Proceedings of the Edinburgh Mathematical Society (Series 2)

Table of Contents - Volume 34 - Issue02

Research Article

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

Yongzhi Xua1*

a1 Institute for Mathematics and its Applications University of Minnesota Minneapolis, MN 55455, USA

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.

(Received August 28 1989)

Footnotes

* This work is supported in part by Sea Grant NA86AA-D-SG040.

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