Velocity analysis for transversely isotropic media

The main difficulty in extending seismic processing to anisotropic media is the recovery of anisotropic velocity fields from surface reflection data. We suggest carrying out velocity analysis for transversely isotropic media by inverting the dip-dependence of P-wave moveout velocities. The inversion technique is based on the analytic equation for the normal moveout (NMO) velocity for dipping reflectors in anisotropic media, derived by Tsvankin (1994). Our inversion procedure makes it possible to obtain a family of solutions for the vertical velocity VPo and Thomsen (1986) parameters e and 6, all of which have the same NMO velocity as a function of ray parameter. It is shown that all models in this family have the same horizontal velocity, long-spread (nonhyperbolic) P-wave moveout for horizontal reflectors, as well as the same time-migration impulse response. In order to describe this family of models, we introduce an effective parameter η that reduces to the difference ∈ - δ in the limit of weak anisotropy. Therefore, inversion of dip moveout provides enough information to perform all essential time-processing steps including DMO, prestack and poststack time migration using only surface P-wave data. Generalization of Tsvankin's single-layer NMO equation for layered anisotropic media with a dipping reflector allows us to apply the anisotropic velocity analysis in vertically inhomogeneous media.