Inverse scattering by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium

TL;DR

This paper addresses the inverse scattering problem for inhomogeneous obstacles in layered media, establishing uniqueness results for determining interfaces and inhomogeneities from far-field data using integral equations and reciprocity relations.

Contribution

It introduces a new approach combining integral equations, reciprocity, and a priori estimates to uniquely recover interfaces and inhomogeneities in layered media.

Findings

Unique determination of penetrable interfaces from far-field data

Establishment of well-posedness of the direct scattering problem

Development of tools for inverse problem analysis in layered media

Abstract

This paper is concerned with the inverse problem of scattering of time-harmonic acoustic waves by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is first established by using the integral equation method. We then proceed to establish two tools that play an important role for the inverse problem: one is a mixed reciprocity relation and the other is a priori estimates of the solution on some part of the interfaces between the layered media. For the inverse problem, we prove in this paper that both the penetrable interfaces and the possible inside inhomogeneity can be uniquely determined from a knowledge of the far field pattern for incident plane waves.