Reconstruction of Lame moduli and density at the boundary enabling directional elastic wavefield decomposition

TL;DR

This paper presents an explicit method to reconstruct elastic parameters and density at the boundary of a domain from boundary measurements, enabling wavefield decomposition in isotropic elastic media.

Contribution

It introduces a boundary reconstruction technique using the symbol of the Dirichlet-to-Neumann map for elastic waves, providing new insights into wavefield decomposition.

Findings

Explicit boundary reconstruction of Lamé parameters and density.

Reconstruction includes derivatives of parameters at the boundary.

Enables decomposition of incoming and outgoing elastic waves.

Abstract

We consider the inverse boundary value problem for the system of equations describing elastic waves in isotropic media on a bounded domain in $\mathbb{R}^3$ via a finite-time Laplace transform. The data is the dynamical Dirichlet-to-Neumann map. More precisely, using the full symbol of the transformed Dirichlet-to-Neumann map viewed as a semiclassical pseudodifferential operator, we give an explicit reconstruction of both Lam\'{e} parameters and the density, as well as their derivatives, at the boundary. We also show how this boundary reconstruction leads to a decomposition of incoming and outgoing waves.