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Optimized Implicit Finite-difference Migration For TTI Media

I develop an implicit finite-difference migration method for vertical transversely isotropic (VTI) media with laterally varying anisotropy parameters. I approximate the dispersion relation of VTI media with a rational function series, the coefficients of which are estimated by least-squares optimization. These coefficients are functions of Thomsen anisotropy parameters. They are calculated and stored in a table before the wavefield extrapolation. The implicit finite-difference scheme for VTI media is almost the same as that of the isotropic media, except that the coefficients are derived from the pre-calculated table. In the 3D case, a phase-correction filter is applied after the finitedifference operator to eliminate the numerical-anisotropy error caused by two-way splitting. This finite-difference operator for VTI media is accurate to 60 for the 2nd order approximation and 80 for the 4th order approximation. Its computational cost is almost the same as the isotropic migration. I apply this method to a 2D synthetic dataset to validate the method.