model by the homogenization technique. Homogenization for wave propagation in deterministic media with no scale separation, such as geological media, has been recently developed. With such an asymptotic theory, it is possible to compute an effective medium valid for a given frequency band such that effective waveforms and true waveforms are the same up to a controlled error. In this work we make the link between limited frequency band inversion, mainly FWI, and homogenization. We establish the relation between a true model and an FWI result model. This relation is important for a proper interpretation of FWI images. We numerically illustrate, in the 2-D case, that an FWI result is at best the homogenized version of the true model. Moreover, it appears that the homogenized FWI model is quite independent of the FWI parametrization, as long as it has enough degrees of freedom. In particular, inverting for the full elastic tensor is, in each of our tests, always a good choice. We show how the homogenization can help to understand FWI behaviour and help to improve its robustness and convergence by efficiently constraining the solution space of the inverse problem.

3. A Method for Assessing Material Flammability for Micro-Gravity Environments

Steinhaus, T.; Olenick, S. M.; Sifuentes, A.; Long, R. T.; Torero, J. L.

1999-01-01

4. A solution of nonlinear equation for the gravity wave spectra from Adomian decomposition method: a first approach

Antonio Gledson Goulart

2013-12-01

Full Text Available In this paper, the equation for the gravity wave spectra in mean atmosphere is analytically solved without linearization by the Adomian decomposition method. As a consequence, the nonlinear nature of problem is preserved and the errors found in the results are only due to the parameterization. The results, with the parameterization applied in the simulations, indicate that the linear solution of the equation is a good approximation only for heights shorter than ten kilometers, because the linearization the equation leads to a solution that does not correctly describe the kinetic energy spectra.

5. Studying the Transient Thermal Contact Conductance Between the Exhaust Valve and Its Seat Using the Inverse Method

2016-02-01

In this study, the experiments aimed at analyzing thermally the exhaust valve in an air-cooled internal combustion engine and estimating the thermal contact conductance in fixed and periodic contacts. Due to the nature of internal combustion engines, the duration of contact between the valve and its seat is too short, and much time is needed to reach the quasi-steady state in the periodic contact between the exhaust valve and its seat. Using the methods of linear extrapolation and the inverse solution, the surface contact temperatures and the fixed and periodic thermal contact conductance were calculated. The results of linear extrapolation and inverse methods have similar trends, and based on the error analysis, they are accurate enough to estimate the thermal contact conductance. Moreover, due to the error analysis, a linear extrapolation method using inverse ratio is preferred. The effects of pressure, contact frequency, heat flux, and cooling air speed on thermal contact conductance have been investigated. The results show that by increasing the contact pressure the thermal contact conductance increases substantially. In addition, by increasing the engine speed the thermal contact conductance decreases. On the other hand, by boosting the air speed the thermal contact conductance increases, and by raising the heat flux the thermal contact conductance reduces. The average calculated error equals to 12.9 %.

6. H-Shaped Multiple Linear Motor Drive Platform Control System Design Based on an Inverse System Method

Caiyan Qin

2017-12-01

Full Text Available Due to its simple mechanical structure and high motion stability, the H-shaped platform has been increasingly widely used in precision measuring, numerical control machining and semiconductor packaging equipment, etc. The H-shaped platform is normally driven by multiple (three permanent magnet synchronous linear motors. The main challenges for H-shaped platform-control include synchronous control between the two linear motors in the Y direction as well as total positioning error of the platform mover, a combination of position deviation in X and Y directions. To deal with the above challenges, this paper proposes a control strategy based on the inverse system method through state feedback and dynamic decoupling of the thrust force. First, mechanical dynamics equations have been deduced through the analysis of system coupling based on the platform structure. Second, the mathematical model of the linear motors and the relevant coordinate transformation between dq-axis currents and ABC-phase currents are analyzed. Third, after the main concept of inverse system method being explained, the inverse system model of the platform control system has been designed after defining relevant system variables. Inverse system model compensates the original nonlinear coupled system into pseudo-linear decoupled linear system, for which typical linear control methods, like PID, can be adopted to control the system. The simulation model of the control system is built in MATLAB/Simulink and the simulation result shows that the designed control system has both small synchronous deviation and small total trajectory tracking error. Furthermore, the control program has been run on NI controller for both fixed-loop-time and free-loop-time modes, and the test result shows that the average loop computation time needed is rather small, which makes it suitable for real industrial applications. Overall, it proves that the proposed new control strategy can be used in

7. 3-D minimum-structure inversion of magnetotelluric data using the finite-element method and tetrahedral grids

Jahandari, H.; Farquharson, C. G.

