Velocity analysis after migration

The double‐square‐root (DSR) equation used in pre‐stack migration is formulated in terms of velocity‐dependent and velocity‐independent terms. The velocity‐dependent term is shown to be the hyperbolic normal moveout (NMO) correction, whereas the velocity‐independent term is related to the recording geometry only. This separation of the velocity‐dependent term offers a means of applying vertical corrections to an initial migration velocity field. Using this concept, procedures are described both for velocity determination and for achieving improved structural imaging.
This decoupling is accurate both for constant‐velocity media and for media whose velocity varies as a function of depth. In media whose velocity varies as a function of both space and depth, a procedure is described for building velocity models through common‐image gather (CIG) stacking following prestack depth migration (PSDM) and time conversion (TC). This so‐called PSDM‐TC stack procedure provides a means of (a) incorporating both vertical and lateral velocity updates into an initial velocity model, (b) obtaining improved structural imaging by using a non‐optimal velocity model for the prestack depth migration, and (c) updating velocity by flattening CIGs and maximizing stack energy. The procedure can be applied to both P‐P wave and P‐SV wave migration.