Pre-stack reverse-time migration based on the time–space domain adaptive high-order finite-difference method in acoustic VTI medium

With the increment of seismic exploration precision requirement, it is significant to develop the anisotropic migration methods. Pre-stack reverse-time migration (RTM) is performed based on acoustic vertical transversely isotropic (VTI) wave equations, and the accuracy and efficiency of RTM strongly depend on the algorithms used for wave equation numerical solution. Finite-difference (FD) methods have been widely used in numerical solution of wave equations. The conventional FD method derives spatial FD coefficients from the space domain dispersion relation, and it is difficult to satisfy the time–space domain dispersion relation of the wave equation exactly. In this paper, we adopt a time–space domain FD method to solve acoustic VTI wave equations. Dispersion analysis and numerical modelling results demonstrate that the time–space domain FD method has greater accuracy than the conventional FD method under the same discretizations. The time–space domain high-order FD method is also applied in the wavefield extrapolation of acoustic VTI pre-stack RTM. The model tests demonstrate that the acoustic VTI pre-stack RTM based on the time–space domain FD method can obtain better images than that based on the conventional FD method, and the processing results show that the imaging quality of the acoustic VTI RTM is clearer and more correct than that of acoustic isotropic RTM. Meanwhile, in the process of wavefield forward and backward extrapolation, we employ adaptive variable-length spatial operators to compute spatial derivatives to improve the computational efficiency effectively almost without reducing the imaging accuracy. (paper)