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Image-space aliasing can be corrected during processing
without losing resolution
by decreasing the spatial sampling of the image,
because the image sampling is a processing parameter.
In contrast,
operator aliasing can
only be avoided by suppressing some high-frequency components
from the image,
because the data sampling depends on acquisition parameters.
Unfortunately this lowpass filtering
decreases the image resolution.
We therefore face a dilemma when imaging aliased data:
on one side we need to apply anti-aliasing filters to avoid
aliasing noise,
on the other side we do not want to lose image resolution.
Figure exemplifies
the problem.
It shows the results of 3-D zero-offset time migration
of a salt-dome flank in the Gulf of Mexico.
The section on the left (Figure a)
was 3-D migrated without applying any anti-aliasing filter,
while the section on the right (Figure b)
was obtained by applying a standard anti-aliased migration.
Whereas the image obtained without anti-aliasing
is much noisier than the anti-aliased one, it also has higher resolution.
In the shallow part of the section shown
in Figure a,
the aliasing noise
is so strong that is impossible to
appreciate the higher resolution of Figure a
compared with Figure b.
But when comparing zooms into the deeper part of the sections
(Figure ),
it is apparent that by applying anti-aliasing we lose resolution.
In particular, the high-frequency dipping event at about CMP X=700 m
and Time=2.2 s is poorly resolved in the anti-aliased migration
(Figure b).
The anti-aliased migration misses a whole wavelet cycle
of the sediment truncation against the salt flank.
If we consider that hydrocarbon reservoirs are often
located at the sediment-salt interfaces,
we appreciate the potential advantages
of improving the resolution of events
such as the sediment truncation shown in
Figure .
Comp-WL-intro
Figure 1
3-D migrations of a salt-dome flank in the Gulf of Mexico:
(a) migration obtained without any anti-aliasing filter,
(b) migration obtained with the application of a ``standard''
anti-aliasing filter.
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Comp-WB-intro
Figure 2
Zoom into the 3-D migrations of a salt-dome flank in the Gulf of Mexico
shown in Figure :
(a) migration obtained without any anti-aliasing filter,
(b) migration obtained with the application of a ``standard''
anti-aliasing filter.
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Migration without anti-aliasing
achieves higher resolution than the anti-aliased
one because it images data components that are
aliased in the data space.
In particular, the steeply
dipping energy reflected from the salt flanks
visible in the data window shown in
Figure are aliased.
Figure shows the frequency-wavenumber
spectrum of the data window in Figure .
In addition to the central unaliased band of the spectrum,
Figure shows also the
two spatially aliased bands on either side.
The vertical black lines correspond to the Nyquist wavenumbers.
The aliased dipping events correspond to a ``cloud'' in the
spectrum that starts in the main band
but crosses the positive Nyquist line and
trespasses upon the aliased band.
However, because there are no events dipping
with negative time dips,
the aliased components are still recoverable
by the simple anti-aliasing method presented in this paper.
Wind-data
Figure 3
Data window containing aliased reflections from the salt flanks.
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Wind-spec
Figure 4
Frequency-wavenumber spectrum of the data window shown in
Figure .
Notice that the aliased events correspond to
a ``cloud'' in the spectrum that starts in the main band
but crosses the positive Nyquist line and
trespasses upon the aliased band.
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Next: Aliasing in image space
Up: Rickett, et al.: STANFORD
Previous: Introduction
Stanford Exploration Project
7/5/1998