Inverse source problems in elastodynamics

TL;DR

This paper addresses inverse source problems in elastodynamics, proposing frequency and time domain methods for unique and stable recovery of source terms, along with practical algorithms and numerical validation in 2D and 3D.

Contribution

It introduces new inversion schemes for elastodynamic inverse source problems, including a Landweber iterative method and a non-iterative approach, with proven uniqueness and stability.

Findings

Successful numerical reconstructions in 2D and 3D

Proved uniqueness and stability for source recovery

Developed implementable inversion algorithms

Abstract

We are concerned with time-dependent inverse source problems in elastodynamics. The source term is supposed to be the product of a spatial function and a temporal function with compact support. We present frequency-domain and time-domain approaches to show uniqueness in determining the spatial function from wave fields on a large sphere over a finite interval. Stability estimate of the temporal function from the data of one receiver and uniqueness result using partial boundary data are proved. Our arguments rely heavily on the use of the Fourier transform, which motivated inversion schemes that can be easily implemented. A Landweber iterative algorithm for recovering the spatial function and a non-iterative inversion scheme based on the uniqueness proof for recovering the temporal function are proposed. Numerical examples are demonstrated in both two and three dimensions.