2017-11-01

Unstructured grids enable representing arbitrary structures more accurately and with fewer cells compared to regular structured grids. These grids also allow more efficient refinements compared to rectilinear meshes. In this study, tetrahedral grids are used for the inversion of magnetotelluric (MT) data, which allows for the direct inclusion of topography in the model, for constraining an inversion using a wireframe-based geological model and for local refinement at the observation stations. A minimum-structure method with an iterative model-space Gauss-Newton algorithm for optimization is used. An iterative solver is employed for solving the normal system of equations at each Gauss-Newton step and the sensitivity matrix-vector products that are required by this solver are calculated using pseudo-forward problems. This method alleviates the need to explicitly form the Hessian or Jacobian matrices which significantly reduces the required computation memory. Forward problems are formulated using an edge-based finite-element approach and a sparse direct solver is used for the solutions. This solver allows saving and re-using the factorization of matrices for similar pseudo-forward problems within a Gauss-Newton iteration which greatly minimizes the computation time. Two examples are presented to show the capability of the algorithm: the first example uses a benchmark model while the second example represents a realistic geological setting with topography and a sulphide deposit. The data that are inverted are the full-tensor impedance and the magnetic transfer function vector. The inversions sufficiently recovered the models and reproduced the data, which shows the effectiveness of unstructured grids for complex and realistic MT inversion scenarios. The first example is also used to demonstrate the computational efficiency of the presented model-space method by comparison with its data-space counterpart.

8. Killing vector fields in three dimensions: a method to solve massive gravity field equations

Guerses, Metin, E-mail: gurses@fen.bilkent.edu.t [Department of Mathematics, Faculty of Sciences, Bilkent University, 06800 Ankara (Turkey)

2010-10-21

Killing vector fields in three dimensions play an important role in the construction of the related spacetime geometry. In this work we show that when a three-dimensional geometry admits a Killing vector field then the Ricci tensor of the geometry is determined in terms of the Killing vector field and its scalars. In this way we can generate all products and covariant derivatives at any order of the Ricci tensor. Using this property we give ways to solve the field equations of topologically massive gravity (TMG) and new massive gravity (NMG) introduced recently. In particular when the scalars of the Killing vector field (timelike, spacelike and null cases) are constants then all three-dimensional symmetric tensors of the geometry, the Ricci and Einstein tensors, their covariant derivatives at all orders, and their products of all orders are completely determined by the Killing vector field and the metric. Hence, the corresponding three-dimensional metrics are strong candidates for solving all higher derivative gravitational field equations in three dimensions.

9. Massive Gravity

de Rham, Claudia

2014-01-01

We review recent progress in massive gravity. We start by showing how different theories of massive gravity emerge from a higher-dimensional theory of general relativity, leading to the Dvali–Gabadadze–Porrati model (DGP), cascading gravity, and ghost-free massive gravity. We then explore their theoretical and phenomenological consistency, proving the absence of Boulware–Deser ghosts and reviewing the Vainshtein mechanism and the cosmological solutions in these models. Finally, we present alt...

10. Principle and application of low energy inverse photoemission spectroscopy: A new method for measuring unoccupied states of organic semiconductors

Yoshida, Hiroyuki, E-mail: hyoshida@chiba-u.jp

2015-10-01

Highlights: • Principle of low energy inverse photoemission spectroscopy is described. • Instruments including electron sources and photon detectors are shown. • Recent results about organic devices and fundamental studies are reviewed. • Electron affinities of typical organic semiconductors are compiled. - Abstract: Information about the unoccupied states is crucial to both fundamental and applied physics of organic semiconductors. However, there were no available experimental methods that meet the requirement of such research. In this review, we describe a new experimental method to examine the unoccupied states, called low-energy inverse photoemission spectroscopy (LEIPS). An electron having the kinetic energy lower than the damage threshold of organic molecules is introduced to a sample film, and an emitted photon in the near-ultraviolet range is detected with high resolution and sensitivity. Unlike the previous inverse photoemission spectroscopy, the sample damage is negligible and the overall resolution is a factor of two improved to 0.25 eV. Using LEIPS, electron affinity of organic semiconductor can be determined with the same precision as photoemission spectroscopy for ionization energy. The instruments including an electron source and photon detectors as well as application to organic semiconductors are presented.

11. Principle and application of low energy inverse photoemission spectroscopy: A new method for measuring unoccupied states of organic semiconductors

Yoshida, Hiroyuki

2015-01-01

Highlights: • Principle of low energy inverse photoemission spectroscopy is described. • Instruments including electron sources and photon detectors are shown. • Recent results about organic devices and fundamental studies are reviewed. • Electron affinities of typical organic semiconductors are compiled. - Abstract: Information about the unoccupied states is crucial to both fundamental and applied physics of organic semiconductors. However, there were no available experimental methods that meet the requirement of such research. In this review, we describe a new experimental method to examine the unoccupied states, called low-energy inverse photoemission spectroscopy (LEIPS). An electron having the kinetic energy lower than the damage threshold of organic molecules is introduced to a sample film, and an emitted photon in the near-ultraviolet range is detected with high resolution and sensitivity. Unlike the previous inverse photoemission spectroscopy, the sample damage is negligible and the overall resolution is a factor of two improved to 0.25 eV. Using LEIPS, electron affinity of organic semiconductor can be determined with the same precision as photoemission spectroscopy for ionization energy. The instruments including an electron source and photon detectors as well as application to organic semiconductors are presented.

