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The scattering of acoustic waves by a spherically stratified inhomogeneous medium*†

Published online by Cambridge University Press:  14 February 2012

David Colton
David Colton
Affiliation:
Department of Mathematics, University of Strathclyde
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Synopsis

Integral operators are used to solve the direct and inverse problems of the scattering of acoustic waves by a spherically stratified inhomogeneous medium of compact support. The results are valid for all values of the wave number and an arbitrarily large index of refraction. In the limiting case of small wave number or small inhomogeneities the results are in agreement with those of Rorres and Born.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 76 , Issue 4 , 1977 , pp. 345 - 350
Copyright
Copyright © Royal Society of Edinburgh 1977

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References

1Colton, D.. Solution of boundary value problems by the method of integral operators (London: Pitman Press, 1976).Google Scholar
2Colton, D.. The inverse scattering problem for acoustic waves in a spherically stratified medium. Proc. Edinburgh Math. Soc, to appear.Google Scholar
3Colton, D. and Wendland, W.. Constructive methods for solving the exterior Neumann problem for the reduced wave equation in a spherically symmetric medium. Proc. Roy. Soc. Edinburgh Sect. A 75 (1976), 97–107.Google Scholar
4De Alfaro, V. and Regge, T.. Potential scattering (Amsterdam: North-Holland Pub. Co., 1965).Google Scholar
5Friedman, A.. Partial differential equations (New York: Holt, Rinehardt and Winston, 1969.)Google Scholar
6Gilbert, R. P.. Constructive methods for elliptic equations. Lecture notes in mathematics 365 (Berlin: Springer, 1974).Google Scholar
7Gilbert, R. P. and Linz, P.. The numerical solution of some elliptic boundary value problems by integral operator methods. In Constructive and computational methods for differential and integral equations 430 (Berlin: Springer, 1974).Google Scholar
8Morse, P. M. and Feshbach, H.. Methods of mathematical physics Pt II (New York: McGraw-Hill, 1953).Google Scholar
9Rorres, C.. Low energy scattering by an inhomogeneous medium and by a potential. Arch. Rational Mech. Anal. 39 (1970), 340–357.Google Scholar