We propose a new anisotropic wave equations system for 3D TTI media, which is an extension to 3D VTI media and 2D TTI media equations of Zhou et al. This system is based on two 3D rotations which permit us to deduce 3D TTI equations from 3D VTI equations. We propose to use a hybrid Finite Difference (FD) pseudospectral algorithm to solve it, 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 the cross derivatives of the TTI equations. In this work, we develop the 3D TTI equation formalization, 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.


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