12. Preparation of Co-Zn ferrite nano-based materials and their enhanced magnetic performance via inverse miniemulsion method

Ji, Juejin; Zhang, Zhenqian; Fang, Bijun; Ding, Jianning

2017-11-01

The well dispersed CZF/PAM nanoparticles were prepared by the inverse miniemulsion method, which present high calcining and sintering activity for preparing Co0.875Zn0.125Fe2O4 (CZF) films, powders and ceramics at rather low temperatures. The prepared CZF/PAM inverse miniemulsion exhibits excellent film-formation performance, which is feasible for coating CZF films. XRD and FT-IR measurements confirmed that phase pure spinel structure and well crystalline CZF powders can be prepared calcined at the least temperature of 400 °C. The 450 °C-calcined CZF powders exhibit nearly spherical shape grains with average particle size 20-30 nm accompanied by apparent conglomeration. Improved external magnetic performance and electrical properties are obtained in the synthesized CZF powders and ceramics, which provide versatile promising applications.

13. Method for solving an inverse problem of wing type by using a simple panel method; Kanbenna panel ho ni yoru yokugata gyaku mondai no ichikaiho

Ando, J; Matsumoto, D; Maita, S; Nakatake, K [Kyushu University, Fukuoka (Japan). Faculty of Engineering

1997-10-01

This paper describes one method for solving an inverse problem of wing type based on the source and quasi continuous vortex lattice method (SQCM) in designing marine propellers and underwater wings. With the SQCM, vortices and control points are distributed on wing camber according to the QCM, and wing surface is divided into certain number of panels. This is the method to decide vortex intensity and blow-out intensity simultaneously from the condition that vertical speed on the camber and the wing surface is zero, upon having distributed blow-out with certain intensity inside the panel. The method solves the inverse problem with the following process: specific point distribution is so determined that the targeted velocity on the wing surface is satisfied when wing surface pressure distribution and uniform flow velocity are given; and then the panels are so rearranged as in parallel with direction of the flow on the surface of the wing calculated by using these specific points to derive the targeted wing shape. This paper describes the problem solving procedure in great detail. It also introduces examples of numerical calculations. It shows one method for solving the inverse problem in wing type using the SQCM as a simple panel method, whereas its good convergence and stability were verified. Considerations on effects of free surface and expansion of the method into three-dimensional problems will be implemented in the future. 11 refs., 8 figs.

14. Regularization and Bayesian methods for inverse problems in signal and image processing

Giovannelli , Jean-François

2015-01-01

The focus of this book is on "ill-posed inverse problems". These problems cannot be solved only on the basis of observed data. The building of solutions involves the recognition of other pieces of a priori information. These solutions are then specific to the pieces of information taken into account. Clarifying and taking these pieces of information into account is necessary for grasping the domain of validity and the field of application for the solutions built.  For too long, the interest in these problems has remained very limited in the signal-image community. However, the community has si

15. Measurement of ground-water storage change and specific yield using the temporal-gravity method near Rillito Creek, Tucson, Arizona

Pool, Donald R.; Schmidt, Werner

1997-01-01

The temporal-gravity method was used to estimate ground-water storage change and specific -yield values at wells near Rillito Creek, Tucson, Arizona, between early December 1992 and early January 1994. The method applies Newton's Law of Gravitation to measure changes in the local gravitational field of the Earth that are caused by changes in the mass and volume of ground water. Gravity at 50 stations in a 6-square-mile area was measured repeatedly relative to gravity at two bedrock stations. Ephemeral recharge through streamflow infiltration during the winter of 1992-93 resulted in water-level rises and gravity increases near Rillito Creek as the volume of ground water in storage increased. Water levels in wells rose as much as 30 feet, and gravity increased as much as 90 microgals. Water levels declined and gravity decreased near the stream after the last major winter flow but continued to rise and increase, respectively, in downgradient areas. Water levels and gravity relative to bedrock were measured at 10 wells. Good linear correlations between water levels and gravity values at five wells nearest the stream allowed for the estimation of specific-yield values for corresponding stratigraphic units assuming the mass change occurred in an infinite horizonal slab of uniform thickness. Specific-yield values for the stream-channel deposits at three wells ranged from 0.15 to 0.34, and correlation coefficients ranged from 0.81 to 0.99. Specific-yield values for the Fort Lowell Formation at three wells ranged from 0.07 to 0.18, and correlation coefficients ranged from 0.82 to 0.93. Specific-yield values were not calculated for the five wells farthest from the stream because of insufficient water-level and gravity change or poor correlations between water level and gravity. Poor correlations between water levels and gravity resulted from ground-water storage change in perched aquifers and in the unsaturated zone near ephemeral streams. Seasonal distributions of ground

