Seismic anisotropy in dipping shales causes imaging and positioning problems for underlying structures. We developed an anisotropic depth‐migration approach for P-wave seismic data in transversely isotropic (TI) media with a tilted axis of symmetry normal to bedding. We added anisotropic and dip parameters to the depth‐imaging velocity model and used prestack depth‐migrated image gathers in a diagnostic manner to refine the anisotropic velocity model. The apparent position of structures below dipping anisotropic overburden changes considerably between isotropic and anisotropic migrations. The ray‐tracing algorithm used in a 2-D prestack Kirchhoff depth migration was modified to calculate traveltimes in the presence of TI media with a tilted symmetry axis. The resulting anisotropic depth‐migration algorithm was applied to physical‐model seismic data and field seismic data from the Canadian Rocky Mountain Thrust and Fold Belt. The anisotropic depth migrations offer significant improvements in positioning and reflector continuity over those obtained using isotropic algorithms.

Two numerical inversions were designed to calculate the 21 independent stiffnesses that define, in general, an anisotropic medium from either group-or phasevelocity data. The accuracy, robustness and computational complexity of the two inversion procedures-group velocity to stiffnesses and phase velocity to stiffnesseswere then compared. This group-velocity inversion overcomes the difficulty of calculating group velocity in a prescribed direction and can calculate group velocities accurately even in directions near shear-wave singularities. Although phase velocities are easier to calculate than group velocities, the group-velocity inversion performed better in laboratory tests because group velocities are easier to measure.

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