Propagation invariants, reflection and transmission in anisotropic, laterally heterogeneous media

Abstract

For quasi‐stratified media in which the principal variation in seismic properties is with depth, propagation invariants can be constructed from certain combinations of the displacement and tractions elements of two seismic wavefields. These invariants are independent of depth and vanish for identical wavefields, and are constructed for anisotropic, laterally varying media in the spatial and wavenumber domains. These propagation invariants can be exploited to substantially simplify the construction of reflection and transmission processes in laterally varying media, including coupling between wavenumbers. The implementation of this approach is illustrated by application to the incidence of SH‐waves on an irregular interface below a free surface. The results are in excellent agreement with those from other schemes but take about 20 per cent less computation time. Even greater improvements in calculation speed are possible in more complex models. Copyright © 1990, Wiley Blackwell. All rights reserved