Inverse Random Source Scattering for Elastic Waves

Abstract

This paper is concerned with the direct and inverse random source scattering problems for elastic waves, where the source is assumed to be driven by an additive white noise. Given the source, the direct problem is to determine the displacement of the random wave field. The inverse problem is to reconstruct the mean and variance of the random source from the boundary measurement of the wave field at multiple frequencies. The direct problem is shown to have a unique mild solution by using a constructive proof. Based on the explicit mild solution, Fredholm integral equations of the first kind are deduced for the inverse problem. The regularized block Kaczmarz method is developed to solve the ill-posed integral equations. The convergence is proved for the method. Numerical experiments are shown to demonstrate the effectiveness of the proposed method.