16. Modal–Physical Hybrid System Identification of High-rise Building via Subspace and Inverse-Mode Methods

Kohei Fujita

2017-08-01

Full Text Available A system identification (SI problem of high-rise buildings is investigated under restricted data environments. The shear and bending stiffnesses of a shear-bending model (SB model representing the high-rise buildings are identified via the smart combination of the subspace and inverse-mode methods. Since the shear and bending stiffnesses of the SB model can be identified in the inverse-mode method by using the lowest mode of horizontal displacements and floor rotation angles, the lowest mode of the objective building is identified first by using the subspace method. Identification of the lowest mode is performed by using the amplitude of transfer functions derived in the subspace method. Considering the resolution in measuring the floor rotation angles in lower stories, floor rotation angles in most stories are predicted from the floor rotation angle at the top floor. An empirical equation of floor rotation angles is proposed by investigating those for various building models. From the viewpoint of application of the present SI method to practical situations, a non-simultaneous measurement system is also proposed. In order to investigate the reliability and accuracy of the proposed SI method, a 10-story building frame subjected to micro-tremor is examined.

17. Subsurface images of the Eastern Rift, Africa, from the joint inversion of body waves, surface waves and gravity: investigating the role of fluids in early-stage continental rifting

Roecker, S.; Ebinger, C.; Tiberi, C.; Mulibo, G.; Ferdinand-Wambura, R.; Mtelela, K.; Kianji, G.; Muzuka, A.; Gautier, S.; Albaric, J.; Peyrat, S.

2017-08-01

The Eastern Rift System (ERS) of northern Tanzania and southern Kenya, where a cratonic lithosphere is in the early stages of rifting, offers an ideal venue for investigating the roles of magma and other fluids in such an environment. To illuminate these roles, we jointly invert arrival times of locally recorded P and S body waves, phase delays of ambient noise generated Rayleigh waves and Bouguer anomalies from gravity observations to generate a 3-D image of P and S wave speeds in the upper 25 km of the crust. While joint inversion of gravity and arrival times requires a relationship between density and wave speeds, the improvement in resolution obtained by the combination of these disparate data sets serves to further constrain models, and reduce uncertainties. The most significant features in the 3-D model are (1) P and S wave speeds that are 10-15 per cent lower beneath the rift zone than in the surrounding regions, (2) a relatively high wave speed tabular feature located along the western edge of the Natron and Manyara rifts, and (3) low (∼1.71) values of Vp/Vs throughout the upper crust, with the lowest ratios along the boundaries of the rift zones. The low P and S wave speeds at mid-crustal levels beneath the rift valley are an expected consequence of active volcanism, and the tabular, high-wave speed feature is interpreted to be an uplifted footwall at the western edge of the rift. Given the high levels of CO2 outgassing observed at the surface along border fault zones, and the sensitivity of Vp/Vs to pore-fluid compressibility, we infer that the low Vp/Vs values in and around the rift zone are caused by the volcanic plumbing in the upper crust being suffused by a gaseous CO2 froth on top of a deeper, crystalline mush. The repository for molten rock is likely located in the lower crust and upper mantle, where the Vp/Vs ratios are significantly higher.

18. Solitons in Newtonian gravity

Goetz, G.

1988-01-01

It is shown that the plane-wave solutions for the equations governing the motion of a self-gravitating isothermal fluid in Newtonian hydrodynamics are generated by a sine-Gordon equation which is solvable by an 'inverse scattering' transformation. A transformation procedure is outlined by means of which one can construct solutions of the gravity system out of a pair of solutions of the sine-Gordon equation, which are interrelated via an auto-Baecklund transformation. In general the solutions to the gravity system are obtained in a parametric representation in terms of characteristic coordinates. All solutions of the gravity system generated by the one-and two-soliton solutions of the sine-Gordon equation can be constructed explicitly. These might provide models for the evolution of flat structures as they are predicted to arise in the process of galaxy formation. (author)

19. Cybernetic group method of data handling (GMDH) statistical learning for hyperspectral remote sensing inverse problems in coastal ocean optics

