Scattering Techniques for the Geophysical Inverse Problem
Santosa, Fadil
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Permalink
https://hdl.handle.net/2142/68514
Description
Title
Scattering Techniques for the Geophysical Inverse Problem
Author(s)
Santosa, Fadil
Issue Date
1980
Department of Study
Theoretical and Applied Mechanics
Discipline
Theoretical and Applied Mechanics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Applied Mechanics
Geological Survey
Language
eng
Abstract
We consider the inverse problem for the propagation of elastic waves in stratified media. The one-dimensional inverse problem for the propagation of shear waves is studied in the context of spectral theory. We generalize certain inverse scattering methods in quantum mechanics to determine the properties of the stratification from experimental knowledge gathered at the origin of the half-line. We further apply this method with some mathematical manipulations to arrive at a procedure to solve the inverse problem for a three-dimensional layered half space. This formulation of the problem lead to the complete and unique reconstruction of the depth dependences of the Lame parameters and the density from surface data. A discussion on the applicability of the proposed profile inversion method is given, and it is demonstrated with a numerical example.
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