Optimized implicit finite-difference migration for TTI media

I develop an implicit finite-difference migration algorithm for tilted transversely isotropic (TTI) media. I approximate the dispersion relation of TTI media with a rational function series, whose coefficients are estimated by least-squares optimization. The dispersion relation of TTI media is not a symmetric function, so an odd rational function series is required in addition to the even one. These coefficients are functions of Thomsen anisotropy parameters. They are calculated and stored in a table before the wavefield extrapolation. Similar to the isotropic and VTI media, in 3D a phase-correction filter is applied after the finite-difference operator to eliminate the numerical error caused by two-way splitting. I generate impulse responses for this algorithm and compare them to those generated using the phase-shift method.