Direct imaging for the moment tensor point sources of elastic waves

TL;DR

This paper introduces novel sampling-based numerical schemes to accurately identify the locations and moment tensors of elastic wave sources from near-field measurements, supported by theoretical proofs and numerical validation.

Contribution

It proposes new sampling-type methods for inverse elastic source problems, with rigorous proofs of uniqueness and practical numerical demonstrations.

Findings

Unique determination of source locations and moment tensors from multi-frequency data

The proposed methods are validated through numerical examples

The schemes are robust and effective in identifying elastic wave sources

Abstract

We investigate an inverse source problem of the time-harmonic elastic wave equation. Some novel sampling-type numerical schemes are proposed to identify the moment tensor point sources in the Lam\'e system from near-field measurements. Rigorous theoretical justifications are provided to show that the locations and moment tensors of the elastic sources can be uniquely determined from the multi-frequency displacement data. Several numerical examples are also presented to illustrate the validity and robustness of the proposed method.