Wide-angle phase-slowness approximations in VTI media

An anisotropic medium with vertical symmetry axis (VTI) often presents a good model for describing real rocks. Propagation of quasi-P- and quasi-SV-waves in such media requires an expression of the vertical phase slowness, a complicated function of the horizontal phase slowness and the medium parameters. For converted-wave phase-shift migration methods, it is desired to have slowness expressions that are simple and accurate at wide angles of propagation. Taylor-series representations of the squared vertical slowness for quasi-P- and quasi-SV-waves result in new wide-angle phase-slowness approximations based on truncated series and continued-fraction representations. Slowness approximations that are exact for both vertical propagation and at a horizontal slowness corresponding to horizontally traveling qP-waves are derived. The approximation for quasi-SV-waves can be used in phase-shift migration in media where the quasi-SV wavefront contains triplications. These approximations are tested on several models and compared to previously published approximations. The numerical tests suggest that the new continued-fraction approximations are more accurate. They can be used in phase-shift migration algorithms, which are more efficient for large angles than the existing approximations.