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Impedance inversion from transmission data for the wave equation

✍ Scribed by Rakesh; Paul Sacks

Publisher
Elsevier Science
Year
1996
Tongue
English
Weight
789 KB
Volume
24
Category
Article
ISSN
0165-2125

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✦ Synopsis

We study the problem of determining an unknown impedance q(x) in the wave equation q(x)~ -(q(x)u,), = 0 using transmission data u(X, t) for X 5 t 5 3X. Here u(x, t) is an impulse response function, satisfying u(n, t) = 0 for t 5 0 and -ux(O, t) = s(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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