Unique determination of a transversely isotropic perturbation in a linearized inverse boundary value problem for elasticity

TL;DR

This paper proves that specific elastic and density perturbations in a medium can be uniquely identified using linearized boundary measurements at zero and positive frequencies, advancing inverse boundary value problem theory.

Contribution

It demonstrates unique determination of transversely isotropic perturbations in elasticity and density from linearized Dirichlet-to-Neumann maps at different frequencies.

Findings

Unique identification of elastic perturbations at zero frequency.

Simultaneous determination of density perturbations at positive frequencies.

Advancement in inverse boundary value problem techniques.

Abstract

We consider a linearized inverse boundary value problem for the elasticity system. From the linearized Dirichlet-to-Neumann map at zero frequency, we show that a transversely isotropic perturbation of a homogeneous isotropic elastic tensor can be uniquely determined. From the linearized Dirichlet-to-Neumann map at two distinct positive frequencies, we show that a transversely isotropic perturbation of a homogeneous isotropic density can be identified at the same time.