Velocity continuation and the anatomy of residual prestack time migration |

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:

- Kinematics of Zero-Offset Velocity Continuation
- Kinematics of Residual NMO
- Kinematics of Residual DMO

Velocity continuation and the anatomy of residual prestack time migration |

2014-04-01