An optimal absorbing boundary condition for finite difference modeling of acoustic and elastic wave propagation

Abstract

This paper presents an optimal absorbing boundary condition designed to model acoustic and elastic wave propagation in two-dimensional and three-dimensional media using the finite difference method. In this condition, extrapolation on the artificial boundaries of a finite difference domain is expressed as a linear combination of wave fields at previous time steps and/or interior grids. The acoustic and elastic reflection coefficients from the artificial boundaries are derived. They are found to be identical to the transfer functions of two cascaded systems—the inverse of a causal system and an anticausal system. The method makes use of the zeros and poles of reflection coefficients in a complex plane. The optimal absorbing boundary condition described in this paper yields, on the average, reflection coefficients about 10-dB smaller than Higdon’s absorbing boundary condition, and about 20-dB smaller than Reynolds’ absorbing boundary condition.