Experimental detection of inclusions for the time-harmonic elastic wave equation

TL;DR

This paper presents a method for reconstructing inclusions in elastic bodies using time-harmonic elastic wave measurements, demonstrating improved results over stationary models and addressing noisy data through a modified linearized monotonicity approach.

Contribution

It introduces a novel application of the linearized monotonicity method to noisy time-harmonic elastic wave data for inclusion detection, with numerical validation.

Findings

Harmonic problem yields better reconstruction than stationary models.

Modified monotonicity method effectively handles noisy measurement data.

Numerical reconstructions successfully identify inclusions in elastic bodies.

Abstract

We are concerned with the reconstruction of inclusions in elastic bodies based on measurements from a laboratory experiment. In doing so, we solve the inverse problem of the time-harmonic elastic wave equation, in contrast to the stationary wave equation and the corresponding lab experiment proposed earlier in Eberle and Moll (2021). The investigation of the harmonic problem leads to a better reconstruction compared to the stationary one. Since we deal with real measurement data, we have to take into account, that those measurements always include measurement errors, so that we have to handle noisy data. Thus, we consider the linearized monotonicity method for noisy data and introduce a modified version of this method. Based on this, we reconstruct the inclusions numerically.