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In a previous section,
we demonstrated
that in an ADCIG cube the imaging point lies on the
line normal to the apparent geological dip and passing
through the point where the source and receiver rays cross
(Figure ).
This geometric property enabled us to define
the analytical relationship between reflector movement
and traveltime perturbation
expressed
in equation (15).
This important result is verified by the numerical
experiment shown in
Figure .
This figure compares the images of the spherical reflector
obtained using the low velocity
(slowness scaled by )with the reflector position computed analytically under
the assumption that is indeed the image point
in an ADCIG.
Because both the true and the migration velocity
functions are constant, the migrated reflector
location can be computed exactly by a simple
``kinematic migration'' of the recorded events.
This process takes into account the difference
in propagation directions between the ``true'' events
and the ``migrated'' events
caused by the scaling of the velocity function.
Appendix C derives the equations used to compute the
migrated reflector location as a function of , ,and .
The images shown in the six panels in
Figure correspond to
six different apparent aperture angles:
a) ,b) ,c) ,d) ,e) ,f) .The black lines superimposed onto the images
are the corresponding
reflector locations predicted by the relationships derived
in Appendix C.
The analytical lines perfectly track the migrated images
for all values of .The lines terminate when the corresponding event
was not recorded by the data acquisition geometry (described above).
The images extend beyond the termination of the analytical lines
because the truncation artifacts are affected
by the finite-frequency nature of the seismic signal,
and thus they are not predicted by the simple kinematic modeling
described in Appendix C.

**Tomo-slow-4p-overn
**

Figure 13
Comparison of the actual images
obtained using the low velocity,
with the reflector position computed analytically under
the assumption that the image point
lies on the normal to the apparent geological dip
( in Figure ).
The black lines superimposed onto the images
are the reflector locations predicted by the relationships presented
in Appendix C.
The six panels correspond to
six different apparent aperture angles:
a) b) c) d) e) f) .

** Next:** Residual moveout in ADCIGs
** Up:** Illustration of CIGs kinematic
** Previous:** Transformation of HOCIGs and
Stanford Exploration Project

7/8/2003