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Applications of interbed multiple attenuation

Surface-related multiple attenuation schemes have proven useful in attenuating a significant proportion of the high-

amplitude multiple content in seismic data. Although generally sufficient for exploration purposes, there is growing recognition that more complicated interbed multiples exist within the data and that they may interfere with the interpretation of reservoirs and other areas of interest. In this paper, we examine a data-driven method and a model-driven method for attenuating internal multiples showing both synthetic and real-world examples of their application.

IntroductionInterbed multiple contamination has been observed previously during reservoir studies from the North Sea, Middle East, and Asia Pacific regions, where shallow carbonates or volcanics gen-erate strong reverberations. Frustrating to all parties, this noise has, for a long time, been categorized as "too difficult" to ad-dress because it resists traditional multiple attenuation meth-ods; the multiples and primaries have similar moveout reducing the effectiveness of Radon-based methods, the multiples and primaries have similar frequencies and amplitudes reducing the effectiveness of predictive filtering, and the multiples and pri-maries have similar dips reducing the effectiveness of f-k filters, tau-p demultiple, and migration methods implementing dip-discrimination techniques during the imaging (for example, controlled-beam migration).

The discovery of the Tupi/Lula Field, offshore Brazil, in 2006, and later discoveries of Jupiter, Sugarloaf, Iara, Azulao, and Iracema have confirmed the potential for significant, presalt, oil accumulations in the Santos Basin. One of the seismic imag-ing challenges in the basin, however, is the existence of high-am-plitude interbed multiple contamination across the reservoir. An example can be seen in Figure 1 which shows a migrated image.

Figure 2 shows near-offset data from a second line in the Santos Basin. Note that the first surface-related multiple appears well below the presalt target. Strong interbed multiples, how-ever, contaminate the presalt primaries. The interbed multiples are generated by a series of strong reflectors above the target. The water bottom, top of Albian layer, top of salt, and layered evaporites can all contribute toward generating strong interbed multiples. The strongest of these multiples appear below syn-cline structures in the top of salt and layered evaporites, due to a focusing effect that traps multiple energy in the minibasin (Pica and Delmas, 2008). The migrated results, Figures 1 and 2b, show the interbed multiples cross-cutting the reservoir. These interfere with the interpretation of the base of salt event, the reservoir, and the presalt faulting.

Following the advent of data-driven surface-related multiple attenuation by Berkhout et al. (Berkhout and de Graaff, 1982; Verschuur, 1991; Berkhout and Verschuur, 1998), many authors have extended the data-driven concept to include interbed mul-tiple attenuation. Many methods based on the work of Jakubo-wicz (1998) have appeared in the literature, for example Ikelle

MalcolM Griffiths, Jeshurun heMbd, and hervé PriGent, CGGVeritas

(2004). These all require a two-trace convolution followed by a single-trace correlation or some combination thereof. Equivalent model-driven methods also exist based on the same concept, no-tably from Pica and Delmas (2008). The concept has also been converted to the inverse data space by Luo et al., (2007). The implicit limitation of this method is that it predicts only inter-nal multiples associated with a single horizon, typically defined inside a single layer, predicting internal multiples from the sur-rounding reflectors that will cross this horizon along their path.

A second extension to the data-driven internal multiple at-tenuation methods, again pioneered by Berkhout et al., (Berk-hout and Verschuur, 1997 and 1999; Berkhout, 1999), utilizes common focal point transforms (CFP) to partially redatum (receiver side) and fully redatum the input seismic to the level of the multiple-generating horizon. The method is similar to Jakubowicz’s method in that it requires a two-trace convolu-tion followed by a single-trace correlation and predicts only the multiples associated with a single horizon or layer, but it also requires two redatuming steps and the associated CFP operators. Kelamis et al. (2002) and Ala’i et al. (2006) demonstrated this method on land data highlighting the difficulty associated with the estimation of the CFP operators.

