An optimal absorbing boundary condition is designed to model acoustic and elastic wavepropagation in 2D and 3D media using the finite difference method. In our method,extrapolation on the artificial boundaries of a finite difference domain is expressed asa linear combination of wave fields at previous time steps and/or interior grids. Theacoustic and elastic reflection coefficients from the artificial boundaries are derived.They are found to be identical with the transfer functions of two cascaded systems: oneis the inverse of a causal system and the other is an anticausal system. This methodmakes use of the zeros and poles of reflection coefficients in a complex plane. Theoptimal absorbing boundary condition designed in this paper yields about 10 dB smallerin magnitude of reflection coefficients than Higdon's absorbing boundary condition, andaround 20 dB smaller than Reynolds' absorbing boundary condition. This conclusion issupported by a simulation of elastic wave propagation in a 3D medium on an nCUBEparallel computer.
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