Sponge boundary condition for frequency-domain modeling

Abstract

Several techniques have been developed to get rid of edge reflections from artificial boundaries. One of them is to use paraxial approximations of the scalar and elastic wave equations. The other is to attenuate the seismic waves inside the artificial boundary by a gradual reduction of amplitudes. These techniques have been successfully applied to minimize unwanted seismic waves for time-domain seismic modeling. Unlike time-domain seismic modeling, suppression of edge reflections from artificial boundaries has not been successful in frequency-domain seismic modeling. Rayleigh waves caused by coupled motions of P- and S-waves near the surface have been a particularly difficult problem to overcome in seismic modeling. In this paper, I design a damping matrix for frequencydomain modeling that damps out seismic waves by adding a diffusion term to the wave equation. This technique can suppress unwanted seismic waves, including Rayleigh waves and P- and S-waves from an artificial boundary.