The ups and downs of ocean-bottom seismic processing ... · Up-down deconvolution: “What comes up must have gone down” The theory of using up-down deconvolution to address sur-face-related

936 The Leading Edge October 2010

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The ups and downs of ocean-bottom seismic processing: Applications of wavefield separation and up-down deconvolution

A key advantage of acquiring multicomponent data using ocean-bottom sensors, whether using cables or nodes, is

the ability to separate the wavefield into up- and downgoing parts. This opens up a host of attractive possibilities such as mirror imaging using the downgoing wave, attenuating receiver-side multiples using the upgoing wave only, or combining both up- and downgoing waves to completely remove the free-surface effect using up-down deconvolution. We focus here on the latter.

We have implemented both 2D and 3D up-down decon-volution in the f-k and τ-px-py domains, respectively. In prin-ciple, up-down deconvolution is only correct for a horizon-tally layered medium, but it can be shown to work very well for a slightly dipping sea floor with quite complex subsurface structure.

Besides PP multiple attenuation, up-down deconvolution presents some additional, perhaps surprising, benefits. It is well known that it acts as source designature. It is less well known that up-down deconvolution can be used to improve the repeatability of 4D data sets in the presence of water-col-umn changes. Additionally, for 4C acquisition, free-surface multiples on PS data can also be suppressed by deconvolu-tion of the horizontal components with the same downgoing wavefield. We illustrate these advantages of up-down decon-volution using both 2D synthetic data and 3D field data.

Figure 1 illustrates a choice of processing options which exploit the separation of up- and downgoing waves. There are basically two choices: how to perform the separation, and whether to use the upgoing, downgoing, or both wavefields. The choice of separation level, just below or just above the sea bottom, is explained in the next section.

In the case where we perform separation just above the seabed, we may use the downgoing wave for mirror migra-tion. Mirror migration is appropriate for either node surveys with very sparse receiver spacing, or cable surveys with sig-nificant cable separation, and where the main objective is to improve illumination of shallow events. One advantage of mirror imaging is illumination of the seabed itself. It is an important method, but not one we will focus on here.

Alternatively we can use up- and downgoing wavefields jointly, to perform a complete free-surface demultiple via up-down deconvolution.

Wavefield separationWavefield separation (Barr and Sanders, 1989; Soubaras, 1996; Schalkwijk et al., 1999; Osen et al., 1999) using hy-drophone (P) and vertical geophone (Z) measurements can be thought of as occurring either infinitesimally below or infinitesimally above the sea floor. In Figure 2 there are two

Yi Wang, RichaRd Bale, SeRgio gRion, and Julian holden, CGGVeritas

contributions to Uabove, one from the Earth (right) and one from the seabed bounce (left). However, if we perform wave-field separation at a location just below the seabed, then we estimate Ubelow, which eliminates the seabed bounce.

For the simple case of vertically propagating waves, the

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Figure 1. Flow chart of different processing options for hydrophone (P) and geophone (Z) combinations. Wavefield separation can be either just above or just below the sea floor. Separation below the sea floor is effective for attenuation of receiver-side multiples. Separation above the sea floor allows either up-down deconvolution for removal of all free-surface multiples, or mirror migration of the downgoing wave.

Figure 2. Upgoing and downgoing events just above and just below the seabed. Wavefield separation (PZ summation) can be applied either above or below the seabed, by adjusting the scaling of the Z component before summation. If applied below the seabed, the upgoing estimate (Ubelow) excludes the receiver-side, water-layer multiples.


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medium is well known (see, for example, Sonneland and Berg, 1987). Amundsen (2001) discusses the method in de-tail and extends the method to more complex geology.

