Prestack time migration for anisotropic media

Prestack phase-shift migration is implemented by evaluating the offset-wavenumber (kh) integral using the stationary-phase method. Thus, unlike zero-offset migration, the stationary point along kh must be calculated prior to applying the phase shift. This type of imple mentation allows for migration of separate offsets, as opposed to migrating the whole prestack data when using the original formulas. For non-zero-offset data, we first evaluate kh that corresponds to the stationary point solution either numerically or through analytical approximations. The insensitivity of the phase to kh around the stationary point solution (its maximum) implies that even an imperfect kh obtained analytically can go a long way to getting an accurate image. In transversely isotropic (TI) media, the analytical solutions of the stationary point (kh) include more approximations than those corresponding to isotropic media (i.e., approximations corresponding to weaker anisotropy). Nevertheless, the resultant equations, obtained using perturbation theory, produce accurate migration signatures for strong anisotropy (η≈0.3) and even large offset-to-depth ratios (>2). The analytical solutions are particularly accurate in predicting the nonhyperbolic moveout behavior associated with anisotropic media, a key ingredient to performing accurate non-hyperbolic moveout inversion for strongly anisotropic media. Synthetic and field data applications of this prestack migration demonstrates its usefulness.