Filippi, Anthony Matthew

For complex systems, sufficient a priori knowledge is often lacking about the mathematical or empirical relationship between cause and effect or between inputs and outputs of a given system. Automated machine learning may offer a useful solution in such cases. Coastal marine optical environments represent such a case, as the optical remote sensing inverse problem remains largely unsolved. A self-organizing, cybernetic mathematical modeling approach known as the group method of data handling (GMDH), a type of statistical learning network (SLN), was used to generate explicit spectral inversion models for optically shallow coastal waters. Optically shallow water light fields represent a particularly difficult challenge in oceanographic remote sensing. Several algorithm-input data treatment combinations were utilized in multiple experiments to automatically generate inverse solutions for various inherent optical property (IOP), bottom optical property (BOP), constituent concentration, and bottom depth estimations. The objective was to identify the optimal remote-sensing reflectance Rrs(lambda) inversion algorithm. The GMDH also has the potential of inductive discovery of physical hydro-optical laws. Simulated data were used to develop generalized, quasi-universal relationships. The Hydrolight numerical forward model, based on radiative transfer theory, was used to compute simulated above-water remote-sensing reflectance Rrs(lambda) psuedodata, matching the spectral channels and resolution of the experimental Naval Research Laboratory Ocean PHILLS (Portable Hyperspectral Imager for Low-Light Spectroscopy) sensor. The input-output pairs were for GMDH and artificial neural network (ANN) model development, the latter of which was used as a baseline, or control, algorithm. Both types of models were applied to in situ and aircraft data. Also, in situ spectroradiometer-derived Rrs(lambda) were used as input to an optimization-based inversion procedure. Target variables

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

Li Yao

2013-01-01

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

1. 3D Inversion of Magnetic Data through Wavelet based Regularization Method

Maysam Abedi

2015-06-01

Full Text Available This study deals with the 3D recovering of magnetic susceptibility model by incorporating the sparsity-based constraints in the inversion algorithm. For this purpose, the area under prospect was divided into a large number of rectangular prisms in a mesh with unknown susceptibilities. Tikhonov cost functions with two sparsity functions were used to recover the smooth parts as well as the sharp boundaries of model parameters. A pre-selected basis namely wavelet can recover the region of smooth behaviour of susceptibility distribution while Haar or finite-difference (FD domains yield a solution with rough boundaries. Therefore, a regularizer function which can benefit from the advantages of both wavelets and Haar/FD operators in representation of the 3D magnetic susceptibility distributionwas chosen as a candidate for modeling magnetic anomalies. The optimum wavelet and parameter β which controls the weight of the two sparsifying operators were also considered. The algorithm assumed that there was no remanent magnetization and observed that magnetometry data represent only induced magnetization effect. The proposed approach is applied to a noise-corrupted synthetic data in order to demonstrate its suitability for 3D inversion of magnetic data. On obtaining satisfactory results, a case study pertaining to the ground based measurement of magnetic anomaly over a porphyry-Cu deposit located in Kerman providence of Iran. Now Chun deposit was presented to be 3D inverted. The low susceptibility in the constructed model coincides with the known location of copper ore mineralization.

2. Inverse kinematics for the variable geometry truss manipulator via a Lagrangian dual method

Yanchun Zhao

2016-11-01

Full Text Available This article studies the inverse kinematics problem of the variable geometry truss manipulator. The problem is cast as an optimization process which can be divided into two steps. Firstly, according to the information about the location of the end effector and fixed base, an optimal center curve and the corresponding distribution of the intermediate platforms along this center line are generated. This procedure is implemented by solving a non-convex optimization problem that has a quadratic objective function subject to quadratic constraints. Then, in accordance with the distribution of the intermediate platforms along the optimal center curve, all lengths of the actuators are calculated via the inverse kinematics of each variable geometry truss module. Hence, the approach that we present is an optimization procedure that attempts to generate the optimal intermediate platform distribution along the optimal central curve, while the performance index and kinematic constraints are satisfied. By using the Lagrangian duality theory, a closed-form optimal solution of the original optimization is given. The numerical simulation substantiates the effectiveness of the introduced approach.

3. Inverse methods for the mechanical characterization of materials at high strain rates

Casas-Rodriguez J.P.

2012-08-01

Full Text Available Mechanical material characterization represents a research challenge. Furthermore, special attention is directed to material characterization at high strain rates as the mechanical properties of some materials are influenced by the rate of loading. Diverse experimental techniques at high strain rates are available, such as the drop-test, the Taylor impact test or the Split Hopkinson pressure bar among others. However, the determination of the material parameters associated to a given mathematical constitutive model from the experimental data is a complex and indirect problem. This paper presents a material characterization methodology to determine the material parameters of a given material constitutive model from a given high strain rate experiment. The characterization methodology is based on an inverse technique in which an inverse problem is formulated and solved as an optimization procedure. The input of the optimization procedure is the characteristic signal from the high strain rate experiment. The output of the procedure is the optimum set of material parameters determined by fitting a numerical simulation to the high strain rate experimental signal.

