Wavelength-dependent Fresnel beam propagator and migration in VTI media

Ray-based wave propagators are widely applied in seismic migration due to implementation flexibility and computational efficiency. The classic ray theory that under the high-frequency assumption requires sufficiently smooth velocity models, which limits the applications of ray-based methods because seismic waves are band-limited. Besides, it is desirable to extend seismic propagation and migration to general anisotropic case since the reality of subsurface. We adapt a wavelength-dependent smoothing (WDS) operator for transversely isotropic media with a vertical symmetry axis (VTI), which considers both characteristics of band-limited wave propagation and local anisotropic heterogeneity. Frequency-dependent traveltimes are computed with the WDS models by using an anisotropic dynamic programming approach. Then, a wavelength-dependent Fresnel beam propagator is constructed based on the frequency-dependent traveltimes. Analysis of traveltime fields demonstrates that wavelength-dependent Fresnel beam propagator can provide accurate wave propagating directions and traveltimes. We develop a wavelength-dependent Fresnel beam migration (WDFBM) method based on the wavelength-dependent Fresnel beam propagator for VTI media, which generates angle domain common imaging gathers (ADCIGs) efficiently. Numerical examples are included to demonstrate the effectiveness of our approach, which shows its potential application for subsequent velocity estimation via ADCIGs.