H026 Random Sampling for Seismic Acquisition

Transcription

1 H026 Random Sampling for Seismic Acquisition N. Moldoveanu* (WesternGeco) & J. Quigley (WesternGeco) SUMMARY Seismic data acquired in land or marine acquisition is typically undersampled for both receivers and sources, and regularly distributed along parallel lines. The theory of compressive sampling considers that if data is undersampled, the seismic wavefield is better reconstructed if the measurements are randomly distributed. In this paper we investigate how random sampling can be implemented in different types of marine acquisition geometries. 3D finite-difference modeling data were generated to simulate acquisition geometries with regular and random sampling. We will present also a land synthetic data example for node type geometry to illustrate the benefit of random sampling for ground roll attenuation. (note: this example was not included in the abstract)

2 Introduction One important consideration in designing a seismic survey, land or marine, is how we obey the Nyquist condition for proper sampling of the seismic wavefield. The seismic wavefield is a function of time coordinate, t, and space coordinates for sources (Xs,Ys,Zs), and receivers (Xr,Yr,Zr), and each of these coordinates must be sampled properly to allow accurate reconstruction of the measured wavefield for processing and interpretation purposes. The time coordinate is always sampled according to Nyquist because is easily done, but not the X and Y coordinates. For surface seismic surveys we are not concerned about the Z coordinate. Sampling requirements are different for signal and noise and this must be considered in survey design. Table 1 shows the Nyquist sampling interval and the practical sampling interval used for towed-streamer, ocean-bottom cable (OBC), node (marine) and for vibroseis (land) acquisitions, considering that the seismic signal has a maximum frequency of 75 Hz and a minimum signal propagation velocity of 1500 m/s. For towed-streamer marine the X-direction is along the streamers or inline, and the Y-direction is perpendicular to the streamer, or crossline. Nyquist sampling streamer marine OBC nodes vibroseis land Receiver - X 10 m m 25 m m 7.5 m - 70 m Receiver - Y 10 m m m m 120 m 624 m Shot - X 10 m m m m 7.5 m 80 m Shot - Y 10 m m m m 90 m 924 m Table 1: Required and practical sampling interval for towed-streamer, OBC, nodes (marine) and vibroseis (land) acquisitions; it is assumed that the signal has 75 Hz maximum frequency and 1500 m/s minimum velocity From this comparison we can see that for streamer acquisition, the receivers could be properly sampled in the inline direction, and the sources are undersampled in both inline and crossline. For OBC and node-type acquisition, it can be observed that neither receivers nor sources fulfil the sampling requirements. For land vibroseis acquisition most of the current surveys are undersampled for both receiver and sources. However, with the development of the new generation of land systems that could have up to 160,000 channels and the use of simultaneous sources, the sampling of receivers and sources can improve considerably. The receiver sampling of 7.5 m inline and 120 m crossline and source sampling of 7.5m inline and 90 m crossline were used for an ultrahigh-density full-azimuth land survey (Seni et. al., 2009). In the last six years, compressive sampling theory emerged. This has significant interactions and bearings in some fields of the applied sciences and engineering such as signal processing, information theory, medical imaging, coding theory, analog-to-digital conversion and others. The fundamental concept of this theory is that if the measurements are not sampled according to Nyquist condition, it is better to have randomly distributed measurements rather than regularly distributed (Donoho, 2006). For seismic data processing the compressive sampling theory has been used by Herrmann and his colleagues from the University of British Columbia. Hennenfent and Herrmann (2008) demonstrated that random undersampled data produced a better wavefield reconstruction than regularly undersampled data. Neelamani et al. (2010) demonstrated the benefit of simultaneous random sources and sparsity for forward modeling. Other applications for noise attenuation and interpolation were presented by Herrmann (2010). The concept of compressive sampling is very appealing to a seismic survey designer. The possible applications of this theory could be for seismic signal processing (noise attenuation, interpolation, and data regularization) and for seismic imaging. Both applications require random measurements. In 1995 Zhou and Schuster (1995) presented the theory of quasi-random Monte Carlo sampling for 3D migration and showed the benefits for reducing migration aliasing artifacts on the final image. Following this paper, random sampling for land acquisition was analyzed and proposed for use by Cordsen et al. (2000) as an alternative to regular 3D design, which can cause at times severe acquisition footprint. Field implementation of random sampling for land acquisition is straight forward, if the field operations are feasible. In this paper we will investigate how random sampling

