Where are the Fault Plane Reflections ?

Two imaging methodologies that we expect to give comparable results are 1) DMO followed by CMP stack and poststack time migration and 2) prestack f-k time migration. For the most part, these two approaches do indeed give similar images; yet in one important area they are nearly always different. Specifically, the approach of DMO-stackmigration routinely images reflections from fault planes; whereas the approach of prestack f-k migration routinely does not. This observation is not limited to anyone geologic basin, but is seen worldwide. This paper investigates several possible reasons that could explain the differences in fault-plane imaging: 3-D effects, vertical velocity variation, acquisition geometry issues, and transverse isotropy. We find that only transverse isotropy can single-handed explain the different responses of the imaging approaches. We further show that the sensitivity of prestack f-k migration to transverse isotropy can be used to estimate the amount, in some average sense, of transverse isotropy. This has importance not only for selection of imaging parameters, but also for interpretation and time-to-depth conversion. In this paper we also show that using an aneliptic dispersion relation in prestack f-k migration compensates for the effects of transverse isotropy, thus reducing the dip dependency of migration velocities.