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![]() | Interpolation of near offsets using multiples and prediction-error filters | ![]() |
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realshot
Figure 1. A single shot profile from a 2D Gulf of Mexico seismic survey. The nearest offset is at ![]() ![]() |
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Near-offset traces are particularly valuable. Many methods attempt to recreate zero-offset data from larger offsets; standard multiple-removal techniques, such as surface-related multiple elimination (SRME) (Verschuur et al., 1992), require zero-offset data. Moveout differences between primaries and free-surface multiples are slight at these near-offsets thus compromising the performance of radon-based multiple removal algorithms that discriminate based on differential moveout.
There are many methods that could be used to reconstruct this near-offset gap. A simple way of recreating the missing near offsets is to replace the missing offsets with an NMO-corrected trace from the nearest offset. More sophisticated radon-based methods (Sacchi and Ulrych, 1995; Trad et al., 2002) are commonly used, as are Fourier-based methods (Liu and Sacchi, 2001; Xu et al., 2005). These methods all use existing data recorded adjacent to the missing near offsets to create the missing data, so the performance degrades as the gap increases in size, common in undershooting situations.
Another approach to generating data at the missing near offsets starts by first creating pseudo-primary data. Pseudo-primary data are created by crosscorrelating every trace with every other trace within a shot (Berkhout and Verschuur, 2003; , ). The free-surface multiples correlate with the primaries at lags comparable to times when a primary reflection would arrive if one of the receiver locations was the source. Since the receivers now act as virtual sources, near-offset traces can be generated by crosscorrelating traces from nearby receivers, and zero-offset traces by autocorrelating a single trace. These crosscorrelated traces contain many spurious events from correlations other than those between primaries and free-surface multiples or between free-surface multiples and higher-order free-surface multiples, so that the pseudo-primary signal-to-noise ratio for a single crosscorrelation is poor. This can be improved by summing crosscorrelations of the same receiver location pair for many source positions, so the desired pseudo-primary correlations sum while the other correlations interfere destructively. The resulting pseudo-primaries are data that honor the kinematics of the recorded data, but also contain noise, have a different amplitude scale, and have a squared wavelet compared to the recorded data.
Simply substituting these pseudo-primaries for the missing data does not produce an adequate result, as the data contain a squared wavelet, a high level of noise, and spurious events that do not correspond to primary reflections. Instead, here we use the pseudo-primary data as training data for a nonstationary prediction-error filter; whereas the data are inadequate as an interpolation result, they are quite acceptable as training data. The PEF estimation process is relatively insensitive to the phase, amplitude, and squared-wavelet issues that make direct substitution undesirable. This PEF is then used for the interpolation step to fill in the inline near-offset gap.
This approach of using the pseudo-primaries as training data for a PEF
can be performed in the time and offset (-
) domain, the time,
offset and source (
-
-
) domain or the frequency, offset and
source (
-
-
) domain. In the
-
domain, we interpolate
each shot record independently, using a separate non-stationary 2D
-
PEF generated from the corresponding pseudo-primary shot,
while in
-
-
a single PEF is estimated for the entire data
set. In the
-
-
domain, the process is performed on
overlapping time windows of shot records NMO-corrected using water
velocity. A non-stationary 2D PEF is estimated on each frequency
slice of each time window of the pseudo-primaries, which is then used
to interpolate the near-offset gap of the data for the same frequency
slice and time window of the original data. The interpolated result
is then inverse Fourier transformed back to the time domain, the time
windows reassembled, and the NMO correction removed.
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![]() | Interpolation of near offsets using multiples and prediction-error filters | ![]() |
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