Modeling of seismic waves in layers with shadow boundaries in terms of unsparse propagation-absorption matrices: realization and optimization

The conventional Green's function introduced for an unbounded medium and applied in domains with complex boundaries may contain physically unfeasible components. These components would not be observed in an experimental study and thus lead to misinterpretation of the wave-field structure. The feasible Green's function that does not contain unfeasible components satisfies the principle of absorption of the part of the wavefield which penetrate the shadow zones formed by the concave parts of layer boundaries [9, 7]. Recently the feasible Green's function has been introduced as the superposition of the conventional Green's function and cascade diffraction. Cascade diffraction compensates for the unfeasible parts of the conventional Green's function and takes into account the actual shape of the boundaries. We represent a new algorithm for modelling the single-diffraction approximation of the cascade diffraction in terms of unsparse propagation-absorption matrices and provide numerical examples for an acoustic half-space with a wedge-shaped boundary, which illustrate the accuracy and efficiency of the algorithm.