Inverse problems for a coupled system of wave equations with point source-receiver data

TL;DR

This paper investigates the uniqueness of recovering matrix-valued potentials in coupled wave equations from time-dependent data, considering both coincident and separated source-receiver configurations in three-dimensional space.

Contribution

It establishes the fundamental solution for the operator and proves uniqueness results for inverse problems with additional assumptions on the potential.

Findings

Proved uniqueness of potential recovery in coupled wave systems.

Analyzed both coincident and separated source-receiver setups.

Established fundamental solutions for the operator.

Abstract

The present manuscript consists of inverse problems for a coupled system of wave equations with potential in $\mathbb{R}^3$. By establishing the fundamental solution to the aforementioned operator, we study the uniqueness aspects of the inverse problem of recovering the matrix-valued potential coefficient from time-dependent measurements. We consider these inverse problems in two different cases: (i) the {\it coincident} setup, where the source and receiver are located at a single point, and (ii) the {\it non-coincidence or separated} setup, in which case source and receiver are situated at distinct locations. The problems considered here are under-determined; hence, some additional assumptions for the potential are expected to guarantee the uniqueness of the inverse problems considered in this article. We proved the desired uniqueness results under some extra assumptions on the coefficients.