Acoustic approximations for processing in transversely isotropic media

When transversely isotropic (VTI) media with vertical symmetry axes are characterized using the zero-dip normal moveout (NMO) velocity [V-nmo(0)] and the anisotropy parameter eta instead of Thomsen's parameters, time-related processing [moveout correction, dip moveout (DMO), and time migration] become nearly independent of the vertical P-and S-wave velocities (V-P0 and V-S0, respectively). The independence on V-P0 and V-S0 is well within the limits of seismic accuracy, even for relatively strong anisotropy. The dependency on Vpg and V-S0 reduces even further as the ratio V-S0/V-P0 decreases. In fact, for V-S0 = 0, all time-related processing depends exactly on only V-nmo(0) and eta. This fortunate dependence on two parameters is demonstrated here through analytical derivations of time-related processing equations in terms of V-nmo(0) and eta. The time-migration dispersion relation, the NMO velocity for dipping events, and the ray-tracing equations extracted by setting C-S0 = 0 (i.e., by considering VTI as acoustic) not only depend solely on V-nmo(0) and eta but are much simpler than the counterpart expressions for elastic media. Errors attributed to this use of the acoustic assumption are small and may be neglected. Therefore, as in isotropic media, the acoustic model arising from setting V-S0 = 0, although not exactly true for VTI media, can serve as a useful approximation to the elastic model for the kinematics of P-wave data. This approximation can boost the efficiency of imaging and DMO programs for VTI media as well as simplify their description.