The approximation for relative geometric spreading in the elastic vertical transversely isotropic medium

In seismic data processing, compensation for geometric spreading along the raypath is necessary. The accurate approximation of the relative geometric spreading is critical because the traveltime parameters in the approximation can be estimated from velocity analysis. Two approximation types (direct and indirect) are generalized based on the procedure to derive the explicit expression. We develop perturbation-based approximations of the relative geometric spreading for P and S waves with these two types in the elastic transversely isotropic media with a vertical symmetry axis (VTI). The rational approximation and the general moveout approximation counterparts are compared to verify the superiority of our approach. Our study compares the performance of direct and indirect approximations for optimal selection under different cases. In the numerical examples, we apply the error sensitivity in the layer depth, anellipticity value, and vertical velocity ratio. It is found that the P-wave case ismuch more accurate than the S-wave case, and the direct type obtains relatively higher accuracy than the indirect one. In addition, the perturbation coefficients for the acoustic VTI model are derived not only with a much simpler expression but also achieve a highly accurate result that is recommended for the P-wave seismic processing.