SEISMIC MIGRATION IN ELLIPTICALLY ANISOTROPIC MEDIA¹

The study of wave propagation in media with elliptical velocity anisotropy shows that seismic energy is focused according to the horizontal component of the velocity field while the vertical component controls the time‐to‐depth relation. This implies that the vertical component cannot be determined from surface seismic velocity analysis but must be obtained using borehole or regional geological information. Both components of the velocity field are required to produce a correctly focused depth image. A paraxial wave equation is developed for elliptical anisotropic wave propagation which can be used for modelling or migration. This equation is then transformed by a change of variable to a second paraxial equation which only depends on one effective velocity field. A complete anisotropic depth migration using this transformed equation involves an imaging step followed by a depth stretching operation. This allows an approximate separation or splitting of the focusing and depth conversion steps of depth migration allowing a different velocity model to be used for each step. This split anisotropic depth migration produces a more accurate result than that obtained by a time migration using the horizontal velocity field followed by an image‐ray depth conversion using the vertical velocity field. The results are also more accurate than isotropic depth migration and yield accurate imaging in depth as long as the lateral variations in the anisotropy are slow.