Accuracy comparison of nonhyperbolic moveout approximations for qP-waves in VTI media

Abstract

There are many non-hyperbolic moveout approximations for VTI media with various accuracy claims. We perform an analytical and numerical comparison of the 11 moveout approximations developed for a homogeneous transversely isotropic medium with vertical symmetry axis (VTI). The comparison is based on evaluating their long-offset asymptotes and higher-order Taylor series coefficients computed for a VTI medium. To make the different approximations comparable we select approximation coefficients to preserve the fourth-order coefficient in Taylor series for traveltime squared. To make the comparison simpler, we define the traveltime as a function of normalized offset and one parameter which is the anelliptical parameter. We select the six best approximations and perform comparative analysis by plotting the asymptotic traveltime parameters and high-order Taylor coefficients versus anelliptical parameter. We also compute the relative error in traveltime for selected approximations for homogeneous and horizontally layered VTI models.