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Statistical Stability and Time-Reversal Imgaing in Random Media

Description: Localization of targets imbedded in a heterogeneous background medium is a common problem in seismic, ultrasonic, and electromagnetic imaging problems. The best imaging techniques make direct use of the eigenfunctions and eigenvalues of the array response matrix, as recent work on time-reversal acoustics has shown. Of the various imaging functionals studied, one that is representative of a preferred class is a time-domain generalization of MUSIC (MUltiple Signal Classification), which is a well-known linear subspace method normally applied only in the frequency domain. Since statistical stability is not characteristic of the frequency domain, a transform back to the time domain after first diagonalizing the array data in the frequency domain takes optimum advantage of both the time-domain stability and the frequency-domain orthogonality of the relevant eigenfunctions.
Date: February 5, 2002
Creator: Berryman, J; Borcea, L; Papanicolaou, G & Tsogka, C
Partner: UNT Libraries Government Documents Department

Network asymptotics for high contrast impedance tomography

Description: Fluid contaminant plumes underground are often electrically conducting and, therefore, can be imaged using electrical impedance tomography. The authors introduce an output least-squares method for impedance tomography problems that have regions of high conductivity surrounded by regions of lower conductivity. The high conductivity is modeled on network approximation results from an asymptotic analysis and its recovery is based on this model. The smoothly varying part of the conductivity is recovered by a linearization process as is usual. The authors present the results of several numerical experiments that illustrate the performance of the method.
Date: May 1, 1996
Creator: Borcea, L.; Papanicolaou, G.C. & Berryman, J.G.
Partner: UNT Libraries Government Documents Department

Optimization and geophysical inverse problems

Description: A fundamental part of geophysics is to make inferences about the interior of the earth on the basis of data collected at or near the surface of the earth. In almost all cases these measured data are only indirectly related to the properties of the earth that are of interest, so an inverse problem must be solved in order to obtain estimates of the physical properties within the earth. In February of 1999 the U.S. Department of Energy sponsored a workshop that was intended to examine the methods currently being used to solve geophysical inverse problems and to consider what new approaches should be explored in the future. The interdisciplinary area between inverse problems in geophysics and optimization methods in mathematics was specifically targeted as one where an interchange of ideas was likely to be fruitful. Thus about half of the participants were actively involved in solving geophysical inverse problems and about half were actively involved in research on general optimization methods. This report presents some of the topics that were explored at the workshop and the conclusions that were reached. In general, the objective of a geophysical inverse problem is to find an earth model, described by a set of physical parameters, that is consistent with the observational data. It is usually assumed that the forward problem, that of calculating simulated data for an earth model, is well enough understood so that reasonably accurate synthetic data can be generated for an arbitrary model. The inverse problem is then posed as an optimization problem, where the function to be optimized is variously called the objective function, misfit function, or fitness function. The objective function is typically some measure of the difference between observational data and synthetic data calculated for a trial model. However, because of incomplete and inaccurate data, the ...
Date: October 1, 2000
Creator: Barhen, J.; Berryman, J.G.; Borcea, L.; Dennis, J.; de Groot-Hedlin, C.; Gilbert, F. et al.
Partner: UNT Libraries Government Documents Department