Local Uniqueness of The Density From Partial Boundary Data for Isotropic Elastodynamics

TL;DR

This paper proves local uniqueness of the density in an isotropic elastodynamic medium using partial boundary measurements, advancing seismic imaging techniques by enabling density determination from limited data.

Contribution

It demonstrates that the density of a non-homogeneous isotropic elastic body can be uniquely identified from partial boundary data, extending previous results on wave speeds.

Findings

Density can be uniquely determined locally from partial boundary measurements.

Partial boundary Dirichlet to Neumann map suffices for density recovery.

Advances seismic imaging by enabling density estimation with limited data.

Abstract

We consider an inverse problem in elastodynamics arising in seismic imaging. We prove locally uniqueness of the density of a non-homogeneous, isotropic elastic body from measurements taken on a part of the boundary. We measure the Dirichlet to Neumann map, only on a part of the boundary, corresponding to the isotropic elasticity equation of a 3-dimensional object. In earlier works it has been shown that one can determine the sheer and compressional speeds on a neighborhood of the part of the boundary (accessible part) where the measurements have been taken. In this article we show that one can determine the density of the medium as well, on a neighborhood of the accessible part of the boundary.