4. An Improved TA-SVM Method Without Matrix Inversion and Its Fast Implementation for Nonstationary Datasets.

Shi, Yingzhong; Chung, Fu-Lai; Wang, Shitong

2015-09-01

Recently, a time-adaptive support vector machine (TA-SVM) is proposed for handling nonstationary datasets. While attractive performance has been reported and the new classifier is distinctive in simultaneously solving several SVM subclassifiers locally and globally by using an elegant SVM formulation in an alternative kernel space, the coupling of subclassifiers brings in the computation of matrix inversion, thus resulting to suffer from high computational burden in large nonstationary dataset applications. To overcome this shortcoming, an improved TA-SVM (ITA-SVM) is proposed using a common vector shared by all the SVM subclassifiers involved. ITA-SVM not only keeps an SVM formulation, but also avoids the computation of matrix inversion. Thus, we can realize its fast version, that is, improved time-adaptive core vector machine (ITA-CVM) for large nonstationary datasets by using the CVM technique. ITA-CVM has the merit of asymptotic linear time complexity for large nonstationary datasets as well as inherits the advantage of TA-SVM. The effectiveness of the proposed classifiers ITA-SVM and ITA-CVM is also experimentally confirmed.

5. Inversion Method for Early Detection of ARES-1 Case Breach Failure

Mackey, Ryan M.; Kulikov, Igor K.; Bajwa, Anupa; Berg, Peter; Smelyanskiy, Vadim

2010-01-01

A document describes research into the problem of detecting a case breach formation at an early stage of a rocket flight. An inversion algorithm for case breach allocation is proposed and analyzed. It is shown how the case breach can be allocated at an early stage of its development by using the rocket sensor data and the output data from the control block of the rocket navigation system. The results are simulated with MATLAB/Simulink software. The efficiency of an inversion algorithm for a case breach location is discussed. The research was devoted to the analysis of the ARES-l flight during the first 120 seconds after the launch and early prediction of case breach failure. During this time, the rocket is propelled by its first-stage Solid Rocket Booster (SRB). If a breach appears in SRB case, the gases escaping through it will produce the (side) thrust directed perpendicular to the rocket axis. The side thrust creates torque influencing the rocket attitude. The ARES-l control system will compensate for the side thrust until it reaches some critical value, after which the flight will be uncontrollable. The objective of this work was to obtain the start time of case breach development and its location using the rocket inertial navigation sensors and GNC data. The algorithm was effective for the detection and location of a breach in an SRB field joint at an early stage of its development.

6. Determination of temperature dependency of material parameters for lead-free alkali niobate piezoceramics by the inverse method

K. Ogo

2016-06-01

Full Text Available Sodium potassium niobate (NKN piezoceramics have been paid much attention as lead-free piezoelectric materials in high temperature devices because of their high Curie temperature. The temperature dependency of their material parameters, however, has not been determined in detail up to now. For this purpose, we exploit the so-called Inverse Method denoting a simulation-based characterization approach. Compared with other characterization methods, the Inverse Method requires only one sample shape of the piezoceramic material and has further decisive advantages. The identification of material parameters showed that NKN is mechanically softer in shear direction compared with lead zirconate titanate (PZT at room temperature. The temperature dependency of the material parameters of NKN was evaluated in the temperature range from 30 °C to 150 °C. As a result, we figured out that dielectric constants and piezoelectric constants show a monotonous and isotropic increment with increasing temperature. On the other hand, elastic stiffness constant c 44 E of NKN significantly decreased in contrast to other elastic stiffness constants. It could be revealed that the decrement of c 44 E is associated with an orthorhombic-tetragonal phase transition. Furthermore, ratio of elastic compliance constants s 44 E / s 33 E exhibited similar temperature dependent behavior to the ratio of piezoelectric constants d15/d33. It is suspected that mechanical softness in shear direction is one origin of the large piezoelectric shear mode of NKN. Our results show that NKN are suitable for high temperature devices, and that the Inverse Method should be a helpful approach to characterize material parameters under their practical operating conditions for NKN.

7. The measurement problem on classical diffusion process: inverse method on stochastic processes

Bigerelle, M.; Iost, A.

2004-01-01

In a high number of diffusive systems, measures are processed to calculate material parameters such as diffusion coefficients, or to verify the accuracy of mathematical models. However, the precision of the parameter determination or of the model relevance depends on the location of the measure itself. The aim of this paper is first to analyse, for a mono-dimensional system, the precision of the measure in relation with its location by an inverse problem algorithm and secondly to examine the physical meaning of the results. Statistical mechanic considerations show that, passing over a time-distance criterion, measurement becomes uncertain whatever the initial conditions. The criterion proves that this chaotic mode is related to the production of anti-entropy at a mesoscopique scale that is in violation to quantum theory about measurement

8. Noise source localization on tyres using an inverse boundary element method

Schuhmacher, Andreas; Saemann, E-U; Hald, J

1998-01-01

A dominating part of tyre noise is radiated from a region close to the tyre/road contact patch, where it is very difficult to measure both the tyre vibration and the acoustic near field. The approach taken in the present paper is to model the tyre and road surfaces with a Boundary Element Model...... (BEM), with unknown node vibration data on the tyre surface. The BEM model is used to calculate a set of transfer functions from the node vibrations to the sound pressure at a set of microphone positions around the tyre. By approximate inversion of the matrix of transfer functions, the surface...... from tyre noise measurements will be presented at the conference....

