Optimized implicit finite-difference migration for VTI media

Guojian Shan

shan@sep.stanford.edu

ABSTRACT

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 finite-difference operator to eliminate the numerical-anisotropy error caused by two-way splitting. This finite-difference operator for VTI media is accurate to $60^\circ$, and its computational cost is almost the same as the isotropic migration. I apply this method to a 2D synthetic dataset and a 2D slice of a real 3D dataset to validate the method.