Optimization of nonhyperbolic moveout correction equation of long-offset seismic data in VTI media

The conventional Alkhalifah moveout correction equation is characterized by low precision, and even worse it may fail to describe relation of traveltime-offset of long-offset seismic data in VTI media. Aiming at improving accuracy of the moveout correction equation of long-offset seismic data in VTI media, we analyze the Alkhalifah's NMO equation at first. Then based on the least-error principle, chart of optimal correction coefficients are calculated to compensate errors resulted from long offset cases using the conventional moveout correction equation. Therefore, the optimal Alkhalifah moveout correction equation is proposed here to improve the conventional moveout correction equation. Subsequently, we derive the traveltime-offset function with a high precision model from the Fomel's group velocity equation for VU. The moveout correction equation with high precision is put forward. Above moveout correction equations are applied to inversion calculation of anisotropic parameters from long-offset seismic data. Numerical results show that the accuracy of inversion using optimal Alkhalifah moveout equation is twice that of inversion using the conventional moveout equation, and the inversion method using the high precision moveout correction equation is the most accurate.