PRESTACK GAUSSIAN BEAM DEPTH MIGRATION

The prestack Gaussian beam scheme is implemented as common-shot profile migration, the implementation of which is similar to that of finite difference $\omega-x$ depth migration. All the frequency components of all surface recorded seismograms are downward continued as in the poststack case. The final migrated reflectivity image is obtained after application of the imaging condition to the downward continued wavefields $U(x,z,\omega)$, as in conventional migration (Claerbout, 1976, 1985; Reshef and Kosloff, 1986). When each surface seismogram is taken as a source and migrated separately, the reflectivity image is the wavefield of Equation (17) evaluated at t=t_d at each depth point, where t=t_d is the arrival time of the direct wave from the source to the depth points (x,z). The reflectivity image is formed by superposition of the contributions of all surface seismograms.