3D TTI Implicit Finite Difference Migration With Nonlinear Optimized Four-direction Splitting Expansion

This paper presents an implicit finite difference algorithm for 3D TTI media. We first give the detailed derivation of 3-D TTI dispersion relation equation. We approximate the 3-D TTI dispersion equation with four-direction splitting partial fractional expansion to enable the cascading implementation with implicit finite difference. The expansion coefficients are obtained through a nonlinear optimization of the dispersion error cost function. The strong-amplitude evanescent energy is attenuated with a frequency-dependent phase shift at each depth step. We test and verify our method and implementation with few synthetic examples.