To implement prestack phase-shift migration, we need to evaluate the phase (or *T*)
for which the data will be shifted.
Unlike zero-offset migration,
where *p*_{h}=0, and therefore the phase can be determined directly, in separate-offset prestack migration
we must first obtain *p*_{h} and then use it to evaluate the phase. The value of *p*_{h} can be determined
numerically using any number of existing
numerical methods (some based on evaluating derivatives), or through using analytical
approximations. The efficiency in the numerical implementations is achieved by setting up numerous precomputed
traveltime tables at different stages of the migration. These tables are necessary to avoid
redundancy in calculations. The analytical
solutions, on the other hand, are restricted, at this point, to homogeneous isotropic and VTI media.
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11/11/1997