Direct Geometrical Spreading Approximations in Anisotropic Media

We propose a family of the direct approximation for the relative geometrical spreading of P-wave in an acoustic transversely isotropic medium with a vertical symmetry axis (VTI). We analyze three types of approximation: shifted hyperbola, rational and perturbation based approximation and develop the generalized nonhyperbolic moveout approximation (GMA) with parameters defined from two rays for both direct and indirect form approximation for comparison. For numerical examples, we consider two choices for parameter selection by using two specific orientations for reference ray. We test these approximations of the relative geometrical spreading in a homogeneous VTI media. From numerical examples, we observe that the GMA form approximations are the most accurate ones. For most of cases, the direct type approximations are more accurate compared with the indirect ones.