Acoustic approximations for processing in transversely isotropic media

Abstract

When transversely isotropic (VTI) media with vertical symmetry axes are characterized using the zero‐dip normal moveout (NMO) velocity [[Formula: see text]] and the anisotropy parameter ηinstead 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 ([Formula: see text] and [Formula: see text], respectively). The independence on [Formula: see text] and [Formula: see text] is well within the limits of seismic accuracy, even for relatively strong anisotropy. The dependency on [Formula: see text] and [Formula: see text] reduces even further as the ratio [Formula: see text] decreases. In fact, for [Formula: see text], all time‐related processing depends exactly on only [Formula: see text] and η. This fortunate dependence on two parameters is demonstrated here through analytical derivations of time‐related processing equations in terms of [Formula: see text] and η. The time‐migration dispersion relation, the NMO velocity for dipping events, and the ray‐tracing equations extracted by setting [Formula: see text] (i.e., by considering VTI as acoustic) not only depend solely on [Formula: see text] and η 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 [Formula: see text], 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.