The fundamental principle of up-down deconvolution can be summarized as: what comes up must have gone down. The source wavefield is generated near the ocean surface (the free surface). The downgoing wave originates from the source wavefield and its various bounces off the free surface. Every-thing that we ultimately record as an upgoing wave originates from this downgoing wave, which we also record. Mathemati-cally, the upgoing wave is the integral result of the down-going wave and the very subsurface response which we seek to estimate. Figure 3 illustrates for a simple raypath how we can represent a recorded upgoing signal as the combination of a downgoing signal with the response of the subsurface. Although illustrated for a single raypath, this concept is ap-plicable to the wavefield as a whole. For a simple horizontally layered medium, the addition of traveltimes implied by com-bining these two raypaths is represented by a convolution for a common ray parameter, or in the f-k domain as a multipli-cation. So we have a simple equation:

(3)

where U is the measured upgoing wavefield, R is the Earth’s reflectivity, and D is the downgoing wavefield, all expressed in the f-k domain (or f-kx-ky for 3D). This is very easily inverted,


equation which describes summation just above the seabed is:

(1)

where P and Z are the hydrophone and the vertical geophone recordings respectively, and U is the estimated upgoing wave-field just above the seabed. Here, for simplicity, we assume Z has been scaled by the water impedance ρc, where ρ is the water density and c the water velocity in the proximity of the sensor. Additionally, we assume that upgoing events have the same polarity on P and Z.

For wavefield separation just below the seabed the cor-responding equation is:

(2)

where the term in square brackets involving the seabed reflec-tion coefficient, r, accounts for the bounce off the seabed at the receiver.

Conventional wavefield separation is aimed at the remov-al of multiple energy (left branch in Figure 1). This dictates the choice of separation below the seabed, which provides a more effective attenuation of the receiver-side multiples. However, this does require estimation of the seabed reflectiv-ity and has the drawback that shot-side multiples are not re-moved. Hence a subsequent multiple attenuation is required.

Up-down deconvolution: “What comes up must have gone down”The theory of using up-down deconvolution to address sur-face-related water-column multiples in a horizontally layered

Figure 3. (a) The upgoing wave U is the convolution of the downgoing waves D with the Earth’s response R. (b) The up-down method calculates R by deconvolving D from U and redatuming the calculated Earth’s response from seabed to sea surface using a set of chosen water-column parameters irrespective of the actual water column characteristics.

Figure 4. Up-down deconvolution works well for the multiple shown in the top panel, where the downgoing wave only travels through a layered medium. The method is less effective for the multiple on the bottom panel, since the downgoing wave “notices” the structure.


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using a stabilization factor to prevent noise resulting from spectral notches, to obtain an estimate of the Earth’s reflectiv-ity:

(4)

Applicability for structureThe simple deconvolution described above implicitly assumes a 1D Earth (i.e., a horizontally layered medium). Amundsen described a generalization which is valid in complex geology, but at the cost of a convolution over all wavenumbers. This would require a fully sampled geometry for 3D applications, which is not achievable in practice. On the other hand, up-down deconvolution only requires properly sampled com-mon-receiver gathers and practical experience has repeatedly proven that the method is robust in the presence of structure.

We have recently investigated the reasons for this success under violation of the assumptions (Wang et al., 2010). A

mathematical argument is given there, but here we will pres-ent a diagrammatic treatment.

Figure 4 illustrates the concept in terms of true source position and ray parameter, Xs and ps, true receiver position and ray-parameter, Xr and pr, and the position and ray param-eter X and p at the subsurface position on the seabed which forms the “virtual” source for the deconvolved data. In most cases, up-down deconvolution is applied using receiver gath-ers. Assuming this to be the case, the important question is whether the ray parameters ps and p are equal. As can be seen from Figure 4 (if the seabed is flat), this will hold true for peg legs which don’t bounce in the subsurface prior to their final downgoing leg, but will not necessarily hold true for multiples which contain a subsurface bounce before the final downgoing leg. However, in general, the former will be the stronger and more problematic multiples. So, for this class of multiples, up-down deconvolution is effective, irrespective of the complexity of subsurface structure.

Figure 5. The P-wave velocity model of the Chevron 3C-2D finite-difference synthetic data.

Figure 6. A hydrophone (P) and calibrated vertical component of particle velocity (Vz) common receiver gather (CRG) are shown in (a) and (b). Events M1 and M2 are the first- and second-order water-layer multiples. The upgoing and downgoing wavefields are shown in (c) and (d) and the up-down deconvolution result in (e).

