Exact Analytical Solution for the Seismic Tunneling Problem

An exact analytical solution for the tunneling problem is presented. The canonical configuration consists of two acoustic half-spaces in contact including a source. Classical solutions are based on numerical schemes or on other well known methods like the Cagniard-de Hoop method, the WKBJ method, or the steepest descent method. In common with the Cagniard-de Hoop method and as opposed to the other methods mentioned above, the one presented here doesn't use approximations and is explicit in the space-time domain. Furthennore uniqueness of the solution is established which is not the case with the Cagniard-de Hoop method or any other classical solution known. The Green's functions and the seismograms calculated with the method presented here diverge significantly from that obtained with the Cagniard-de Hoop method.