Radiation from a Finite Reverse Fault in a Half Space

— Using a set of well-known results for the seismic field radiated by a simple dip-slip dislocation in a half space, we study interesting details of the motion at the surface of the half space. The static solution for a dislocation in a half space was found by Freund and Barnett in 1976. The corresponding elastodynamic solution was solved exactly in the Fourier and Laplace domain by several authors about 20 years ago, however its properties remained unexplored because of analytical difficulties. We remove these difficulties and show that the solution contains three important phenomena: Seismic wave fronts of P, S and SP type; the near-field pulse associated with the propagation of the dislocation front; and the long-time elastic response that converges toward the static solution of Freund and Barnett. Based on these results we show that solutions to all these problems are self-similar and homogeneous in x/h and αt/h so that when the fault depth h approaches 0, the solutions become concentrated near the origin and around the P, S and surface wave travel times. This explains several paradoxes in the radiation from dip-slip faults; among these the most notable are the presence of a point force singularity at the tip of a surface breaking fault and the reduction in high frequency radiation near the surface.