Figure 7. Depth-migrated stacked sections for the (a) vertical component, (b) hydrophone, (c) a conventional PZ summation approach, and (d) up-down deconvolution.

Figure 8. Geometry of a 3D receiver gather with dense shot geometry. Results shown in Figure 9 are from the receiver location with the yellow shot line.

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Synthetic example with structureWe apply up-down deconvolution to a 3C-2D isotropic fi-nite-difference synthetic data set provided by Chevron. The data set consists of 170 OBS nodes at depths between 1375 and 1837 m, and 1280 shots at a depth of 12.5 m. Shot and receiver sampling is 12.5 m and 100 m, respectively. The sea bottom is gently dipping with an average dip of 1.6° but sig-nificant subsurface structure is present (Figure 5). The syn-thetic data have a zero-phase wavelet with 50-Hz bandwidth, therefore aliased energy (at about 60 Hz) is well beyond the bandwidth of interest. In our processing flow, we choose to calibrate the vertical velocity component Z to the pressure component P using the cross-ghosting method (Soubaras, 1996). Following this geophone calibration (P and Z com-

Figure 9. Up-down deconvolution on a 3D receiver gather: (a) upgoing wavefield (separation just above seabed), showing strong residual multiple energy; (b) the result of full 3D up-down deconvolution, showing significant reduction in multiple energy; (c) the result of applying NMO correction on (b); (d) the result of 2D application of the up-down method along a constant azimuthal direction.

Figure 10. Application of “radial-down deconvolution” method on radial data to suppress multiples for PS processing. Radial (a) and radial-down deconvolution result (b).

ponents (Figures 6a and 6b), we separate up- and downgoing waves just above the seabed in the f-k domain (Figures 6c and 6d). Then we deconvolve the downgoing waves from the upgoing waves for each receiver. The up-down deconvolution result clearly shows that all free-surface multiples are success-fully and completely removed (Figure 6e). As an example, note the removal of multiples M1 and M2. For comparison purposes, we also process the data using a conventional PZ demultiple approach. The data after these different process-ing routes are then migrated using a prestack depth Kirch-hoff algorithm adapted for OBS geometry. Compared to the original Z- or P-component migrations (Figures 7a and 7b), conventional PZ demultiple shows considerable attenuation of the multiples but residual shot-side multiples are clearly present (Figure 7c). The up-down deconvolution result (Fig-ure 7d) delivers improved multiple attenuation with respect to the conventional PZ summation, especially in the reser-voir area. Migrated stack sections have confirmed the effi-cacy of the up-down method in removing multiples.

Application of 3D up-down deconvolution to field dataIn our first field data example, we have applied the 3D up-down deconvolution in the τ-px-py domain to a 4C data set recorded in shallow water. The data were acquired using a dense “carpet” of shots spaced at 25 by 25 m. Figure 8 shows the geometry for one receiver location with shots limited to an offset of 3000 m. The data were first interpolated to a shot spacing of 12.5 by 12.5m, to increase the range of frequen-



cies which remain unaliased during the τ-px-py transform.

In Figure 9, the up-down decon-volution results (9a) are compared with the upgoing data (9b). The up-going wavefield, using separation just above the seabed, shows considerable reverberations from the water column, which are greatly suppressed by the up-down deconvolution. In Figure 9c, the up-down deconvolution re-sult from 9b is shown after applying NMO with primary velocities. We also compare with an alternative up-down deconvolution approach which uses a 2D method applied in a constant azimuthal direction, shown in Figure 9d, also after NMO. This 2D approach could be expected to work successfully when the medium can be assumed to be spatially invariant. While this is moderately effective for mul-tiple suppression, comparison with Figure 9c suggests that, in this case, a full 3D approach is needed for the most effective multiple suppression.

