Abstract：The research of anisotropic medium migration has become nowadays a hot topic. In this paper,we develop an anisotropic one-way wave Fourier finite-difference (FFD) propagator for quasi-P (qP) waves in transversely isotropic media with a vertical symmetry axis (VTI). The qP waves' dispersion relation in VTI media is derived from elastic wave equations under the assumption of acoustic approximation. With a rational approximation we construct FFD propagators with different precisions. All of these propagators are made up of the phase-shift term in the frequency wavenumber domain,the time-shift term and the finite-difference term in the frequency space domain. So high order FFD prestack depth migration method for VTI media is formed. It contains great efficiency of one-way wave migration,can be applied to medium containing large lateral perturbations of velocity,and focus on the anisotropic effect to waves propagation,so higher imaging precision for steep structure can be obtained. Finally,the value of the propagator is demonstrated by error analysis,impulse responses,and prestack depth migration of SEG/EAGE salt model.
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