Anisotropic reverse-time migration for tilted TI media

Xiang Du, John C. Bancroft, Laurence R. Lines

Seismic anisotropy in dipping shales results in imaging and positioning problems for underlying structures. We develop an anisotropic reverse-time depth migration approach for P-wave and SV-wave seismic data in transversely isotropic (TI) media with a tilted axis of symmetry normal to bedding. Based on an accurate phase velocity formula and dispersion relationships for weak anisotropy, we derive the wave equation for P-wave and SV-wave propagation in tilted transversely isotropic (TTI) media. The accuracy of the P-wave equation and the SV-wave equation is analyzed and compared with other acoustic wave equations for TTI media. Using this analysis and the pseudo-spectral method, we apply reverse-time migration to numerical and physical-model data. According to the comparison between the isotropic and anisotropic migration results, the anisotropic reverse-time depth migration offers significant improvements in positioning and reflector continuity over those obtained using isotropic algorithms.