New travel-time approximations for a transversely isotropic medium

Abstract

In seismic data processing it is common to use a non-hyperbolic travel-time approximation assuming weak anisotropy in a transversely isotropic medium with vertical symmetry axis. It has the correct short-spread (normal) moveout velocity, but higher order terms in offset squared are only approximations. Using Taylor expansions for the squared vertical slowness for P- and SV-waves result in new approximations for the phase velocities which may be used in pre-stack migration algorithms. These approximations are combined with expressions for travel time and offset as functions of horizontal slowness, giving three new approximations for travel time squared as functions of offset squared, without the assumption of weak anisotropy. Numerical examples show that these new approximations all have better accuracy than the standard weak-anisotropy approximation. Based on the numerical results, we propose a new travel-time approximation for reflected PP-, SS- and PS-waves to be used in seismic data processing. They have almost the same functional form as the weak-anisotropy approximations, with the same normal moveout velocities but with a different heterogeneity factor which is non-linear in the anisotropy parameters.