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

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.

Automatic estimation of traveltime parameters in VTI mediausing similarity-weighted clustering

Compared with hyperbolic velocity estimation methods,nonhyperbolic methods(such as shifted hyperbola)are better choices for large offsets or vertical transverse isotropy(VTI)media.Since local seismic event slope contains subsurface information,they can be used to estimate zero-offset two-way traveltime and normal moveout velocity.The traditional velocity estimation methods require a great deal of manual work and are also prone to human error.In order to estimate the traveltime parameters for VTI media automatically,in this paper,we propose to use predictive painting and similarity-weighted clustering to obtain traveltime parameters.The predictive painting is used to estimate zero-offset two-way traveltime,and the shifted-hyperbola traveltime equation is used to obtain velocity and anisotropy attributes.We first map local slopes to zero-offset two-way traveltime and moveout-parameters domain and then use similarity-weightedk-means clustering to find the maximum likelihood anisotropy parameters of the main subsurface structures.In order to demonstrate that,we apply the similarity-weighted clustering method to synthetic and field data examples and the results are of higher accuracy when compared to the ones obtained using multiparameter semblance-based method.From estimation error section,it can be seen that the estimation error of multiparameter semblance-based method is about 3-5 times that of the proposed method.