Fast and Accurate Seismic Computations in Laterally Varying Environments

The parabolic equation method provides an unrivaled combination of computational efficiency and accuracy for wave propagation problems in the geosciences in which the environment has strong vertical variations and gradual horizontal variations. The development of this approach has been an active area of research for several decades in ocean acoustics, which includes problems involving sediment layers and ice cover that support shear waves. It is demonstrated here that this progress has culminated in a parabolic equation model for fast and accurate seismic computations in laterally varying environments. The model is tested for problems involving sloping boundaries and interfaces, variable layer thickness, continuous variations of the elastic parameters within layers, and a Rayleigh wave propagating along variable topography. The seismic parabolic equation model is based on an outgoing wave equation and rational approximations of operators for generating initial conditions, propagating the solution through stratified regions that approximate a laterally varying environment, and estimating transmitted fields across the vertical interfaces between regions.