P‐ and S‐wave‐separated elastic wave‐equation numerical modeling using 2D staggered grid

Abstract

Traditional numerical modeling method using second‐order elastic wave equation can only generate the synthetic seismograms of the Z and X component in isotropic medium, in which the P‐ and S‐wavefields are coupled. To obtain wavefield of the pure P‐ and S‐waves, the general method is wavefield separation processing of the coupled wavefield of each component, but it is difficult to get completely separated seismograms. If we use P‐ and S‐wave equation respectively to generate P‐ and S‐wave, the converted P‐ and S‐wave will not appear in wavefield, thus it is not equal to full wavefield modeling. Carrying out full separation of wavefield modeling of pure P‐ and S‐wave (In reconstructed wavefield, X and Z component comprise P‐ and S‐wave that is fully separated.) makes no need of wavefield separation in following multi‐wave processing, what's more, it is of great practical importance for us to study seismic wave propagation mechanism and structure of geology as well as oil reservoir characterization. Based on P‐ and S‐wave separation of second‐order elastic wave equation and first‐order staggered‐grid method, a P‐ and S‐wave separated modeling equation in first‐order staggered‐grid is presented. In this method, P‐and S‐wave are fully separated instead of coupled together to produce synthetic seismograms of pure P‐ and S‐wave. The feasibility and accuracy are shown by a couple of examples of numerical modeling.