Simultaneous recovery of a locally rough interface and the embedded obstacle with its surrounding medium

TL;DR

This paper develops a mathematical framework for uniquely recovering a rough interface, embedded obstacles, and medium properties in a scattering problem using near-field measurements, with well-posed integral formulations.

Contribution

It introduces a novel integral equation approach and proves global uniqueness for the simultaneous recovery of interface, obstacles, and medium parameters.

Findings

Well-posed integral equation formulation in $L^p$

Global uniqueness theorem for inverse scattering problem

Recovery of interface, obstacles, and wave number from near-field data

Abstract

Consider the scattering of time-harmonic point sources by an infinite locally rough interface with bounded obstacles embedded in the lower half-space. The model problem is first reduced to an equivalent integral equation formulation defined in a bounded domain, where the well-posedness is obtained in $L^p$ by the classical Fredholm theory. Then a global uniqueness theorem is proved for the inverse problem of recovering the locally rough interface, the embedded obstacles and the wave number in the lower-half space by means of near-field measurements above the interface.