Gauge freedoms in the anisotropic elastic Dirichlet-to-Neumann map

TL;DR

This paper investigates the invariance properties and gauge freedoms of the elastic Dirichlet-to-Neumann map, aiding in the inverse problem of determining material parameters from boundary measurements.

Contribution

It characterizes gauge freedoms in the elastic wave equation and the Dirichlet-to-Neumann map, advancing understanding of inverse problems in anisotropic elasticity.

Findings

Identifies gauge invariances in elastic wave equations

Describes how parameters can be transformed without changing the Dirichlet-to-Neumann map

Provides insights into the uniqueness of inverse boundary value problems

Abstract

We address the inverse problem of recovering the stiffness tensor and density of mass from the Dirichlet-to-Neumann map. We study the invariance of the Euclidean and Riemannian elastic wave equation under coordinate transformations. Furthermore, we present gauge freedoms between the parameters that leave the elastic wave equations invariant. We use these results to present gauge freedoms in the Dirichlet-to-Neumann map associated to the Riemannian elastic wave equation.