Attenuation of water-layer-related multiples Clement Kostov*, Richard Bisley, Ian Moore, Gary Wool, Mohamed Hegazy, Glenn Miers, Schlumberger

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1 Clement Kostov*, Richard Bisley, Ian Moore, Gary Wool, Mohamed Hegazy, Glenn Miers, Schlumberger Summary We present a method for modeling and separation of waterlayer-related multiples in towed streamer acquisitions. Our method models accurately the kinematics of multiples with bounces in the water layer, both on the source and receiver sides, and extends the capabilities of previous methods in particular for the cases with complex topography on the sea bed. We illustrate the method with synthetic data and with field data from a shallow-water 3D towed-streamers marine survey. differences due to source array directivity, for instance). However, traveltime differences between source-side and receiver-side multiples exist even in presence of a horizontal water bottom due to the interaction with deeper non-horizontal reflectors. When both the sea bottom and the deeper structures are non-horizontal, such traveltime differences increase in particular with the number of bounces in the water layer. Introduction Water-layer-related multiples are free-surface multiples, that have a bounce in the water-layer on the source or receiver side. Typically, the water-layer-related multiples have large amplitudes because of the strong contrasts in material properties at the air/water (free surface) and at the water/sediments interfaces. Deconvolution, initially, and later wavefield extrapolation methods were developed to attenuate such water-layerrelated multiples. The development of 3D surface-related multiple elimination (SRME) and wave-equation modeling methods, which predict all free-surface multiples, led to redefining the applications for water-layer-related multiples removal. The preferred application cases of the latter technique are now in shallow-water surveys; sea-bed surveys, or other surveys that don t meet some of the requirements for 3D SRME methods; or, used in combination with imaging methods extracting information from the multiples. Here, we extend the deterministic water-layer demultiple (DWD) method of Moore and Bisley (2006) to handle complex topography on the near water-bottom multiplegenerating reflectors by using the modeling approach described by Verschuur (2006). After presenting a brief outline of our method, we illustrate the method with synthetic data examples, indicate directions for further developments in modeling, and apply our method in a case study with data from a shallow-water survey acquired offshore Canada. Theory and Method It is well established that multiples with bounces on the source side or on the receiver side have different raypaths and attributes, and, therefore both types of multiples should be modeled. Figure 1 illustrates the definition of sourceside and receiver-side water-layer-related multiples. Note that in a horizontally-layered medium, source-side and receiver-side multiples would be the same (ignoring Figure 1: Raypaths for two water-layer-related multiples, with same source and receiver positions. The raypaths Sab (multiple on the source side) and b c R (multiple on the receiver side) are significantly different for this source-receiver offset (S-R). At near offsets in this model, the corresponding raypaths would be very similar. The equations for prediction of all water-layer-related multiples by wavefield extrapolation are given by Lokshtanov (2001) and by Verschuur (2006). Following Verschuur (2006), the equation for the model of waterlayer-related multiples is M = W R D + (D D w ) W S W R D W S, (1) with notations as follows: M is the model of multiples; D is data; D w is the water bottom reflection; and W R and W S wavefield extrapolation operators acting respectively on common shot and common receiver gathers. The denotes the wavefield extrapolation of the data, performed by multi-dimensional convolution with a (vertical derivative of) Green s function for the water layer. Implicitly, all the wavefields are functions of temporal frequency and spatial coordinates of the sources and receivers. To reduce the number of multi-dimensional convolutions, one can group the terms in equation (1) as in Moore (2004), M R = W R D, and (2) M = M R + (D Dw f M R ) W S, (3) SEG New Orleans Annual Meeting Page 4448

