Elastic Wavefield Modeling by Phase Shift Cascade
A numerical technique for 2-D elastic wavefield modeling in a stratified medium is presented. A cylindrical source waveform is decomposed into Fourier plane waves. Plane wave potentials, P and S, are advanced in depth by phase shift across each layer of the stratified system. Every Fourier plane wave is propagated through a computation grid and all multiples and mode conversions can be computed in a phase shift cascade.
At an interface, the four incoming potentials are related to the four scattered potentials by the 4x4 scattering matrix, in which scattering coefficients are computed using the Zoeppritz equations. The explicit use of the scattering matrix allows a partitioned modeling which can also be depth dependent.
After cascading, options for free-surface effects and displacement conversions are made. The seismograms are obtained by inverse Fourier transformation. A connection between phase shift cascade to the propagator method is explored.