Yet another method of internal multiple attenuation has been pioneered by Weglein et al. (1997) using the inverse-scat-tering series. This method is again fully data-driven but has the added benefit of being capable of predicting all interbed mul-tiples in a single iteration, (Weglein et al., 2008). Depending upon the implementation complexity, it is possible to predict either an approximation to the internal multiples (leading term), or through an infinite series, the exact internal multiple contri-bution, (Ramirez, 2008). This method has been previously dem-onstrated on marine data by Otnes et al. (2004) and on land data by Fu et al. (2010).

With the exception of these inverse-scattering infinite series, all these methods rely upon some form of adaptive subtraction in order to attenuate the internal multiple. This has a plethora of problems associated with it, foremost of which is potential primary damage. None of these issues are covered in this pa-per—see Abma et al. (2002) for a detailed analysis of adaptive subtraction techniques.

This paper describes the application of two of the above

Figure 1. Migrated image showing strong interbed multiples in data from the Santos Basin. (Courtesy of Petrobras)

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methods for attenuating internal multiples: a 3D data-driven method derived from Jakubowicz, and the 3D model-driven method from Pica. The focus is on the interbed multiple con-tamination at the reservoir level for various exploration inter-ests within the Santos Basin, Brazil. The results, however, are equally applicable to reservoir-level contamination observed in the North Sea, Middle East, and Asia Pacific.

MethodologyMany factors influence the effectiveness of the various internal multiple attenuation algorithms; geological complexity (mul-tiple periodicity) and acquisition design (offset coverage and spatial sampling) are two key factors. It is then not surprising that the application of any algorithm should first consider the input limitations.

The 3D data-driven method, following Jakubowicz, is il-lustrated in Figure 3. An arbitrary horizon is chosen at a point deeper than the known multiple-generating horizon. The inter-nal multiples predicted are then limited using various muting methods but are always those having the first upward reflection below the user-defined horizon, a downward reflection above the user-defined horizon, and a final upward reflection below the user-defined horizon. The prediction is given mathemati-cally in Equation 1.

P212 = P2P1*P3 (1)

P1 refers to the wavefields from the surface to the multi-ple-generating horizons, P2 refers to the source-side wavefield reflecting from below the multiple-generating horizon, and P3

Figure 2. Interbed multiples in data from the Santos Basin. Note the strong interbed multiples obscuring the presalt target in the near-offset data (left). The first surface-related multiple appears at the bottom of the figure, below the target. The Kirchhoff-migrated image (right) shows that migration swings crossing the base of the target and interfering with fault interpretation at the target. (From Hembd et al., 2011)

Figure 3. Prediction of multiples reflecting downward from horizon 1.

Figure 4. Backward extrapolation of the muted input data. (From Pica and Delmas 2008)

Figure 5. Previously stored wavefield will illuminate the reflectivity section. (From Pica and Delmas, 2008)

Figure 6. Downward extrapolation of the wavefield resulting from the secondary sources created at stage 2. (From Pica and Delmas, 2008)

Figure 7. Final upward extrapolation. (From Pica and Delmas, 2008)

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refers to the receiver-side wavefield reflecting from below the multiple-generating horizon. P1* refers to the complex conju-gate of P1. Equation 1 neglects both the source term and the surface reflectivity which can both be compensated for using a least-squares matching filter during the subtraction stage. It also includes both primary and higher-order multiple contributions to the interbed multiple prediction. The task of localized wavelet matching falls upon the subtraction.

Without knowledge of the downward reflection point, how-ever, it becomes necessary to sum Equation 1 over a user-defined aperture. The method places a high reliance upon the input ac-quisition density. For accuracy, it requires shot and receiver sta-tions at all possible surface locations as well as measurements of the wavefield at zero offset. Not surprisingly, these are the

same limitations found in the surface multiple implementation and, as such, the method is found to work reasonably well in deeper water where the near offsets can be easily extrapolated and in wide-azimuth acquisitions where the azimuthal sampling is closer to ideal.

The 3D model-driven method also follows the logic of Jakubowicz. In it, the input data are backward-propagated though a predefined model to the user-defined arbitrary horizon (Figure 4). The horizon is defined in the same way as in the data-driven method. Prior to the back-propagation, the input data must first be muted to remove all reflections above the tar-get horizon. Once at the target horizon, the wavefield is upward extrapolated through the model to illuminate the shallow events, thus identifying the downward reflection points in Figure 5.