One of the motivations for acquiring 4C data here is to obtain a converted-wave (PS) image from the horizontal components. The PS processing first requires rotation to ra-dial and transverse directions, though subsequently anisot-ropy analysis may reveal a more appropriate “natural” coordi-nate system. We consider only the radial data here, as a first approximation to the true PS data. There are of course no downgoing multiples for PS data, since water does not al-low S-wave propagation, but there is still source-side multiple energy. The concepts involved in up-down deconvolution can also be readily adopted for PS demultiple by using the downgoing wavefield (estimated as above) together with the radial wavefield, to produce a radial-down deconvolved data set. Figure 10 shows the result of applying 3D radial-down deconvolution (10b) compared with the original radial data (10a). The reduction in reverberations is clear.

Advantages of up-down deconvolution for 4D dataFor 4D OBS surveys, receiver positions can be made repeat-able by permanent deployment of buried hydrophone and geophone sensors at the ocean bottom. It is extremely difficult to achieve complete repeatability on the source side because of variations in the water column and in shot locations. The latter can be addressed by repeating the exact shot locations as closely as possible. The former is due to variations in the water column caused, for example, by tidal effects and sea-water temperature and salinity changes, as well as source-side ghost variations due to variations in sea-surface conditions.

The conventional approach to the attenuation of these un-desirable changes consists of a combination of moveout cor-rections and static shifts which require knowledge of water velocities and tides (Lacombe et al., 2009), often difficult to obtain. Also, sea-surface variability (rough sea) is not handled by these corrections. Often a poststack matching step is re-

quired to account for unresolved differences.As an alternative approach, we show that the up-down

deconvolution method can compensate for water-column changes without knowledge of water velocity and depth chang-es between vintages. The principle behind this application of the up-down method is that the effect of the water column is identical on both the downgoing and upgoing wavefields and is therefore cancelled by the deconvolution. Thus the up-down method can be used to process two or more surveys ac-quired at different times to minimize water-column-induced variations.

To demonstrate this we generated two vintages of a 2D isotropic finite-difference elastic synthetic data set using dis-tinct water velocities, and compared up-down deconvolution and conventional PZ summation results. The sea bottom is mostly flat at a depth of 1300-1850 m but significant subsur-face structure is present. The average sea-bottom dip is about 2°. Figure 10 shows the baseline P-velocity model. The moni-tor P-velocity model is characterized by a decrease of 0.3% (~5 m/s) in water velocity and a decrease of 5% in the res-ervoir velocity, while S-velocity and density are unchanged. We perform 2D wavefield separation and up-down deconvo-lution. We then image the data using a reverse time migra-tion (RTM) algorithm adapted for OBS geometry. When the

Figure 11. The baseline P-velocity model. The two green pockets indicated by red arrows are the reservoir areas of interest.

Figure 12. (left to right) RTM images for the baseline model, the monitor model, and their difference when the water-column variation is ignored. The conventional PZ summation method is used to attenuate receiver-side multiples. The subsurface structure shows very poor repeatability.


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correct water-column velocity is not accounted for in the im-aging, the conventional PZ summation method results show very poor data repeatability (Figure 11). A poststack match-ing step would be required to compensate for unresolved dif-ferences. The conventional PZ summation results show good data repeatability provided we use the correct water-column models (Figure 12) in imaging each vintage, with a normal-ized root mean squared (NRMS) value of 0.11 ± 0.04 in the overburden (Figures 14a and 14c). However, some residual shot-side multiples are still present in the baseline and moni-tor images. These multiples are imaged to different locations in the baseline and the monitor surveys, and therefore ap-pear in the 4D difference when a conventional PZ summa-tion is used. The up-down deconvolution results show good data repeatability between the baseline model and the moni-tor model (Figure 13) with a NRMS value of 0.09 ± 0.03 in the overburden (Figures 14b and 14d). This result is obtained without a priori knowledge of the water velocity or its varia-tions between monitor and base surveys. Additionally, notice how repeatability is poorer in the overburden when using the conventional PZ summation method, even when the exact velocities are used and no multiples are present in the shal-

Figure 13. (left to right) RTM images for the baseline model, the monitor model, and their difference when the water-column velocity variation is known and is used in imaging. Receiver-side multiples are attenuated using a conventional PZ summation approach. The repeatability of the subsurface structure is significantly improved between the baseline model and the monitor model. But the residual multiples are not repeatable even when the correct water-column velocity is used.

