Inverse scattering by an inhomogeneous penetrable obstacle in a piecewise homogeneous medium
Provides theoretical uniqueness results for an inverse scattering problem in piecewise homogeneous media, which is a niche but rigorous contribution.
The paper establishes uniqueness for recovering both the penetrable interfaces and internal inhomogeneity of an obstacle in a layered medium from far-field data, using integral equation methods and new reciprocity relations.
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.