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![]() | Interpolation of near offsets using multiples and prediction-error filters | ![]() |
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In Figure 11 the time axis ( samples long) of
both the input sampled data and the pseudo-primaries were broken into
overlapping windows of
points each. Both sets of windows
were then Fourier transformed to produce
2D frequency slices.
Each frequency slice is treated as a separate problem, with a 2D
nonstationary PEF estimated on the pseudo-primary frequency slice; the
2D PEF was four samples long on both the offset and shot axes, and the
filter varied every four points on each axis, for a total of
filter coefficients for each
-shot by
-offset frequency
slice, estimated with
iterations of a conjugate-direction
solver. The data were then interpolated using
iterations of a
conjugate-direction solver on equation 4, again
with an initial model of the missing data an NMO-corrected
nearest-offset-trace from the same midpoint.
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fxinterp
Figure 11. Interpolation with pseudo-primaries with 2D ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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The frequency-domain interpolation in Figure 11
differs in several respects from the -
domain interpolation in
Figure 9. First, the
-
-
result still has
some crosstalk present, while the
-
and
-
-
results have
almost no crosstalk from spurious events. This is most visible prior
to the water-bottom reflection. We believe this is in part due to the
stationarity assumption within each time window. However, the large
spurious event at a (
) and (
) is not present in the result in
either case. Second, the
-
-
result shows less shot-to-shot
variation than does the
-
result, and less amplitude variability
than the
-
-
result. This is because in the
-
result
each shot is interpolated separately as an independent problem, while
the
-
-
interpolation estimates a PEF that spans both the
offset and source axes, minimizing this jitter. Finally, the
-
-
result appears to contain more detail in the result than
does the
-
result. In particular, events below the water-bottom
in the shot that were not interpolated in the
-
case, in the
right panel of Figure 9, were interpolated in the
-
-
case on the right panel of Figure 11.
This synthetic data example produced promising results for
interpolation of a large gap using information only from the recorded
data. The -
-
approach improved results and was still
multiple times faster than the
-
or
-
-
interpolation
methods. The synthetic data were noise-free, and only contained the
desired primaries and multiples, with an idealized 2D geometry. Next,
we examine how this method works on field data.
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![]() | Interpolation of near offsets using multiples and prediction-error filters | ![]() |
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