Single-diffraction Approximation of the Feasible Green’s Function in Geometrical Shadow Zones

The subsurface image is often generated by applying an imaging condition, which implies the knowledge of the conventional Green's function satisfying the Fermat's principle. The presence of geometrical shadow zones in the model limits its applicability and requires a Green's function satisfying the generalized Fermat's (Hadamard’s) principle for complex subsurface geometries. We show that the feasible Green's function in the vicinity of geological discontinuities (salt domes, reef edges, pinchouts, etc.) contains a cascade diffraction which corrects the conventional Green's function. We provide numerical examples for an acoustic model with a concave boundary, which illustrate the dependence of the single-diffraction approximation of the feasible Green's function on the curvature of boundary in a vicinity of the line of ray tangency.