On anelliptic approximations for qP velocities in transversally isotropic media

I develop a unified approach for approximating phase and group velocities of qP seismic waves in a transversally isotropic medium with the vertical axis of symmetry (VTI). While the exact phase velocity expressions involve four independent parameters to characterize the elastic medium, the proposed approximate expressions use only three parameters. This makes them more convenient for use in surface seismic experiments, where estimation of all the four parameters is problematic. The three-parameter phase-velocity approximation coincides with the previously published “acoustic” approximation of Alkhalifah. The group velocity approximation is ‘new and noticeably more accurate than some of the previously published approximations. I demonstrate an application of the group velocity approximation for finite-difference computation of traveltimes.