From the kinematic point of view, it is convenient to describe the
reflector as a locally smooth surface *z* = *z*(*x*), where *z* is the
depth, and *x* is the point on the surface (*x* 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 *h* and a
constant velocity *v* is the surface *z* = *z*(*x*;*h*,*v*). 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 analogues of the kinematic
relationships in order to describe continuation of migrated sections in the velocity space.

The kinematic equation for prestack velocity continuation, derived in Appendix A, takes the following form:

(1) |

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

11/12/1997