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An injective far-field pattern operator and inverse scattering problem in a finite depth ocean

Published online by Cambridge University Press:  20 January 2009

Yongzhi Xu
Yongzhi Xu
Affiliation:
Institute for Mathematics and its ApplicationsUniversity of MinnesotaMinneapolis, MN 55455, USA
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The inverse scattering problem for acoustic waves in shallow oceans are different from that in the spaces of R2 and R3 in the way that the “propagating” far-field pattern can only carry the information from the N +1 propagating modes. This loss of information leads to the fact that the far-field pattern operator is not injective. In this paper, we will present some properties of the far-field pattern operator and use this information to construct an injective far-field pattern operator in a suitable subspace of L2(∂Ω). Based on this construction an optimal scheme for solving the inverse scattering problem is presented using the minimizing Tikhonov functional.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , Issue 2 , June 1991 , pp. 295 - 311
Copyright
Copyright © Edinburgh Mathematical Society 1991

References

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