Improved geometric-spreading approximation in layered transversely isotropic media

Abstract

A new approximation (direct approximation) for the relative geometric spreading of qP-waves in a layered transversely isotropic medium uses three traveltime parameters: two-way vertical traveltime, normal-moveout velocity, and the heterogeneity coefficient. These traveltime parameters, which can be estimated in velocity analysis, enter the parameters of geometric-spreading approximation. The new approximation is based on the acoustic approximation for a single-layer vertical transversely isotropic (VTI) medium with coefficients defined from Taylor expansion and asymptotic behavior at infinite offset. The acoustic approximation is used to reduce the number of parameters and to make the expression for the direct geometric-spreading approximation similar to a well-known traveltime approximation. The same traveltime parameters also allow for an independent approximation of the radiation pattern. Two numerical tests (single-layer and multilayered VTI models) prove that the new approximation is more accurate than standard approximations based on shifted hyperbola or two rational approximations.