Prestack depth migration in anisotropic heterogeneous media

Hermes Malcotti

hermes@sep.stanford.edu

ABSTRACT

This paper presents a 2-D and 3-D prestack depth migration in anisotropic media for P-waves. Assuming an acoustic VTI medium, the double square root (DSR) equation becomes dependent only on the migration velocity field and the parameter ${\eta}$. In order to handle lateral velocity variation, I use the extended split-step approximation of the double square root. I tested this algorithm with two different 2-D synthetic seismic data sets in a VTI medium, and the results are encouraging. The first VTI synthetic model consisted of a set of dipping reflectors, from $0^\circ$ to $90^\circ$with Thomsen's parameters ${\epsilon=0.2}$ and ${\delta=0}$. The second model is the anisotropic Marmousi model characterized by strong lateral velocity and ${\eta}$ variation. In order to handle the lateral ${\eta}$ variation, I define a number of reference ${\eta}$'s that in the same fashion that reference velocities are defined. The resulting anisotropic prestack Marmousi section correctly imaged dipping events. In addition, I show other possible implementations of this anisotropic migration, in order to handle ${\eta}$ variation as a function of depth and lateral coordinates. In the case where the anisotropic medium has non-zero ${\delta}$, the extended split-step migration algorithm works in pseudo-depth to avoid the explicit dependency of the DSR operator on the vertical velocity.