In this paper we consider the problem of reconstructing sources in a homogeneous viscoelastic medium from wavefield measurements. We first present a modified time-reversal imaging algorithm based on a weighted Helmholtz decomposition and justify mathematically that it provides a better approximation than by simply time reversing the displacement field, where artifacts appear due to the coupling between the pressure and shear waves. Then we investigate the source inverse problem in an elastic attenuating medium. We provide a regularized time-reversal imaging which corrects the attenuation effect at the first order. The results of this paper yield the fundamental tools for solving imaging problems in elastic media using cross-correlation techniques.

The transient motion in an anisotropic elastic half-space due to a moving surface line load is considered. The load is applied suddenly on the surface and moves off in a fixed direction with nonuniform speed. Integral expressions for the displacements are derived using the reciprocal theorem. The waves generated by the moving load are discussed. Special attention is paid to the singularities in surface displacements generated as the load moves through the Rayleigh wave speed. Explicit expression is obtained for the particle velocity due to a constant load moving with constant speed.