Optimized nonhyperbolic moveout correction equation of long-offset seismic data for TI media with an arbitrary spatial orientation

Abstract

The conventional long-offset nonhyperbolic moveout equation is derived for the transverse isotropic media with a vertical symmetric axis (VTI). It cannot be extended to the transverse isotropic media with an arbitrary spatial orientation of symmetry axis (ATI). In this paper, we optimize a modified long-offset nonhyperbolic moveout equation for ATI media based on the conventional nonhyperbolic moveout equation and the exact analytical solution of the quartic moveout coefficient (A4) and NMO velocity for ATI media that were derived in our previous work. Compared with the exact traveltimes of the ray-tracing algorithm for anisotropic media, this optimized equation can be used to calculate the traveltime varying with survey line azimuth in arbitrary strong or weak ATI media. It can replace the time-consuming, multi-offset, and multi-azimuth ray tracing method for forward modeling of longoffset reflection traveltimes in ATI media, which is useful to further anisotropic parameter inversion using long-offset nonhyperbolic moveout.