Figure 9. RTM comparison of the Santos Basin synthetic data: (left) before and (right) after data-driven interbed multiple attenuation. (From Hembd et al., 2011)

Figure 8. 2D synthetic data of the Santos Basin used for the data-driven interbed multiple attenuation: (left) input, (center) subtraction result, and (right) difference. (From Hembd et al., 2011)

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For each possible reflection point, the wavefield is downward propagated through the model a second time until it reaches the reflecting horizons (Figure 6) where it is finally forward propa-gated to the surface (Figure 7). The entire procedure mimics the data-driven case but has two distinct advantages; it doesn’t re-quire a dense shot sampling on the surface, and it doesn’t require records at zero offset. It does, however, require a reflectivity and

Figure 11. Migrated comparison of Santos Basin 3D data: (left) before and (right) after model-driven interbed multiple attenuation. (Courtesy of Petrobras)

Figure 10. Kirchhoff comparison of Santos Basin 3D data: (left) before and (right) after data-driven interbed multiple attenuation. (From Hembd et al., 2011)

velocity model.

Application3D data-driven interbed multiple prediction was performed on 2D synthetic data and on 3D real data from the Santos Basin. With 3 s of water and shallow multiple generators, these data were well suited to the data-driven interbed algorithm. The syn-

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thetic data (Figure 8) were generated using an acoustic wave-equation modeling package, a velocity field extracted from the 3D real data processing, and an arbitrary density model. The interbed multiples were predicted using the water bottom (at approximately 3 s) and the top of salt horizon (at approximately 4 s) as the multiple generators. Figure 9 shows the synthetic re-sults after migration highlighting the impressive attenuation of the strongly focused interbed multiples beneath the minibasins.

The real data results (Figure 10) were generated using a single iteration of interbed multiple prediction targeting the water-bottom multiples. Analysis of the postmigration interbed attenuation results shows a considerable reduction in the sub-salt migration noise (attributed to interbed multiples). However, some residual multiple-related events are visible on the real data cross-cutting the base of salt. Although the subtraction is by no means perfect, these residuals are most likely related to an im-perfect or incomplete prediction. Interbed multiples generated from the top of salt horizon and from the layered evaporate ho-rizons remain unaccounted for.

3D model-driven prediction was also performed on the real data to target the intrasalt multiples (Figure 11). The reflectiv-ity model was obtained through prestack time migration of a few near offsets and the arbitrary reference horizon was cho-sen 100 ms below the top salt (hence, considered the principal downward reflector). All reflectors down to 1 km below top salt were considered as potential upward generators. A minimum gap separating upward and downward reflectors was also used. This corresponds to the shortest leg of the modeled multiple and is needed to avoid modeling primary signal. After modeling, a conservative 3D adaptation and subtraction was performed in the offset domain. The results (Figure 11) show a promising at-tenuation of some events cross-cutting the base of salt and slight-ly improved continuity on some targeted presalt events.

ConclusionIn this paper, we have demonstrated the impact of interbed multiple attenuation on synthetic and real data from the Santos Basin. It has been shown that clearer images of the reservoir zone can be obtained by attenuating the influence of shallower, internal multiple-generating horizons in an informed and de-liberate fashion. The choice between data-driven and model-driven prediction is shown to be one of convenience with both methods performing admirably.

ReferencesAbma, R., N. Kabir, K. H. Matson, S. A. Shaw, B. McLain, and S. Mi-

chell, 2002, Comparisons of adaptive subtraction techniques for multiple attenuation: 72th Annual International Meeting, SEG, Ex-panded Abstracts, 2186–2189.

Ala’i, R. and E. Verschuur, 2006, Case Study of surface-related and in-ternal multiple elimination on land data: 76th Annual International Meeting, SEG, Expanded Abstracts, 2727–2731.

Berkhout, A. J., 1999, Multiple removal based on the feedback model: The Leading Edge, 18, no. 1, 127–131, doi:10.1190/1.1438140.

