THE INVERSE SCATTERING PROBLEM FOR TIME-HARMONIC ACOUSTIC WAVES IN AN INHOMOGENEOUS MEDIUM
- 1 January 1988
- journal article
- Published by Oxford University Press (OUP) in The Quarterly Journal of Mechanics and Applied Mathematics
- Vol. 41 (1) , 97-125
- https://doi.org/10.1093/qjmam/41.1.97
Abstract
We consider the inverse scattering problem of determining the speed of sound in an inhomogeneous medium of compact support from a knowledge of the far-field patterns of the scattered fields corresponding to many incident time-harmonic plane waves. Based on the investigation of a new class of boundary-value problems for the reduced wave equation, we show that the far-field patterns are all clustered around a hyperplane in L2(δΩ), where δΩ is the unit sphere. This result leads to two distinct optimization schemes for solving the inverse scattering problem. For the case of many incident plane waves, the second of these schemes is numerically more economical and using this scheme we provide numerical examples for the case of a spherically stratified medium.Keywords
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