The synthetic wavefield is often generated by applying an illuminating 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 restricts its applicability and requires a Green's function satisfying the generalized Fermat's (Hadamard’s) principle. We show that the feasible Green's function in the vicinity of geological obstacles (salt domes, reef edges, pinchouts, etc.) includes a cascade diffraction term that improves the conventional Green's function. We provide numerical examples for an acoustic model with a concave boundary which illustrate wave structure of the double-diffraction approximation of the feasible Green's function.