Berkhout, A. J. and M. P. de Graaff, 1982, The inverse scattering problem in terms of multiple elimination and seismic migration: 52nd Annual International Meeting, SEG, Expanded Abstracts, 113–114.

Berkhout, A. J. and D. J. Verschuur, 1997, Estimation of multiple scat-

tering by iterative inversion—part 1: Theoretical considerations: Geo-physics, 62, no. 5, 1586–1595, doi:10.1190/1.1444261.

Berkhout, A. J. and D. J. Verschuur, 1998, Wave theory based multiple removal, an overview: 68th Annual International Meeting, SEG, Ex-panded Abstracts, 1503–1506.

Berkhout, A. J. and D. J. Verschuur, 1999, Removal of internal multi-ples: 69th Annual International Meeting, SEG, Expanded Abstracts, 1334–1337.

Berkhout, A. J. and D. J. Verschuur, 2005, Removal of internal multiples with the common-focus-point (CFP) approach: Part 1—Explanation of the theory: Geophysics, 70, no. 3, V45–V60, doi:10.1190/1.1925753.

Berkhout, A. J. and D. J. Verschuur, 2005, Removal of internal multiples with the common-focus-point (CFP) approach: Part 2—Applica-tion strategies and data examples: Geophysics, 70, no. 3, V61–V72. doi:10.1190/1.1925753

Fu, Q., Y. Luo, P. G. Kelamis, S. Huo, G. Sindi, S. Hsu, and A. B. We-glein, 2010, The inverse scattering series approach toward the elimina-tion of land internal multiples. 80th Annual International Meeting, SEG, Expanded Abstracts, 3456–3461.

Hembd, J., M. Griffiths, C. Ting, and N. Chazalnoel, 2011, Application of 3D interbed multiple attenuation in the Santos Basin, Brazil: 73rd EAGE Conference and Exhibition.

Ikelle, L. T., 2004, A construct of internal multiples from surface data only: 74th Annual International Meeting, SEG, Expanded Abstracts, 2164–2167.

Jakubowicz, H., 1998, Wave equation prediction and removal of inter-bed multiple: 68th Annual International Meeting, SEG, Expanded Abstracts, 1527–1530.

Kelamis, P. G., E. Verschuur, K. E. Erickson, R. L. Clark, and R. M. Burnstad, 2002, Data-driven internal multiple attenuation—Appli-cations and issues on land data: 72nd Annual International Meeting, SEG, Expanded Abstracts, 2035–2038.

Luo, Y., W. Zhu, and P. G. Kelamis, 2007, Internal multiple reduction in inverse-data domain: 77th Annual International Meeting, SEG, Expanded Abstracts, 2485–2489.

Otnes, E., K. Hokstad, and R. Sollie, 2004, Attenuation of internal mul-tiples for multicomponent and towed streamer data: 74th Annual In-ternational Meeting, SEG, Expanded Abstracts, 1297–1300.

Pica, A. and L. Delmas, 2008, Wave equation based internal multiple modeling in 3D: 78th Annual International Meeting, SEG, Expand-ed Abstracts, 2476–2480.

Ramirez, A. C. and A. B. Weglein, 2008, Inverse scattering internal multiple elimination: Leading-order and higher-order closed forms: 78th Annual International Meeting, SEG, Expanded Abstracts, 2471–2475.

Verschuur, D. J., Surface-related multiple elimination: an inversion ap-proach: Ph.D. thesis, Delft University of Technology.

Weglein, A. B., A. C. Ramirez, K. A. Innanen, F. Liu, J. E. Lira, and S. Ji-ang, 2008, The underlying unity of distinct processing algorithms for: (1) the removal of free surface and internal multiples, (2) Q compen-sation (without Q), (3) depth imaging, and (4) nonlinear AVO, that derive from the inverse scattering series. 78th Annual International Meeting, SEG, Expanded Abstracts, 2481–2486.

Acknowledgments: The authors thank CGGVeritas and Petrobras for permission to publish this work, and Antonio Pica, Nicolas Chazal-noel, and Chu-Ong Ting for their helpful contributions.

Corresponding author: malcom.griffiths@cggveritas.com