9. Comparison of lipid and calorie loss from donor human milk among 3 methods of simulated gavage feeding: one-hour, 2-hour, and intermittent gravity feedings.

Brooks, Christine; Vickers, Amy Manning; Aryal, Subhash

2013-04-01

The objective of this study was to compare the differences in lipid loss from 24 samples of banked donor human milk (DHM) among 3 feeding methods: DHM given by syringe pump over 1 hour, 2 hours, and by bolus/gravity gavage. Comparative, descriptive. There were no human subjects. Twenty-four samples of 8 oz of DHM were divided into four 60-mL aliquots. Timed feedings were given by Medfusion 2001 syringe pumps with syringes connected to narrow-lumened extension sets designed for enteral feedings and connected to standard silastic enteral feeding tubes. Gravity feedings were given using the identical syringes connected to the same silastic feeding tubes. All aliquots were analyzed with the York Dairy Analyzer. Univariate repeated-measures analyses of variance were used for the omnibus testing for overall differences between the feeding methods. Lipid content expressed as grams per deciliter at the end of each feeding method was compared with the prefed control samples using the Dunnett's test. The Tukey correction was used for other pairwise multiple comparisons. The univariate repeated-measures analysis of variance conducted to test for overall differences between feeding methods showed a significant difference between the methods (F = 58.57, df = 3, 69, P gravity feeding methods (P = .3296). Pairwise comparison using the Tukey correction revealed a significant difference between both gravity and 1-hour feeding methods (P gravity and 2-hour feeding method (P gravity feedings, the timed feedings resulted in a statistically significant loss of fat as compared with their controls. These findings should raise questions about how those infants in the neonatal intensive care unit are routinely gavage fed.

10. Singularity resolution in quantum gravity

Husain, Viqar; Winkler, Oliver

2004-01-01

We examine the singularity resolution issue in quantum gravity by studying a new quantization of standard Friedmann-Robertson-Walker geometrodynamics. The quantization procedure is inspired by the loop quantum gravity program, and is based on an alternative to the Schroedinger representation normally used in metric variable quantum cosmology. We show that in this representation for quantum geometrodynamics there exists a densely defined inverse scale factor operator, and that the Hamiltonian constraint acts as a difference operator on the basis states. We find that the cosmological singularity is avoided in the quantum dynamics. We discuss these results with a view to identifying the criteria that constitute 'singularity resolution' in quantum gravity

11. Intestinal absorption of radiocalcium. Measurement by the oral and intraveinous activity ratio and by the inverse convolution method

Monnier, L.; Collet, H.; Suquet, P.; Mirouze, J.

1975-01-01

The intestinal absorption of calcium was measured by a double isotopic labelling method, the results being obtained by a mathematical deconvolution technique. This analytical method was compared with the simple measurement of the plasma radioactivity ratio for the two isotopes administered orally and intraveinously respectively. The study covered 29 determinations. It was possible to estimate the total fractional absorption of calcium (TFACa) by calculating the average of the 47 Ca/ 45 Ca quotients measured on the 3rd and 8th hour after simultaneous administration of 45 Ca intraveinously and 47 Ca by mouth. The advantages of this method are obvious: need for only two blood samplings, simplicity of calculations which nevertheless give TFACa values comparable to those obtained by deconvolution analysis. However the only information supplied by the quotients method is the total fractional absorption, whereas inverse convolution analysis provides several interesting parameters such as the maximum absorption and the mean transit time of radiocalcium through the intestinal wall [fr

12. The numerical method of inverse Laplace transform for calculation of overvoltages in power transformers and test results

Mikulović Jovan Č.

2014-01-01

Full Text Available A methodology for calculation of overvoltages in transformer windings, based on a numerical method of inverse Laplace transform, is presented. Mathematical model of transformer windings is described by partial differential equations corresponding to distributed parameters electrical circuits. The procedure of calculating overvoltages is applied to windings having either isolated neutral point, or grounded neutral point, or neutral point grounded through impedance. A comparative analysis of the calculation results obtained by the proposed numerical method and by analytical method of calculation of overvoltages in transformer windings is presented. The results computed by the proposed method and measured voltage distributions, when a voltage surge is applied to a three-phase 30 kVA power transformer, are compared. [Projekat Ministartsva nauke Republike Srbije, br. TR-33037 i br. TR-33020

13. Inverse Kinematics using Quaternions

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....

14. A three-step Maximum-A-Posterior probability method for InSAR data inversion of coseismic rupture with application to four recent large earthquakes in Asia

Sun, J.; Shen, Z.; Burgmann, R.; Liang, F.

