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Noise Characterization

The occurrence of shadow zones below the salt body is strongly conditioned by the concavity of its base. In the Sigsbee2b model, the comparison of the diagonal of the Hessian matrix in Figure 1 with the reflectivity model in Figure 2 shows that where the base of the salt is concave down, the transmitted energy is focused and high illumination values are produced; where the base of the salt is concave up, the transmitted energy is spread along to divergent paths, producing low illumination zones. Unfortunately, for reflected energy and also for multiple energy, this geometry acts in the opposite way, concentrating energy where the base of the salt is concave up and dispersing energy where it is concave down. In the shadow zones it is very likely that the strongest remaining amplitudes correspond to multiple reflections, while in the well-illuminated zones these events produce little or no spurious interference with the primary energy (Figure 3). Consequently, during one-way wave-equation inversion, multiple energy can dominate the residuals, surpassing primaries in the shadow zones.

diag-Sis
Figure 1.
Illumination pattern given by the diagonal of the Hessian matrix of the Sigsbee2B model. Dark gray represents low illumination and light gray represents high illumination. [ER]
diag-Sis
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refle-new
refle-new
Figure 2.
Reflectivity model of Sigsbee2B model. [ER]
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mig-stack
mig-stack
Figure 3.
Migration of Sigsbee2b data - zero-subsurface-offset section. [ER]
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One solution to this problem is to attenuate the multiples (events that, in inversion, do not fit the model) from the migration. This requires that the multiples be separated from the primaries or modeled in such a way that during subtraction the primaries are minimally affected.

Traditional data-space demultiple schemes dealing either with periodicity or differential moveout become ineffective in sub-salt settings for two main reasons: a) complex ray paths make periodicity assumptions fail, and b) salt focusing effects concentrates sub-salt reflections in the near offset range, making Radon-type demultiple schemes ineffective. Sava and Guitton (2005) and Alvarez et al. (2007) demonstrated that primaries and multiples have different behavior in image space (subsurface-offset or reflection-angle), and that multiples can be adaptively subtracted from the migration in the image domain without significantly affecting the primaries.

The Sigsbee2B model (Paffenholz et al., 2002) has a high-reflectivity water-bottom. In contrast with Sigsbee2a, this characteristic generates strong peg-leg multiples, which bounce between the salt edge and the water-bottom. In Figure 4 we use part of the zero-offset section of Sigsbee2b data (non-free-surface data) to highlight these multiples and the salt limits in the time domain. The diffractions labeled 1 correspond to the undulating top of the salt; that labeled 2 is the reflection from its base; $ 1^{st}$-order peg-leg diffracted multiples, concurrent with the base of the salt, are labeled 3; the $ 1^{st}$-order peg-leg multiple from the base of the salt is identified with label 4; and internal multiples generated inside the salt body are labeled 5.

ZOtime
Figure 4.
Sigsbee2b zero-offset time section. The labels correspond to 1) top of the salt; 2) base of the salt; 3) $ 1^{st}$-order peg-leg diffracted multiples; 4) internal multiples originated at the salt limits; and, 5) $ 1^{st}$-order peg-leg multiple from the base of the salt. [ER]
ZOtime
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After prestack depth-migration, multiple reflections are distorted, because they are downward propagated beyond their actual reflection depth, using the incorrect velocities of the time-concurrent primaries. If their reflection traveltimes are coincident with sub-salt reflections, their propagation directions are severely deviated; therefore, the shape they assume shows a strong imprint of the velocity model.

In Figure 5 the migration result of Sigsbee2b is shown in a magnified view. The frame on the left is the zero-subsurface-offset section, and the one on the right is a subsurface offset gather - ODCIG - taken at CMP position 38825 ft. The $ 1^{st}$-order peg-leg diffracted multiples, labeled 1, show the effect of over-migration, because they are migrated with salt velocity; labels 2 and 4 stand for migrated peg-leg multiples from the base of the salt, and immediately above them, labeled 3 and 5, are the migrated internal multiples. Some reflectors show focusing close to zero-offset. Notice the strong correlation between the shape of migrated multiples and the base of the salt caused by the deviation of the propagation direction mentioned above. For comparison, Figure 6 shows the migration of Sigsbee2a. In this case, multiples related to the water-bottom (labels 1, 2 and 4) are much weaker or absent, because the water-bottom in this model is characterized by a ``soft'' interface.

sig2b01
sig2b01
Figure 5.
Sigsbee2b shot-profile migration using the cross-correlation imaging condition. The labels correspond to migrated events from 1) $ 1^{st}$-order peg-leg diffracted multiples; 2) $ 1^{st}$-order peg-leg multiple from the base of the salt; 3) internal multiples originated at the salt limits; 4) $ 1^{st}$-order peg-leg multiple from the base of the salt; and, 5) internal multiples originated at the salt limits. The front face corresponds to the image at zero subsurface-offset, and the side face corresponds to the subsurface-offset gather at $ x=38600$ ft. [ER]
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sig2a01
sig2a01
Figure 6.
Sigsbee2a shot-profile migration using the cross-correlation imaging condition. The labels correspond to migrated events from 1) $ 1^{st}$-order peg-leg diffracted multiples; 2) $ 1^{st}$-order peg-leg multiple from the base of the salt; 3) internal multiples originated at the salt limits; 4) $ 1^{st}$-order peg-leg multiple from the base of the salt; and, 5) internal multiples originated at the salt limits. The front face corresponds to the image at zero subsurface-offset, and the side face corresponds to the subsurface-offset gather at $ x=38600$ ft. Compare with Figure 5. [ER]
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Multiples are more evident in regions of low illumination. In Sigsbee data, these regions are associated with a concave-up base of the salt, in which downgoing energy is defocused and upgoing energy is focused. Much of the remaining energy in these regions corresponds to multiples. Figure 7 exemplifies this problem. The ODCIG on the right frame was selected from a low illumination area. The horizontal to upward-curved events are migrated multiples, which contaminate the entire sub-salt section. Because of the low illumination, some reflectors appear as dipping events below 14000 ft. Notice that, in the zero-subsurface-offset section, because of the imprint of the salt velocity, all the multiple modes show different dips than the reflectors.

The different dip behavior of primaries and multiples can be used as a criterion to separate them using a dip filter in the $ k_x-k_h$ wavenumber domain in a pre-processing step. After discrimination, and prior to subtraction from the original data, amplitude and phase of the estimated multiples must be adjusted. We perform this correction by using non-stationary filters, according to the strategy of Alvarez and Guitton (2007). They advocate that the best adjustment between the estimated multiples and the multiples in the data is achieved by simultaneously matching the estimation of primaries and multiples to the data containing both. The strategy uses small overlapping patches of the input data to compute local filters in a least-squares inverse problem.

The next section presents the results of pre-processing and its impact on the inversion output.

migoff1
migoff1
Figure 7.
Sigsbee2b shot-profile migration (subsurface-offset) using the cross-correlation imaging condition. The front face corresponds to the zero subsurface-offset image, and the side face corresponds to the subsurface-offset gather at $ x=36800$ ft. Poorly illuminated areas are dominated by migrated multiples. [ER]
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next up previous [pdf]

Next: Results Up: Reconciling processing and inversion: Previous: Linear least-squares inversion

2009-04-13