ABSORBING BOUNDARY-CONDITIONS FOR ACOUSTIC AND ELASTIC-WAVES IN STRATIFIED MEDIA

Absorbing boundary conditions are needed for computing numerical models of wave motions in unbounded spatial domains. Prior progress on this problem for acoustic and elastic waves has generally been concerned with waves propagating through uniform media. The present paper is concerned with waves in stratified media, which are of interest, for example, in geophysical problems. Suppose that the medium consists of homogeneous layers separated by parallel horizontal interfaces, and suppose that absorbing boundary conditions are needed along a vertical computational boundary. The boundary conditions that are described in this paper are based on a quantity known as the "ray parameter." According to Snell's law, this parameter remains the same when a plane wave propagates through a stratified medium and undergoes reflection, refraction, and, in the case of elastic waves, conversion. Once can therefore use the same absorbing boundary conditions in all layers. For acoustic waves, the absorption properties are the same in all layers. For elastic waves, the absorption properties vary somewhat from one layer to another; however, one still obtains good absorption in all layers, even in the presence of strong contrasts between layers. The boundary conditions are also effective in absorbing Rayleigh waves, which propagate along free surfaces of elastic media. The boundary formulas developed here can be applied without modification to problems in both two and three dimensions. © 1992.