Uniqueness and Lipschitz stability of an inverse boundary value problem for time-harmonic elastic waves

TL;DR

This paper proves that it is uniquely possible and stably feasible to determine elastic parameters and density in a 3D elastic body from boundary measurements, assuming these parameters are piecewise constant.

Contribution

It establishes the first Lipschitz stability result for the inverse boundary value problem for elastic waves with piecewise constant parameters.

Findings

Uniqueness of the inverse problem solution

Lipschitz stability under piecewise constant assumptions

Applicable to 3D elastic bodies

Abstract

We consider the inverse problem of determining the Lam\'{e} parameters and the density of a three-dimensional elastic body from the local time-harmonic Dirichlet-to-Neumann map. We prove uniqueness and Lipschitz stability of this inverse problem when the Lam\'{e} parameters and the density are assumed to be piecewise constant on a given domain partition.