9C-3D seismic modeling for VTI media

Ritesh Kumar Sharma, Robert James Ferguson

For comparison with real seismic data, and with synthetic da ta derived from fully elastic numerical methods, we present a 9C-3D numerical modelling approach that is posed in the slowness domain. The slowness domain approach has a number of advantages: 1) multi-pathing with no internal reflection "simpler event registration". 2) Parallelizable over temporal frequency. 3) Stable. 4) High frequency. 5) Selectable propagating mode.Implementation of our method proceeds as follows Define a source (P, S V , and S H ) at the surface, and compute the plane wave transform over the time and space coordinates so that wavefield ext rapolation proceeds as a set of distributed, monochromatic extrapolation steps in depth. Compute an anisotropic phase shift operator, and extrapolat e the source spectrum 0 to a reflector at a new depth z . For a given receiver orientation (V , H1 , and H2 ) at each grid point on z , define a rotation matrix according to the azimuth () and dip (1 ) between the grid point and the polarization vector of P wave source. Traveltimes in anisotropic media are accommodated though p lane wave transformation and phase shift, and a propagation angle is produced. For each geophone component, the polarization angle is calculated from the propa gation angle. Apply the rotation matrix to the extrapolated wavefield. Extract the desired component for analysis. Our numerical r esults demonstrate that all 9 source-receiver combinations are reliably estimate u sing our procedure.