Wavelength-dependent Fresnel Beam 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 sufficient smooth velocity models, which limits the developments of ray-based methods for the fact that practical 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 operator for transversely isotropic with a vertical symmetry axis (VTI) media, which considers both characteristics of band-limited wave propagation and local anisotropy. Frequency-dependent traveltimes are computed with the wavelength-dependent smoothed model 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 method by using the wavelength-dependent Fresnel beam propagator for VTI media, which can generate angle domain common imaging point gathers (ADCIGs) conveniently. Numerical examples are included to demonstrate the effectiveness of our approach, which shows its potential application for subsequent velocity estimation via ADCIGs.