3D reverse-time migration with hybrid finite difference-pseudospectral method

We propose a 3D reverse-time migration (RTM) using an hybrid Finite Difference (FD) pseudospectral algorithm to solve the two-way acoustic equation. This mainly consists of forward-backward 2D FFT in lateral dimensions (x-y plane) and 1D FD in the depth dimension. This algorithm allows us to get high order accuracy and simplifies the computation of cross derivatives. Therefore our RTM allows to deal with the case of 3D isotropic media, VTI media (Zhou et al., 2006b) and 3D TTI media. The 3D TTI media case lies on a new anisotropic wave equations system (Lesage et al., 2008), which is an extension of 3D VTI media (Zhou et al., 2006b) and 2D TTI media equations (Zhou et al., 2006a) of Zhou et a. This system is based on the combination of two 3D rotations which permits us to deduce 3D TTI equations from 3D VTI equations. In this work, we recall the formalization for 3D isotropic, 3D VTI and 3D TTI media, we also describe the implementation of the method to solve the proposed 3D TTI equations. To validate our proposal, we carry out impulse response experiments for modeling and migration.