Figure 14. (left to right) RTM images for the baseline model, the monitor model and their difference when the water-column variation is corrected using the up-down deconvolution method. No residual multiples are present in any of the three panels. The blue and red data windows are chosen for analyses above the reservoir (blue) and within the reservoir (red), respectively.

Figure 15. The analysis in the time domain for the conventional PZ summation result (a) and the up-down deconvolution result (b) for the overburden (blue) and reservoir (red). Histograms of values for the conventional PZ summation result (c) and the up-down deconvolution result (d) for the overburden (blue) and the reservoir (red).

Figure 16. The analysis in the frequency domain of the conventional PZ summation result (a) and the up-down deconvolution result (b) for the overburden. (c) and (d) show the same analysis for the reservoir.

low overburden window. The difference in repeatability is due to the fact that when PZ summation is used, differences in water velocity cause illumination differences in the two data vintages, even if the correct imaging velocity is used. How-ever, and to the contrary, the up-down deconvolution result in Figure 13 is not influenced by water-column effects and no matching is required.

The benefit of up-down deconvolution is also evident in the frequency-domain NRMS analysis shown in Figure 15. In




the overburden, the up-down deconvolution result shows a lower and wider NRMS bandwidth compared to the conven-tional PZ summation result.

ConclusionsUp-down deconvolution is an effective and automatic free-surface demultiple method for ocean-bottom data processing. Its application requires accurate separation of the recorded pressure wavefield into its upgoing and downgoing compo-nents. The method is strictly valid only for a horizontally layered Earth. Nevertheless, the examples shown highlight the success of up-down deconvolution even in the presence of complex geology, albeit with a relatively flat sea bottom. Compared to conventional PZ summation methods, up-down deconvolution is able to attenuate the source-side mul-tiples which cannot be eliminated by the conventional meth-ods. Additionally, up-down deconvolution can significantly improve the 4D repeatability of time-lapse ocean bottom data.

ReferencesAmundsen, L., 2001, Elimination of free-surface related multiples

without need of a source wavelet: Geophysics, 66, no. 1, 327–341, doi:10.1190/1.1444912.

Barr, F. J., and J. I. Sanders, 1989, Attenuation of water-column rever-berations using pressure and velocity detectors in a water-bottom cable: 59th Annual International Meeting, SEG, Expanded Ab-stracts, 653–655.

Lacombe, C., S. Butt, G. Mackenzie, M. Schons, and R. Bornard, 2009, Correcting for water-column variations: The Leading Edge, 28, no. 2, 198–201, doi:10.1190/1.3086058.

Osen, A., L. Amundsen, and A. Reitan, 1999, Removal of water-layer multiples from multicomponent sea-bottom data: Geophysics, 64, no. 3, 838–851, doi:10.1190/1.1444594.

Sonneland, L., and L. Berg, 1987, Comparison of two approaches to water layer multiple attenuation by wave field extrapolation, 57th Annual International Meeting, SEG, Expanded Abstract, 276–277

Schalkwijk, K. M., C. P. A. Wapenaar, and D. J. Verschuur, 1999, Application of two-step decomposition to multicomponent ocean-bottom data: Theory and case study: Journal of Seismic Explora-tion, 8, 261–278.

Soubaras, R., 1996, Ocean bottom hydrophone and geophone pro-cessing: 66th Annual International Meeting, SEG, Expanded Ab-stracts, 24–27.

Wang, Y., S. Grion, and R. Bale, 2010, Up-down deconvolution in the presence of subsurface structure, 72nd EAGE Meeting, Extended Abstract D001.

Acknowledgments: We are grateful to Chevron for generation of the synthetic data used in this paper and for permission to publish the results. We thank an anonymous client for permission to publish the work on the real 4C-3D data set. We thank Steve Roche, Ter-ence Krishnasamy, Kevin Douglas, and Linping Dong for their contributions in imaging the synthetic data, and Ivan Gregory for processing the field data examples.

Corresponding author: [email protected]

The ups and downs of ocean-bottom seismic processing ... · Up-down deconvolution: “What comes up must have gone down” The theory of using up-down deconvolution to address sur-face-related

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