Separating P‐ and S‐waves in prestack 3D elastic seismograms using divergence and curl

Abstract

The reflected P‐ and S‐waves in a prestack 3D, three‐component elastic seismic section can be separated by taking the divergence and curl during finite‐difference extrapolation. The elastic seismic data are downward extrapolated from the receiver locations into a homogeneous elastic computational model using the 3D elastic wave equation. During downward extrapolation, divergence (a scalar) and curl (a three‐component vector) of the wavefield are computed and recorded independently, at a fixed depth, as a one‐component seismogram and a three‐component seismogram, respectively. The P‐ and S‐velocities in the elastic computational model are then split into two independent models. The divergence seismogram (containing P‐waves only) is then upward extrapolated (using the scalar wave equation) through the P‐velocity model to the original receiver locations at the surface to obtain the separated P‐waves. The x‐component, y‐component, and z‐component seismograms of the curl (containing S‐waves only) are upward extrapolated independently (using the scalar wave equation) through the S‐velocity model to the original receiver locations at the surface to obtain the separated S‐waves. Tests are successful on synthetic seismograms computed for simple laterally heterogeneous 2D models with a 3D recording geometry even if the velocities used in the extrapolations are not accurate.