Velocity continuation and the anatomy of residual prestack time migration |

with the undetermined function . In the case of , the general solution is easily found to be

where is an arbitrary smooth function. The combination of dynamic equations (44) and (41) leads to an approximate prestack velocity continuation with the residual DMO effect neglected. To accomplish the combination, one can simply add the term from equation (44) to the left-hand side of equation (41). This addition changes the kinematics of velocity continuation, but does not change the amplitude properties embedded in the transport equation (42).

Dunkin and Levin (1973) and Hale (1983) advocate using
an amplitude correction term in the NMO step. This term can be
easily added by selecting an appropriate function in
equation (44). The choice
results in the equation

which has the Dunkin-Levin amplitude correction term.

Velocity continuation and the anatomy of residual prestack time migration |

2014-04-01