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I dip-decomposed the image obtained with the correct slowness
at zero-subsurface offset and corrected it for curvature
according to expression 5.
Figure 4a
shows the dip-decomposed image at the midpoint of one
of the bottoms of the sinusoid (=4.250 km).
Because of the curvature, the dips are not aligned
and the event is frowning down.
Figure 4b
shows the panel in Figure 4a
corrected for image curvature by applying the shift
defined in expression 2.
I selected the radius of curvature to be equal to -90 meters.
This is consistent with the analytical
radius of curvature of the sinusoidal reflector at the same location
of -86 meters.
I set the reflector local dip to be zero; that is,
I set
in expression 2.
The panels shown in
Figure 5
are equivalent to the panels shown in
Figure 4,
except that the midpoint location
is at one of the tops of the sinusoid (=4.750 km).
At this location the curvature is positive and thus the
uncorrected dip panel
(Figure 5a)
smiles upward.
The corrected panel
(Figure 5b)
corresponds to a positive
radius of curvature of 90 meters.
I computed the conventional semblance over aperture angle
and the proposed image-focusing semblance from the
migrated image obtained with the high slowness.
Figure 6
compares the semblance fields computed by the conventional
semblance functional that measures coherency
only over aperture angles
(Figure 6a),
with the semblance cube computed by the proposed
image-focusing semblance functional that measures coherency
over both aperture angles and structural dips
(Figure 6b).
The figure shows the semblance fields at =4.750 km,
that is at one of the local top of the sinusoidal reflector.
The
-range is the same (
)
for the two panels in the figure.
The semblance peak is more sharply defined as a function
of the
parameter in the result of the new image-focusing functional
(right face in Figure 6b)
than in the result of conventional method
(Figure 6a).
Notice that the semblance peak is located at longer radius of curvature
(=125 meters)
than the actual radius of curvature of the reflector
(
=86 meters),
because residual migration in the angle domain
is not exact and does not fully correct for the reflector
curvature.
This error is inconsequential for the proposed method since the aim
is to better estimate
not
.
Refl-sinus-overn
Figure 3. Sinusoidal reflector used to generate the synthetic prestack data set. [ER] |
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ResMig-short-dip-curv-all-X4250-overn
Figure 4. The dip-decomposed images at the midpoint of one of the bottoms of the sinusoidal reflector ( ![]() |
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ResMig-short-dip-curv-all-X4750-overn
Figure 5. The dip-decomposed images at the midpoint of one of the tops of the sinusoidal reflector ( ![]() |
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Wind-Sembl-short-ang-dip-all-X4750-overn
Figure 6. Comparison of the semblance fields computed by the conventional semblance functional that measures coherency only over aperture angles (panel a), with the semblance cube computed by the proposed image-focusing semblance functional that measures coherency over both aperture angles and structural dips (panel b). The figure shows the semblance fields at ![]() |
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![]() | Measuring image focusing for velocity analysis | ![]() |
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