3 can be implemented in marine seismic acquisition. As marine data are typically undersampled, the reason for using random sampling is to alleviate the undersampling effects, such as aliasing and acquisition footprints. Streamer marine acquisition (2D, 3D or wide-azimuth) is parallel-type geometry and sources and receivers are distributed along parallel lines and, theoretically, are very regular if the current effect is negligible. Implementation of random sampling acquisition with parallel geometry is not natural; however, coil shooting acquisition is a streamer marine geometry that allows random sampling. Nonstreamer marine acquisition types that allow implementation of random sampling are node (areal) and 3D vertical seismic profile (VSP) acquisitions. Implementation of random sampling in coil shooting acquisition Coil shooting acquisition is a method to acquire full-azimuth marine data with towed streamers using circular geometry (Moldoveanu, 2008). Circular geometry for single streamer acquisition was introduces in the early 1980s (Cole and French, 1984). Coil shooting can be implemented with a single vessel or with multiple vessels (Moldoveanu and Kapoor, 2009). For single-vessel implementation one streamer vessel equipped with multiple streamers and a single source array sails along overlapping circles. Multivessel coil shooting acquisition can be implemented using a combination of streamer and source vessels: for example, one streamer vessel and one source vessel (1x2), two streamer vessels (2x2), one streamer vessel and two source vessels (1x3), two streamer vessel and three source vessels (1x4) and two streamer vessels and two source vessels (2x4). One specific aspect of coil shooting acquisition is that shot and receiver distribution is not regular. The pseudorandom aspect of shot and receiver distribution is related to sailing along overlapping circles in both x- and y-directions. Another factor that contributes to pseudorandom distribution of receivers is streamer feathering. One design parameter that determines the shot and receiver distribution is the circle center grid, which can be designed to be regular (Figure 2a) or random (Figure 2b). If the circle grid is regular a repeating pattern will be present in shot distribution (Figure 2c). If the circle grid is random the repeating pattern in shot distribution is removed (Figure 2d), and this will have a beneficial effect on the final migrated image. (a) (b) (c) (d) Figure 2: Regular circle grid (a), random circle grid (b), shot distribution for regular circle grid (c) shot distribution for random circle grid (d) A 2x4 coil shooting survey that was designed using random sampling criteria was successfiuly acquired in the Gulf of Mexico in The survey area covered 4460 km². Implementation of random sampling for node and 3D VSP marine acquisitions In node acquisition the receivers (or nodes) are typically deployed by a remotely operated vehicle (ROV) and given the x and y coordinates of the location on the water bottom where the receiver must be deployed. There is no difference in this operation if the receivers are regularly or randomly located. For random location of the sources, the Coil shooting method that deploys the source vessel along overlapping and randomly distributed circles can be employed. The random circle grid can be designed to generate a number of shotpoints similar to the number generated in a regular grid distribution, and with a similar acquisition time. Multiple source vessels can be used to generate random source locations if the simultaneous shooting method is considered for the acquisition.

