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![]() | Velocity continuation and the anatomy of residual prestack time migration | ![]() |
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From the kinematic point of view, it is convenient to describe the
reflector as a locally smooth surface , where
is the
depth, and
is the point on the surface (
is a two-dimensional
vector in the 3-D problem). The image of the reflector obtained after
a common-offset prestack migration with a half-offset
and a
constant velocity
is the surface
. Appendix A
provides the derivations of the partial differential equation
describing the image surface in the depth-midpoint-offset-velocity
space. The purpose of this section is to discuss the laws of kinematic
transformations implied by the velocity continuation equation. Later
in this paper, I obtain dynamic analogs of the kinematic
relationships in order to describe the continuation of migrated
sections in the velocity space.
The kinematic equation for prestack velocity continuation, derived in
Appendix A, takes the following form:
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![]() | Velocity continuation and the anatomy of residual prestack time migration | ![]() |
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