Figure 5 shows the positions of a point ``*P*_{orig}" for several
different values of residual slowness for one initial
dip and 3 different
offsets. The new positions *P _{0}*,

The previous section gave the necessary equations to compute residual constant-offset migration operators; subtracting the residual zero-offset migration part of residual constant-offset migration, obtained from the same equations, gives residual NMO+DMO. Amplitudes of the residual NMO+DMO operators are obtained with the same method used to obtain the amplitudes of residual constant-offset migration operators. Figure 7 shows the residual NMO+DMO operators for a series of depth points for a large offset for and .

Residual constant-offset migration has the desired property that
it performs residual common-reflection-point gathering.
For any residual slowness, any point on the
output images of different constant-offset sections all correspond to
the same reflection point. This is a necessary step for
correct migration
velocity analysis. Velocity analysis
uses the traveltime of reflections
from a single point in the earth; thus, when performing
migration velocity analysis by comparing
traveltimes versus offset, the relevant
part of residual constant-offset migration is
residual NMO+DMO. The residual zero-offset migration part
of residual constant-offset migration confuses velocity
analysis by moving the image of a fixed reflection event
around the image as the migration slowness changes
(Fowler, 1988; Etgen, 1989).
It is preferable to ignore the residual zero-offset migration
term and keep a fixed reflection event at a fixed location
in the image. This is analogous to conventional velocity
analysis where NMO and stacking are performed at a
fixed *t _{0}*. The true-depth position of the reflector can be
calculated and stored, and residual zero-offset migration
can be applied later, after velocity analysis. The
kinematic residual zero-offset migration is needed
by tomographic velocity analysis methods.

1/13/1998