2 where f is a linear filter, determined by matching the model M R to the data. The dashed black arrow points to an internal multiple in the input data, whereas the solid black arrow points to a freesurface multiple that is not reflecting on the sea bed and therefore is not included in the model in Figure 2c. Within this modelling framework, the next steps are the choice of a Green s function for the wavefield extrapolation, implementation of a method for computing efficiently and accurately the Green s function, and the preconditioning of the data as needed for the wavefield extrapolation. In current practice, wavefield extrapolation operators are computed as approximations to Green functions in acoustic media, implicitly focusing on matching the kinematics of pre-critical reflections in the data (Wiggins, 1988; Spadavecchia et al., 2013; Wang et al., 2014). Here, we follow this practice and compute wavefield extrapolation operators using constant, angle-independent sea-bed reflectivity, as in the wave-equation modeling of all freesurface multiples (Stork et al., 2006), except that the reflectivity model consists of the sea-bed reflection, or near-sea-bed reflections, only. The multi-dimensional convolutions involved in the wavefield extrapolation are the same as in the data-driven prediction of surface multiples by 3D SRME methods (Dragoset et al., 2010). Similarly to 3D SRME, the data need to be adequately sampled, either in acquisition, or in pre-processing in order to compute the multi-dimensional convolutions. In our work, we use the efficient on-the-fly interpolation developed as part of the general surface multiple prediction (GSMP) method (Moore and Dragoset, 2008), combined when necessary with interpolation prior to the prediction of water-layer-related multiples. Synthetic Data Example Figure 2a displays a synthetic shot gather computed by a finite-differences method in a three-layer acoustic earth model (Figure 2b). The shot gather includes two primary reflections (the two earliest reflections in the figure), freesurface multiples, as well as internal multiples. Even though the dip on the sea bed is small (0.89 ), traveltime differences between source-side and receiver-side multiples (events identified by thick blue arrow in Figure 2a, with raypaths as in Figure 1) are clearly observed for this shot gather computed for frequencies up to 55 Hz. Figure 2c displays water-layer-related multiples with bounces on the receiver side only. This model of multiples is computed by equation 2. Note that the receiver-side-only model doesn t contain the split arrival events observed in Figure 2a (compare events pointed by the blue arrows). Figure 2: a) Common shot gather of finite-difference synthetic data; b) Three-layer model used for computing the synthetics with water layer at the top (in blue) and dip on the water-layer bottom of 0.89 (plotted with vertically exaggerated scale). c) Model of multiples with receiverside bounce in the water layer. We computed synthetic data for shot and receiver locations as in a field survey similar to the one described in the Field Data Example section that follows. The synthetic data are available not only at the locations of acquired data during the survey, but also at locations where data would have been interpolated during processing. Comparing the multiples modeled by finite differences from the acoustic model (Figure 3a) to the multiples predicted by the method described in this paper (equation 1), we note very good agreement for the kinematics of the water-layer-related multiples, including the splitting starting at mid-offsets between the receiver-side and the source-side peg-leg multiples. Field Data Example To illustrate the approach with field data we use an offshore Canadian survey, acquired in 1997 over the Hebron oil field. The nearly horizontal water bottom (Figure 4) varies in depth from 88 m to 104 m. The particularly hard water bottom makes water-layer-related multiples particularly strong, even for high-order multiples. The data were acquired with two source arrays each shooting alternately every 50 m in flip-flop mode, and were recorded with 8 streamers, each 4 km long, with receiver group interval of 25 m. The crossline separation between streamers is 100 m. SEG New Orleans Annual Meeting Page 4449

3 The multiple-attenuated data are the result of adaptively subtracting a model of water-layer-related multiples including receiver-side and source-side multiples. The adaptive subtraction workflow includes least-squares matching filters as well as curvelet decomposition and has been optimized for this model, thus removing a significant amount of multiples. Figure 3: a) All free-surface-related multiples predicted by finite-difference computations from the acoustic model. The black arrow points to a multiple which does not reflect from the water bottom. b) Water-layer-related multiples computed by the method of equation 1. Note the accurate prediction of the split peg-leg multiple, indicated by the blue arrows. We tested our method of predicting multiples on a subset of the data consisting of 11 sail lines. We determined bathymetry from picked autocorrelations and time-to-depth conversion, as described in Moore and Bisley (2006). Although the sea floor depth is nearly constant, there are small variations in water depth that we were keen to preserve in the model. As mentioned previously, we computed an approximation of the acoustic Green s function using a constant sea-bed reflectivity model (Stork et al., 2006). In Figure 7a we display the trace-by-trace crosscorrelations between input stacked data and the model (source and receiver-side bounces). The significant energy at zero-lag indicates a good match between the model and the data. The crosscorrelations between primary events in the data and multiples in the model contribute to negative crosscorrelation times. At positive crosscorrelation times we have cross-talk between multiple events of different orders, not involving the primaries. Figure 7b displays trace-by-trace crosscorrelations between the data without multiples (as in Figure 6) and the model of multiples. Notice the significant reduction of energy at zero and positive crosscorrelation times indicating good attenuation of multiples, whereas significant energy at negative times is preserved and contains contributions from cross-talk between primaries in the data and multiples in the model. The stack section displayed on the left in Figure 8 consists of data after multiples were subtracted using a model of multiples with bounces on the receiver-side only. The stack section displayed on the right in Figure 8 shows stack traces from the input data. The black arrows indicate several areas where the receiver-side multiple model is not removing multiples as effectively as in the full model (source and receiver-side multiples) shown in Figure 6. A harsher adaptive subtraction may improve the multiple attenuation results using the receiver-side model only, but this would be at the risk of damaging primary reflections. Conclusions Figure 4: Sea-floor bathymetry for the field test area. The full stack is shown in Figure 5; notice the significant contamination from multiples, in particular water-layer multiples with a periodicity of about 120 msec, with several bounces (high-order multiples) and characteristic alternation of polarities within sequences of peg-leg multiples. Stack sections are shown in Figure 6, with data after multiple attenuation on the left, and data before multiple attenuation on the right. The data shown in Figure 6 correspond to the data from the rectangular areas indicated in Figure 5. The general wavefield extrapolation operators that we introduced are capable of modeling water-layer multiples interacting with a seafloor of complex geometry. Our predictions of the multiples are kinematically correct which is important in order to use well-constrained adaptive subtraction. The amplitudes of our models are approximate with respect to handling effects due to scattering from the sea floor, source directivity, and residual ghost effects. Such differences in amplitudes are currently compensated by adaptive subtraction. The prediction of more accurate amplitudes for the multiples is a direction for further work in which the main challenges are the accuracy of the available earth models, the significant cost of full solutions of the acoustic or elastic wave equations, and the acquisition geometries required for accurate wavefield extrapolations. SEG New Orleans Annual Meeting Page 4450

