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Impedance inversion from transmission data for the wave equation

Authors
Journal
Wave Motion
0165-2125
Publisher
Elsevier
Publication Date
Volume
24
Issue
3
Identifiers
DOI: 10.1016/s0165-2125(96)00013-3

Abstract

Abstract We study the problem of determining an unknown impedance η( x) in the wave equation η( x) u tt − ( η( x) u x ) x = 0 using transmission data u( X, t) for X ≤ t ≤ 3 X. Here u( x, t) is an impulse response function, satisfying u( x, t) = 0 for t ≤ 0 and − u x (0, t) = δ( t), the Dirac delta function. We prove a uniqueness result, and discuss a numerical solution method. A central ingredient in the analysis is that we can relate the transmission inverse problem to an inverse problem for reflection data ( X = 0) whose theory is quite well understood.

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