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Inversion of Head Wave Traveltimes for Three-Dimensional Planar Structure

Description: Inversion of head wave arrival times for three-dimensional (3D) planar structure is formulated as a constrained parameter optimization problem, and solved via linear programming techniques. The earth model is characterized by a set of homogeneous and isotropic layers bounded by plane, dipping interfaces. Each interface may possess arbitrary strike and dip. Predicted data consists of traveltimes of critically refracted waves formed on the plane interfaces of the model. The nonlinear inversion procedure is iterative; an initial estimate of the earth model is refined until an acceptable match is obtained between observed and predicted data. Inclusion of a priori constraint information, in the form of inequality relations satisfied by the model parameters, assists the algorithm in converging toward a realistic solution. Although the 3D earth model adopted for the inversion procedure is simple, the algorithm is quite useful in two particular contexts: (i) it can provide an initial model estimate suitable for subsequent improvement by more general techniques (i.e., traveltime tomography), and (ii) it is an effective analysis tool for investigating the power of areal recording geometries for detecting and resolving 3D dipping planar structure.
Date: March 31, 1999
Creator: Aldridge, D.F. & Oldenburg, D.W.
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