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（A_4） 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 long-offset reflection traveltimes in ATI media,which is useful to further anisotropic parameter inversion using long-offset nonhyperbolic moveout.
