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An inverse scattering problem for acoustic waves in a spherically stratified medium*

Published online by Cambridge University Press:  20 January 2009

David Colton
David Colton
Affiliation:
Department of Mathematics, University of Strathclyde, Glasgow, Scotland
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The inverse problem we will consider in this paper has its origins in the following problem connected with the scattering of acoustic waves in a nonhomogeneous medium. Let an incoming plane acoustic wave of frequency ω moving in the direction of the z axis be scattered off a “soft” sphere Ω of radius one which is surrounded by a pocket of rarefied or condensed air in which the local speed of sound is given by c(r) where r = |x| for x ∈ R3. Let us(x)eiωt be the velocity potential of the scattered wave and let r, θ, φ be spherical coordinates in R3. Then from a knowledge of the far field pattern f(θ, φ, λ) for λ = ω/c0 contained in some finite interval 0 < λ0 ≤ λ ≤ λ1,, we would like to determine the unknown function c(r).

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 20 , Issue 3 , March 1977 , pp. 257 - 263
Copyright
Copyright © Edinburgh Mathematical Society 1977

References

REFERENCES

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