Asymptotical Comparison of Non-hyperbolic Moveout Approximations in a VTI Medium

Abstract

In this paper, we perform the analytical and numerical comparison of the 11 moveout approximations for a homogeneous transversely isotropic medium with vertical symmetry axis (VTI) medium based on their long-offset asymptotes and high-order Taylor coefficients computed for VTI medium. To make different approximations comparable we select the approximation coefficients such that 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 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.