Feasible Green’s Function for a Domain with Shadow Zones

The subsurface image if often generated by applying an imaging condition, which implies the knowledge of the Green's function satisfying Fermat's principle. Evaluation of the Green's function for complex subsurface geometries is not straightforward. The presence of diffracting edges and shadow zones limits the applicability of geometrical seismics, which describes a conventional Green's function. We have therefore asked ourselves: What happens to the Green's function near and inside a shadow zone, for example in the vicinity of a salt dome, where the seismic rays do not penetrate? We show that the shadow zones are not completely "dark"; and the feasible Green's function in such areas contains a cascade diffraction which corrects the conventional Green's function. We provide numerical examples for an isotropic model with a wedge-shaped boundary, which illustrate possible applications of the approach.