Unique identification of a multi-layered fluid\u2013solid medium

Yanli Cui,Xiliang Li,Fenglong Qu

doi:10.1186/s13661-020-01397-2

Abstract

This paper is concerned with the inverse scattering of time-harmonic acoustic plane waves by a multi-layered fluid–solid medium in the three dimensional space. We establish the global uniqueness in identifying the embedded penetrable solid obstacle, the surrounding fluid medium and its wave number from the acoustic far-field pattern for all incident plane waves at a fixed frequency. The proof depends on constructing different kinds of interior transmission problems in appropriate small domains and the a priori estimates derived for both the elastic wave fields in the embedded solid obstacle and the acoustic wave fields in the surrounding fluid medium.

Highlights

1 Introduction Consider the inverse problem of scattering of time-harmonic acoustic plane waves by a bounded penetrable elastic obstacle embedded in an inhomogeneous acoustic background medium
The fluid–solid interaction problem under consideration is modeled by the Helmholtz equation with different wave numbers in the layered fluid medium, where the solution is continuous across the interface, and satisfies the Navier equation in the solid obstacle
A coupled transmission condition is imposed on the interface between the solid obstacle and the surrounding fluid medium

Summary

Introduction

Consider the inverse problem of scattering of time-harmonic acoustic plane waves by a bounded penetrable elastic obstacle embedded in an inhomogeneous acoustic background medium. Relying on constructing complex geometrical optics solutions method, [26] proved a uniqueness theorem in recovering a penetrable obstacle, which was extended to the case of the elastic scattering problem [19] and Maxwell’s equations [18].

Results

Conclusion