Optimal Absorbing Boundary Conditions For Finite Difference Modeling Of Acoustic And Elastic Wave Propagation

Abstract

An optimal absorbing boundary condition is designed to model acoustic and elastic wave propagation 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 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 with the transfer functions of two cascaded systems: one is the inverse of a causal system and the other is an anticausal system. This method makes use of the zeros and poles of reflection coefficients in a complex plane. The optimal absorbing boundary condition designed in this paper yields about 10 dB smaller in magnitude of reflection coefficients than Higdon's absorbing boundary condition, and around 20 dB smaller than Reynolds' absorbing boundary condition. This conclusion is supported by a simulation of elastic wave propagation in a 3D medium on an nCUBE parallel computer.