  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 Kaczmarz method is presented to solve the
ill-posed integral equations. Numerical experiments are included to demonstrate
the effectiveness of the proposed method.
