Optimization and geophysical inverse problems
Abstract
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 setmore »
 Authors:
 Publication Date:
 Research Org.:
 Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
 Sponsoring Org.:
 Earth Sciences Division
 OSTI Identifier:
 939130
 Report Number(s):
 LBNL46959
TRN: US200823%%117
 DOE Contract Number:
 DEAC0205CH11231
 Resource Type:
 Technical Report
 Country of Publication:
 United States
 Language:
 English
 Subject:
 58; EVALUATION; GEOPHYSICS; MEDICINE; OPTIMIZATION; PARTIAL DIFFERENTIAL EQUATIONS; PHYSICAL PROPERTIES; PHYSICS; RESOLUTION; ROUGHNESS
Citation Formats
Barhen, J., Berryman, J.G., Borcea, L., Dennis, J., de GrootHedlin, C., Gilbert, F., Gill, P., Heinkenschloss, M., Johnson, L., McEvilly, T., More, J., Newman, G., Oldenburg, D., Parker, P., Porto, B., Sen, M., Torczon, V., Vasco, D., and Woodward, N.B.. Optimization and geophysical inverse problems. United States: N. p., 2000.
Web. doi:10.2172/939130.
Barhen, J., Berryman, J.G., Borcea, L., Dennis, J., de GrootHedlin, C., Gilbert, F., Gill, P., Heinkenschloss, M., Johnson, L., McEvilly, T., More, J., Newman, G., Oldenburg, D., Parker, P., Porto, B., Sen, M., Torczon, V., Vasco, D., & Woodward, N.B.. Optimization and geophysical inverse problems. United States. doi:10.2172/939130.
Barhen, J., Berryman, J.G., Borcea, L., Dennis, J., de GrootHedlin, C., Gilbert, F., Gill, P., Heinkenschloss, M., Johnson, L., McEvilly, T., More, J., Newman, G., Oldenburg, D., Parker, P., Porto, B., Sen, M., Torczon, V., Vasco, D., and Woodward, N.B.. Sun .
"Optimization and geophysical inverse problems". United States.
doi:10.2172/939130. https://www.osti.gov/servlets/purl/939130.
@article{osti_939130,
title = {Optimization and geophysical inverse problems},
author = {Barhen, J. and Berryman, J.G. and Borcea, L. and Dennis, J. and de GrootHedlin, C. and Gilbert, F. and Gill, P. and Heinkenschloss, M. and Johnson, L. and McEvilly, T. and More, J. and Newman, G. and Oldenburg, D. and Parker, P. and Porto, B. and Sen, M. and Torczon, V. and Vasco, D. and Woodward, N.B.},
abstractNote = {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 objective function often incorporates some additional form of regularization, such as a measure of smoothness or distance from a prior model. Various other constraints may also be imposed upon the process. Inverse problems are not restricted to geophysics, but can be found in a wide variety of disciplines where inferences must be made on the basis of indirect measurements. For instance, most imaging problems, whether in the field of medicine or nondestructive evaluation, require the solution of an inverse problem. In this report, however, the examples used for illustration are taken exclusively from the field of geophysics. The generalization of these examples to other disciplines should be straightforward, as all are based on standard secondorder partial differential equations of physics. In fact, sometimes the nongeophysical inverse problems are significantly easier to treat (as in medical imaging) because the limitations on data collection, and in particular on multiple views, are not so severe as they generally are in geophysics. This report begins with an introduction to geophysical inverse problems by briefly describing four canonical problems that are typical of those commonly encountered in geophysics. Next the connection with optimization methods is made by presenting a general formulation of geophysical inverse problems. This leads into the main subject of this report, a discussion of methods for solving such problems with an emphasis upon newer approaches that have not yet become prominent in geophysics. A separate section is devoted to a subject that is not encountered in all optimization problems but is particularly important in geophysics, the need for a careful appraisal of the results in terms of their resolution and uncertainty. The impact on geophysical inverse problems of continuously improving computational resources is then discussed. The main results are then brought together in a final summary and conclusions section.},
doi = {10.2172/939130},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Sun Oct 01 00:00:00 EDT 2000},
month = {Sun Oct 01 00:00:00 EDT 2000}
}

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