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Understanding Inverse Theory

Understanding Inverse Theory Much of our knowledge of the Earth's interior is perforce based on the interpretation of measurements made at the surface, rather than direct sampling of the material in the interior. In the past few years there have been great advances in the mathematical aspects of this problem, and the topic has come to be called geo­ physical inverse theory. To apply these ideas, there must be a valid mathematical model of the physics of the system under study, so that one would be able to calculate the values of observations made on an exactly known structure: the calculation of the behavior of a specified system is the solution of the "forward" or "direct" problem. Frequently it is the forward problem that presents a difficult challenge to the theoretical geophysicist. Illustrations include the mechanism of earthquake rupture or the generation of the Earth's magnetic field; in problems like these, inverse theory is normally quite inappropriate. When the forward problem has been completely solved, there are of course unknown parameters in the mathematical model representing physical properties of the Earth such as Lame parameters, density or electrical conductivity. The goal of inverse theory is to determine the parameters from the http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Annual Review of Earth and Planetary Sciences Annual Reviews

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References (32)

Publisher
Annual Reviews
Copyright
Copyright 1977 Annual Reviews. All rights reserved
Subject
Review Articles
ISSN
0084-6597
eISSN
1545-4495
DOI
10.1146/annurev.ea.05.050177.000343
Publisher site
See Article on Publisher Site

Abstract

Much of our knowledge of the Earth's interior is perforce based on the interpretation of measurements made at the surface, rather than direct sampling of the material in the interior. In the past few years there have been great advances in the mathematical aspects of this problem, and the topic has come to be called geo­ physical inverse theory. To apply these ideas, there must be a valid mathematical model of the physics of the system under study, so that one would be able to calculate the values of observations made on an exactly known structure: the calculation of the behavior of a specified system is the solution of the "forward" or "direct" problem. Frequently it is the forward problem that presents a difficult challenge to the theoretical geophysicist. Illustrations include the mechanism of earthquake rupture or the generation of the Earth's magnetic field; in problems like these, inverse theory is normally quite inappropriate. When the forward problem has been completely solved, there are of course unknown parameters in the mathematical model representing physical properties of the Earth such as Lame parameters, density or electrical conductivity. The goal of inverse theory is to determine the parameters from the

Journal

Annual Review of Earth and Planetary SciencesAnnual Reviews

Published: May 1, 1977

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