Absorbing boundary conditions and surface waves

Abstract

One of the major problems in numerically simulating waves traveling in the Earth is that an artificial boundary must be introduced to produce unique solutions. To eliminate the spurious reflections introduced by this artificial boundary, we use a damping expression based on analogies to shock absorbers. This method can reduce the amplitude of the reflected wave to any prespecified value and is successful for waves at any angle of incidence. The method can eliminate unwanted reflections from the surface, reflections at the corners of the model, and waves reflected off an interface that strike the artificial boundary.Many of the boundary conditions currently used in the numerical solution of waves are approximations to perfectly absorbing boundary conditions and depend upon the angle of incidence of the incoming wave at the artificial boundary. Stability problems often occur with these boundary conditions. The method we use at the artificial boundary allows use of stable Dirichlet or von Neumann conditions.Since the surface motion is easily measured when the waves are induced by normal seismic techniques, approximations of surface waves are needed to obtain information on Rayleigh waves. An implicit finitedifference scheme that is relatively easy to incorporate into existing numerical simulators is used to obtain the surface data for the forward finite-difference approximations.

Comparison of artificial absorbing boundaries for acoustic wave equation modelling

“…Clayton and Engquist, 1977;Reynolds, 1978;Liao et al, 1984;Higdon, 1986;Higdon, 1991) and absorbing boundary layers (e.g. Cerjan et al, 1985;Kosloff and Kosloff, 1986;Compani-Tabrizi, 1986, Sochacki et al, 1987Bérenger, 1994;Komatitsch and Martin, 2007;Sen, 2010, 2012).…”

Acceleration strategies for elastic full waveform inversion workflows in 2D and 3D

“…Our seismic modelling scheme is an eighth order in space and second order in time staggeredgrid finite-difference scheme in time domain [28,47] that uses a mimetic approach to accurately solve the free-surface condition and hence allows for a less restrictive grid spacing criterion in the computations [33]. For the bottom and lateral boundaries, we use sponge zones as reflection-free condition [41]. The model gradient associated with the misfit function E of each source or shot is constructed by cross-correlation of a forward and adjoint wavefield, obtained from an adjoint source as explained by [14].…”

Non-reflecting regions for finite difference methods in modeling of elastic wave propagation in plates

“…Attenuating Buffer Zone --Cerjan et al [9], Sochacki et al [10], and Hanson & Petschek [ 11] presented buffer-domain techniques where the amplitudes of the displacement are gradually reduced when approaching the boundary.…”