4 Our proposed method, illustrated on synthetic and field data, provides accurate predictions of water-layer-related multiples. Use of a model that includes both source- and receiver-side multiples is preferable to use of only a receiver-side model, even in cases of mild structural variations of the seafloor. Figure 7: a) Trace-by-trace crosscorrelations between traces from the input stack (Figure 5) and traces from the model with receiver-side and source-side multiples; b) Trace-by-trace crosscorrelations between traces from the output stack (Figure 6) and traces from the model with receiver-side and source-side multiples. Figure 5: Stack section of input data. The rectangles indicate areas of the stack section displayed in Figures 6 and 8. Figure 6: a) Stack section output, where models of receiverside and source-side multiples have been subtracted from the input data; b) Stack section of input data with no multiple attenuation. The black arrows indicate locations for comparisons between Figures 6 and 8. Figure 8: Stack section output, where a model of receiverside multiples has been matched and subtracted from the input data; b) Stack section of input data with no multiple attenuation. The black arrows indicate locations for comparisons between Figures 6 and 8. Acknowledgments We thank Schlumberger and ExxonMobil for permission to publish this work. We gratefully acknowledge key technical contributions from several colleagues: Yvonne Paisant-Allen and Erik Neumann from ExxonMobil, and Zhiming Wu, Scott Slaton, Frederico Xavier de Melo, Peck Hwa David Ng and Penelope Barnes from Schlumberger. SEG New Orleans Annual Meeting Page 4451

5 EDITED REFERENCES Note: This reference list is a copyedited version of the reference list submitted by the author. Reference lists for the 2015 SEG Technical Program Expanded Abstracts have been copyedited so that references provided with the online metadata for each paper will achieve a high degree of linking to cited sources that appear on the Web. REFERENCES Dragoset, W., E. Verschuur, I. Moore, and R. Bisley, 2010, A perspective on 3D surface-related multiple elimination: Geophysics, 75, no. 5, 75A245 75A261, Lokshtanov, D., 2001, Suppression of water-layer multiples and peg-legs by wave-equation approach: 63rd Conference & Exhibition, EAGE, Extended Abstracts, IM001. Moore, I., 2004, Method for attenuating water-layer multiples: U. S. Patent B1. Moore, I., and R. Bisley, 2006, Multiple attenuation in shallow-water situations: 68th Conference & Exhibition, EAGE, Extended Abstracts, F018. Moore, I., and W. Dragoset, 2008, General surface multiple prediction: A flexible 3D SRME algorithm: First Break, 26, no. 9, Spadavecchia, E., V. Lipari, N. Bienati, and G. Drufuca, 2013, Water-bottom multiple attenuation by Kirchhoff extrapolation: Geophysical Prospecting, 61, no. 4, , Stork, C., J. Kapoor, W. Zhao, W. Dragoset, and K. Dingwall, 2006, Predicting and removing complex 3D surface multiples with WEM modeling An alternative to 3D SRME for wide azimuth surveys?: 76th Annual International Meeting, SEG, Expanded Abstracts, Verschuur, D. J., 2006, Seismic multiple removal techniques: Past, present and future: EAGE. Wang, P., H. Jin, M. Yang, and S. Xu, 2014, A model-based water-layer demultiple algorithm: First Break, 32, no. 3, 63 68, Wiggins, J. W., 1988, Attenuation of complex water-bottom multiples by wave-equation-based prediction and subtraction: Geophysics, 53, , SEG New Orleans Annual Meeting Page 4452