A phase-shift based migration algorithm for transverse isotropy (TI) is described where the downward continuation operators are derived from the corresponding phase-shift propagators. The operators are applied in the space-frequency domgin either explicitly or implicitly. Results demonstrate that an extension to the standard implicit stencil is required when migrating with nonelliptical velocity models. The number of coefficients required depends very much on the degree of anisotropy and the mode in question. Some conclusions are drawn as to the number of coefficients required for a given maximum phase angle . The modification of explicit operators for anisotropy is relatively straightforward and they are used for TI media with tilted symmetry axes. For this implementation (one-way downward continuation) both the ray velocity and phase velocity have to be downwand going. For media with tilted symmetry axes, where some of the upward going energy corresponds to downward going plane waves and vice versa, the range of phase angles used in the operator design has to be limited accordingly. The method has been implemented for both prestack and poststack migration. The issue of deriving the velocity model using modifications to the standard surface seismic processing sequence is also addressed .


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