2012-12-01

We develop a three-step Maximum-A-Posterior probability (MAP) method for coseismic rupture inversion, which aims at maximizing the a posterior probability density function (PDF) of elastic solutions of earthquake rupture. The method originates from the Fully Bayesian Inversion (FBI) and the Mixed linear-nonlinear Bayesian inversion (MBI) methods , shares the same a posterior PDF with them and keeps most of their merits, while overcoming its convergence difficulty when large numbers of low quality data are used and improving the convergence rate greatly using optimization procedures. A highly efficient global optimization algorithm, Adaptive Simulated Annealing (ASA), is used to search for the maximum posterior probability in the first step. The non-slip parameters are determined by the global optimization method, and the slip parameters are inverted for using the least squares method without positivity constraint initially, and then damped to physically reasonable range. This step MAP inversion brings the inversion close to 'true' solution quickly and jumps over local maximum regions in high-dimensional parameter space. The second step inversion approaches the 'true' solution further with positivity constraints subsequently applied on slip parameters using the Monte Carlo Inversion (MCI) technique, with all parameters obtained from step one as the initial solution. Then the slip artifacts are eliminated from slip models in the third step MAP inversion with fault geometry parameters fixed. We first used a designed model with 45 degree dipping angle and oblique slip, and corresponding synthetic InSAR data sets to validate the efficiency and accuracy of method. We then applied the method on four recent large earthquakes in Asia, namely the 2010 Yushu, China earthquake, the 2011 Burma earthquake, the 2011 New Zealand earthquake and the 2008 Qinghai, China earthquake, and compared our results with those results from other groups. Our results show the effectiveness of

15. Gravity Data for Egypt

National Oceanic and Atmospheric Administration, Department of Commerce — The gravity station data (71 records) were gathered by various governmental organizations (and academia) using a variety of methods. This data base was received in...

16. DMA Antarctic Gravity Data

National Oceanic and Atmospheric Administration, Department of Commerce — The gravity station data (65,164 records) were gathered by various governmental organizations (and academia) using a variety of methods. The data base was received...

17. Gravity Data for Minnesota

National Oceanic and Atmospheric Administration, Department of Commerce — The gravity station data (55,907 records) were gathered by various governmental organizations (and academia) using a variety of methods. This data base was received...

18. Developing a Method for Resolving NOx Emission Inventory Biases Using Discrete Kalman Filter Inversion, Direct Sensitivities, and Satellite-Based Columns

An inverse method was developed to integrate satellite observations of atmospheric pollutant column concentrations and direct sensitivities predicted by a regional air quality model in order to discern biases in the emissions of the pollutant precursors.

19. Sofalica Region (GAZIANTEP Chromium on Microgravity Anomalies Modelling of Normalized Full Gradient and Nonlinear Inversion

Birgül Kınalıbalaban

2013-08-01

Full Text Available In this study, the province of Gaziantep, Şehitkamil district, there are thought to be chrome-metallic mine in the village of Sofalıca the localization of gravity and economical method was to investigate whether it has a reserve. Approximately 189 hectares of land gravity measurements over the measurement point in the study area was 220. By differentiating regional and residual Bouguer gravity map of the generated residual maps were obtained on areas likely to be created on the source. The inversion method of pre-NTG was required for the selection model is the appropriate start. On the structure of polygon slices as a result of application received in the form of the inversion in the range of 125 meters and 450 meters long, 25 meters to 70 meters in thickness in the range of existence of geometric structures have been identified.

20. Structural and magnetic properties of multi-core nanoparticles analysed using a generalised numerical inversion method

Bender, P.; Bogart, L. K.; Posth, O.; Szczerba, W.; Rogers, S. E.; Castro, A.; Nilsson, L.; Zeng, L. J.; Sugunan, A.; Sommertune, J.; Fornara, A.; González-Alonso, D.; Barquín, L. Fernández; Johansson, C.

2017-01-01

The structural and magnetic properties of magnetic multi-core particles were determined by numerical inversion of small angle scattering and isothermal magnetisation data. The investigated particles consist of iron oxide nanoparticle cores (9 nm) embedded in poly(styrene) spheres (160 nm). A thorough physical characterisation of the particles included transmission electron microscopy, X-ray diffraction and asymmetrical flow field-flow fractionation. Their structure was ultimately disclosed by an indirect Fourier transform of static light scattering, small angle X-ray scattering and small angle neutron scattering data of the colloidal dispersion. The extracted pair distance distribution functions clearly indicated that the cores were mostly accumulated in the outer surface layers of the poly(styrene) spheres. To investigate the magnetic properties, the isothermal magnetisation curves of the multi-core particles (immobilised and dispersed in water) were analysed. The study stands out by applying the same numerical approach to extract the apparent moment distributions of the particles as for the indirect Fourier transform. It could be shown that the main peak of the apparent moment distributions correlated to the expected intrinsic moment distribution of the cores. Additional peaks were observed which signaled deviations of the isothermal magnetisation behavior from the non-interacting case, indicating weak dipolar interactions. PMID:28397851