OTC 16945 True 3D Data-driven Multiple Removal ... - PGS

4 OTC
defined grid. A data-driven regularization method, such as
described in Schonewille et al. (2003) that uses the exact
source- and receiver coordinates and allows for regularization
to any user-defined grid is preferred. The proposed preprocessing
sequence is very similar to the well-established
pre-processing for the application of 2D SRME to marine data.
The sequence includes: the removal of the direct wave and its
surface reflection, the removal of non-physical noise and the
directivity effects from source- and receiver arrays (optional),
the recovery of missing shots and intermediate missing traces,
shot interpolation (optional), and the extrapolation to zero
offset of the inline component of the offsets. It is remarked
that, after the optimal sequence and parameterizations have
been found, all steps can be integrated into standardized flows
to increase computational efficiency, and to minimize user
interaction.
Step 2: Multiple prediction through reconstruction in the
crossline direction
After pre-processing, the stacking of the multiple-contribution
traces is carried out in two steps, first in the inline direction
and secondly in the cross-line direction. Stacking of the
multiple contribution traces in the inline direction is
straightforward, as the sampling after pre-processing is
sufficient. However, a direct Fresnel summation in the
crossline direction leads to artifacts due to aliasing and
insufficient aperture. Instead, the crossline summation is
carried out implicitly through a reconstruction of the Fresnel
zone, from a sparse-inversion based estimation of hyperbolic
or parabolic events, with discrete curvatures and apex
positions.
In the literature, three methods for sparse-inversion based
Fresnel zone reconstruction have been described: 1) using a
time domain hyperbolic Radon transform (van Dedem and
Verschuur, 2001); 2) using a frequency domain parabolic
Radon transform (Hokstad and Sollie 2003); and 3)
interpolation using Stolt migration operators (Trad, 2003). The
time-domain approach has been shown to provide good results
for 3D SRME, but is rather expensive. The frequency domain
approach is computationally much more efficient, and has
been shown to provide a good uplift compared with 2D SRME
(Hokstad, 2003). However, using the frequency domain
approach, only sparseness in the spatial direction can be
enforced (Cary 1998, Trad 2003). As a result, for more
complex data with events at many different apex positions,
results may not be as good as with the time-domain approach.
Interpolation with Stolt operators can provide sparseness in
both time and space. The basic algorithm is computationally
very efficient, but shows artifacts. These artifacts can be
reduced, but this does increase the computational costs
somewhat. This is a relatively new technique, and the
suitability for 3D SRME is under further investigation.
As the reconstruction has to be carried out for all source and
receiver combinations, computational efficiency is vital for the
economical viability of sparse-inversion based 3D SRME. In
this paper, an approach is used that is based on the standard
time domain approach described by van Dedem and Verschuur
(2001) but which is much more computationally efficient. The
computational speedup has been achieved through more
efficient sparse matrix computations in a modified conjugate
gradient scheme, and a data driven reduction of the model
space. The results are comparable to those from using the
standard time domain approach, and show significant
improvements over any 2D implementation.
After stacking the multiple-contribution traces in the Fresnel
zone, a single trace with the corresponding predicted multiples
is obtained, which can be used in the last step: the adaptive
subtraction of the predicted multiples from the input data.
Step 3: Adaptive subtraction of predicted multiples
In the last step, the predicted free-surface multiples are
subtracted from the input data using the minimum energy
criterion, which states that the total energy after subtraction of
the multiples should be minimized. In adaptive subtraction
techniques, the predicted multiples are removed using Wiener
filters designed in overlapping windows. In general, great care
must be taken in choosing the filter length and the window
size. If the filter length is too long, it is possible to remove
primaries. Also, choosing too small a design window may lead
to primary energy being affected when multiples and primaries
are interfering. In 3D geometries, the application of 2D
multiple prediction methods leads to multiples that are
predicted too late in time. Using a 3D prediction scheme, the
timing of the predicted multiples is better aligned with the
multiples in the input data, leading to better removal of
multiples. The more accurate timing of the predicted multiples
allows the use of more conservative parameters in the adaptive
subtraction, giving better preservation of primary energy.
Field data example from the Norwegian Sea
In this section, results from a 3D data set from the Norwegian
Sea are shown. Data were shot in a dual-source 10-streamer
configuration, with a 100 meter streamer separation and 500
meter sailline separation. Results for a single offset line for
one of the streamers have already been presented in Van
Dedem and Verschuur (2001). Here, a total of 159 offset
planes with a spacing of 12.5 meters were processed to allow
further prestack processing after the application of 3D SRME.
Figure 9 shows the results for a typical shot gather. Figure 9a
shows the input gather after pre-processing. Figure 9b-c show
the predicted multiples after 2D and 3D SRME respectively. A
comparison indicates that, where the 2D multiples have all
been predicted too late in time, the timing of the 3D predicted
multiples is almost perfect. Figures 9d-e show the results after
adaptive subtraction using the 2D and 3D predicted multiples
respectively. It is remarked that a very mild adaptive
subtraction approach was used in order to preserve the primary
energy as much as possible. Note the much-improved removal
of multiple-energy using the 3D predicted multiples. As a
result, the remaining primaries have become much more
visible. Figure 10 shows the same comparison for an inline at
stack level. Note again the difference in timing between the
2D and 3D predicted multiples, shown in Figs. 10b and c. As a
result, after adaptive subtraction, the 3D result compares
favorably to the 2D results. Both the first-order water bottom
multiple (between 1.0 and 1.2 second), and the reverberations