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.
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Peng et al. (1994) studied this question.