![]() |
![]() |
![]() |
![]() | Measuring image focusing for velocity analysis | ![]() |
![]() |
Figure 7a
shows the migrated stack of the analysis window for a particular
choice of the parameter (
=1.04) that maximizes flatness
in the aperture-angle gather at the midpoint location corresponding
to the black line superimposed onto the stack;
that is for
=5.646 km.
Figure 7b
shows the aperture-angle gather and
Figure 7c
the corresponding semblance panel.
Starting from the prestack images,
I computed dip-decomposed images
that are function of both the aperture angle
and the structural dip
.
Figure 8
shows the 3D cube of the dip-decomposed image at
the same midpoint location as the previous figure;
that is for
=5.646 kilometers.
The convex reflector of interest, at depth of 950 meters,
shows an upward-smiling moveout in the structural-dips panel,
consistently with the result observed
when discussing the synthetic-data example in the previous section.
Figure 9 displays
the image-focusing semblance cube at that same midpoint location.
The left panel in the cube displays semblance as a function
of depth and radius of curvature (
) at
=1.04;
the right panel displays semblance as a function
of depth and
at
=125 meters.
The location of the semblance peak in the cube at depth of 950 meters
is consistent with the location of the semblance peak
in the conventional
scan shown in
Figure 7c.
The semblance peak in the image-focusing cube
is slightly tighter than in the conventional scan,
but the differences are not substantial.
![]() |
---|
Wind-ResMig-all-X5646-overn
Figure 7. The migrated stack of the analysis window for ![]() ![]() ![]() ![]() |
![]() ![]() |
Wind-ResMig-dip-ang-X5646-overn
Figure 8. The dip-decomposed image at ![]() |
![]() |
---|---|
![]() ![]() |
Wind-Sembl-dip-ang-X5646-overn
Figure 9. The image-focusing semblance cube at ![]() ![]() |
![]() |
---|---|
![]() ![]() |
Figures 10-12
shows similar analysis of the migrated images presented above,
but at the midpoint location
corresponding to the reflector with negative curvature;
that is for =5.539 kilometers.
The reflector is locally dipping with negative dip of approximately 45 degrees.
The stationary point in the dip-decomposed image shown in
the right panel of Figure 11
is located at that value of the structural dip,
and it is frowning instead of smiling because of the negative
local curvature.
The value of
for which the reflector is the flattest
along the aperture-angle axis (
=.95),
is substantially lower than for the previous
reflector (
=1.04).
This substantial difference in apparent velocity,
notwithstanding the proximity of the two midpoint locations,
is probably related to the fact that the wavefronts that illuminate
the two events propagate through different zones of the velocity
model due to the dip of the second reflector.
The semblance peak in the image-focusing cube (right panel in Figure 12) is now substantially better defined than in the conventional semblance panel shown in Figure 10c, suggesting a potential resolution benefit for velocity estimation. Further analysis of this potential benefit is needed before drawing definitive conclusions.
![]() |
---|
Wind-ResMig-all-X5539-overn
Figure 10. The migrated stack of the analysis window for ![]() ![]() ![]() ![]() |
![]() ![]() |
Wind-ResMig-dip-ang-X5539-overn
Figure 11. The dip-decomposed image at ![]() |
![]() |
---|---|
![]() ![]() |
Another potential advantage of explicitly taking into account, and correcting for, reflectors' curvature in the semblance analysis, is that it automatically enables the simultaneous measurements of coherency for several structural dips, in addition to the stationary dip, at each analysis point. The semblance measurements are thus automatically averaged along the reflector, following both its local dip and its local curvature. To test this hypothesis, I computed a modified version of the conventional semblance functional along the aperture-angle axis according to the following expression:
Wind-Sembl-dip-ang-X5539-overn
Figure 12. The image-focusing semblance cube at ![]() ![]() |
![]() |
---|---|
![]() ![]() |
![]() |
---|
Wind-Sembl-curv-all-X5539-overn
Figure 13. Comparison of the result of computing the semblance functional defined in 10 (panels a and b) with the result of conventional semblance (panel a), at ![]() |
![]() ![]() |
![]() |
![]() |
![]() |
![]() | Measuring image focusing for velocity analysis | ![]() |
![]() |