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Ground roll is nearly always spatially aliased, so the relatively unaliased example of Figure 3
is a somewhat unrealistic exception to the practical rule. To inject some realism, we decimated the
original 2D shot gather (Figure 3) by a factor of two in offset, as shown in Figure
8, so that the ground roll is quite aliased. Figure 9
compares the RTT of the decimated data. The results are disappointing. Looking at the vinterpolation
without infill panel (top), the human eye can easily interpolate vertically to reconstruct the radial
events in RT space. Unfortunately, the vinterpolation panel with infill does not have the desired
vertical coherence. In fact, it would seem that the central premise motivating this paper  that the
RTT maps ground roll to zero temporal frequency  is violated.
Figures 10 and 11 are
analogous to Figures 6 and 7 
they are the estimates of signal and noise, respectively. All implementations (vinterpolation with and
without infill, and xinterpolation) do an relatively poor job of noise suppression.
A simple way to dealias linear ground roll is to apply a linear moveout (LMO) correction. Figure
12 shows the result of applying a 1.5 km/sec LMO correction to the decimated data of
Figure 8. The ground roll is no longer spatially aliased, but the
primaries are also no longer ``flat'', as they were originally. As a result, interpolation errors for
the xinterpolation RTT will increase. Figure 13 compares the RTT panels
for the decimated/LMO'ed data. The ground roll now occupies a higher effective velocity band,
and more importantly, is much closer to zero temporal frequency than in Figure 9.
The noise suppression achieved (Figure 14) is better than the case in which
LMO was not used (Figure 10). As expected, and mentioned above, the xinterpolation
RTT leads to severe losses of signal energy, quite a bit more severe than either of the two vinterpolation
implementations, as can be seen in Figure 15.
Unfortunately, both vinterpolation implementations seem to suffer some small signal losses, which suggests
that LMO may actually be ``aliasing'' the primaries by mapping them to low temporal frequency in the RT domain.
hectoraliasdat
Figure 8 Same 2D shot gather as Figure 3,
only decimated by a factor of two in offset.

 
hectoraliasradialcomp
Figure 9 Top: vinterpolation without infill.
Middle: vinterpolation with infill. Bottom: xinterpolation.
hectoraliasestsig
Figure 10 Estimated signal.
Top: vinterpolation without infill.
Middle: vinterpolation with infill.
Bottom: xinterpolation.
hectoraliasestnoiz
Figure 11 Estimated noise.
Panels defined as in Figure 10.
hectorlmodat
Figure 12 Decimated 2D shot gather (Figure
8), after 1.0 km/sec linear moveout correction.

 
hectorlmoradialcomp
Figure 13 Top: vinterpolation without infill.
Middle: vinterpolation with infill. Bottom: xinterpolation.
hectorlmolmoestsig
Figure 14 Estimated signal.
Top: vinterpolation without infill.
Middle: vinterpolation with infill.
Bottom: xinterpolation.
hectorlmolmoestnoiz
Figure 15 Estimated noise.
Panels defined as in Figure 14.
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Stanford Exploration Project
4/28/2000