Wave Equation Depth Migration with the Optimum Split-Step Fourier Method In 3-D VTI Media

Abstract

A dispersion equation for transversely isotropic media with a vertical symmetry axis (VTI) is derived from the phase velocity expressed in terms of Thomsen parameters. Based on the vertical wavenumber solved from the dispersion equation, the optimum split-step Fourier 3-D wave equation depth migration method in isotropic media is extended to 3-D VTI media. The macro velocity model used for describing VTI media is consistent with the current velocity estimation method and can simultaneously accommodate the isotropy, weak anisotropy and strong anisotropy. The higher order correction terms added to the phase-shift method makes the proposed algorithm be able to model wider-angle wavefield with high accuracy in the presence of severe lateral velocity variations in 3-D VTI media. The accuracy of the proposed algorithm is demonstrated by 2-D and 3-D migration impulse responses.