Globally optimized finite-difference extrapolator for strongly VTI media

The finite-difference (FD) migration is unconditionally stable and is popular in handling strong velocity variations, but its extension to strongly VTI media is difficult. Traditional local optimizations generate the optimized coefficients for each pair of Thomsen anisotropy parameters independently, which can degrade results substantially for large anisotropy variations and lead to a huge table. In this paper, we obtain an implicit FD method using the analytic Taylor-series expansion and present a global optimization scheme to improve its accuracy for wide phase angles. Compared with traditional local optimization, our scheme does not need any table and table lookup. For each order of the FD method, only one group of optimized coefficients is enough to handle strong variations in both velocity and anisotropy. More importantly, our global optimization scheme guarantees the accuracy for various possible ranges of anisotropy parameters, no matter how strong the anisotropy is. For the globally optimized 2nd-order FD method, the accurate phase angle is up to 58° and the increase is about 18°~22°. For the 4th-order FD method, the accurate phase angle is up to 77° and the increase is about 22°~27°.