The linearized monotonicity method for elastic waves and the separation of material parameters

TL;DR

This paper introduces a linearized monotonicity method for elastic wave-based shape reconstruction that reduces computation time and enables partial separation and identification of material parameters.

Contribution

It develops a linearized version of the monotonicity method, offering efficiency and enhanced material parameter analysis in elastic wave imaging.

Findings

Reduces computational complexity of shape reconstruction

Allows partial separation of Lamé parameters

Provides additional information on material properties

Abstract

We derive a linearized version of the monotonicity method for shape reconstruction using time harmonic elastic waves. The linearized method provides an efficient version of the method, drastically reducing computation time. Here we show that the linearized method has some additional advantages. The linearized method can in particular be used to obtain additional information on the material parameters, and is able to partially separate and identify the supports of the Lam\'e parameters.