Recovery of piecewise smooth density and Lam\'e parameters from high-frequency exterior Cauchy data

TL;DR

This paper develops a method to recover both density and Lamé parameters of an elastic medium from high-frequency exterior Cauchy data, extending previous work that only recovered wave speeds, using microlocal analysis and tensor tomography.

Contribution

It introduces a novel approach to simultaneously recover density and elastic parameters from exterior data, expanding the scope of inverse elastic problems.

Findings

Successfully recovers density and Lamé parameters under geometric conditions

Extends previous methods to include density recovery

Uses microlocal analysis and tensor tomography techniques

Abstract

We consider an isotropic elastic medium occupying a bounded domain D whose density and Lam\'e parameters are piecewise smooth. In the elastic wave initial value inverse problem, we are given the solution operator for the elastic wave equation, but only outside the domain D and only for initial data supported outside D, and we study the recovery of the density and Lam\'e parameters. For known density, results have recently been obtained using the scattering control method to recover wave speeds. Here, we extend this result to include the recovery of the density in addition to the Lam\'e parameters under certain geometric conditions using techniques from microlocal analysis and a connection to local tensor tomography.