4 For 3D marine VSP we consider only the source location randomization and the method described above, for the node acquisition, can be applied. Typically, for 3D VSP, the source points are acquired in flip-flop mode with the source vessel sailing along a spiral curve. The proposed random circle shooting method could be more efficient than the spiral shooting method for the 3D VSPs that require a non-regular shape of the source locations. In this study, 3D finite-difference simulation of acquisition geometries with regular and random sampling was performed. Some of the simulation results will be presented in the next sections. 3D finite-difference simulation of regular and random sampled acquisition geometries The earth model used in this simulation is the SEG advanced modelling (SEAM) model, which is an isotropic velocity model with density. The acquisition geometries simulated were 2x4 coil shooting and node (areal). The 2x4 coil shooting acquisition parameters were: two receiver vessels and two source vessels, 7000-m cable length, 10 cables, 120-m cable separation, 25-m receiver interval, 4 sources, 37.5-m shot interval (sequential sources), 600-m shot line interval and 14,30-m maximum offset. The node acquisition was simulated with a 400-m x 400-m receiver (node) grid and a 30-m x 30-m source grid and also with a decimated number of sources and receivers, but randomly distributed. The extent of the shot grid around each receiver is 20 km x 20 km which gives a 14-km maximum offset. The number of traces modelled in the regular node (areal) geometry was approximately 1.4 billion, which is times larger than the total number of traces simulated in 2x4 -oil shooting geometry. 3D acoustic finite-difference modelling was performed with a 20-Hz maximum frequency, appropriate for subsalt targets. Free-surface-related multiples were generated. The processing flow was identical for all datasets and consisted of direct arrival removal and common-shot wave-equation (WEM) migration with a maximum aperture of 10 km and an output grid of 20 m x 20 m x 10 m. In Figure 4a, we present the WEM image of the node geometry with a 30-m x 30-m shot grid and regular sampling of sources and receivers. The results of the 3D finite-difference simulation demonstrated the following: 2x4 coil shooting acquisition with random sampling of sources and receivers produced results that were equivalent or slightly better than node acquisition with 30-m x 30-m shot grid and 400-m x 400-m node grid, although the number of traces for the node acquisition was time larger. Migration of the decimated node data to 25% of the total number of nodes still produced a good image (Figure 4b); both the nodes and the shots were randomly distributed. However, the overall signal level is lower for the decimated data, and decimation of real data is not recommended. The random sampling of coil data did not introduce any footprint in the migrated image. (a) (b) Figure 4: : Migrated image of the node acquisition with 400-m x 400-m nodes and 30-m x 30-m shots, regular sampling (a); Migrated image of the node acquisition decimated to 25 % of total number of nodes and 50-m x 50-m shot grid; the nodes and shots were randomly distributed (b)

5 Discussions and conclusions Processing of randomly sampled marine data is not different from processing of regularly sampled data. For coil shooting acquisition data processing is done mainly in the shot domain, with an exception being common-offset Kirchhoff prestack depth migration which is used for velocity model building or for high-resolution migration of shallow sediments. In the shot domain, receiver distribution is regular, so no sorting or regularization is required for noise attenuation. The general purpose multiple prediction GSMP 3D multiple attenuation method (Dragoset et al., 2008) does not require regular sources and receivers. Processing synthetic and real coil data with GSMP proved that surface-related multiples can be successfully attenuated (Buia et al., 2010). The results obtained from common-shot migration of randomly sampled data for node acquisition show that common-shot WEM migration does not require prior regularization. However, if any processing sequence requires interpolation or data regularization, it is expected that randomly sampled data will perform better than regularly sampled data (Herrmann, 2010). The results of shot regularization performed on random data will be presented. In this study, we looked at implementation of random sampling for marine acquisition and we can conclude: Random sampling of sources and receivers can be implemented for coil shooting acquisition using a single vessel or multivessel configuration. In node acquisition, both the nodes and the sources can be randomly distributed; for random source distribution, the source vessel sails along overlapping random circles, as in coil shooting. A similar method can be used for shot distribution in 3D VSP surveys. 3D finite-difference simulation and processing of randomly sampled data for coil shooting and node acquisition produced very good subsurface images with no acquisition footprints. Simulation of randomly sampled marine acquisition geometries was free of ambient noise, such as swell and current noise; further studies are required to assess residual noise effects and imperfections of the earth model for processing of randomly sampled data. References Buia M., Varcesi R., Tham M., Ng S.L., Valuvo A., Chen S. [2010] 3D Coil shooting on Tulip field: Data processing review and final imaging results: 80 th Annual international Meeting, SEG, Expanded Abstracts, 29, Cole R., French W. [1984] Three dimensional marine seismic data acquisition using controlled streamer feathering: : 64 th Annual international Meeting, SEG, Expanded Abstracts, 3, Cordsen, A., Galbraith M., and Pierce J. [2000] Planning land 3D seismic surveys, SEG Press Book Donoho, L.L. [2006] Compressed sensing: IEEE Transactions on Information Theory, 51(4) Dragoset W., Moore I., Yu M., and Zhao W. [2008] 3D general surface multiple prediction: an algorithm for all surveys: 78th Annual International Meeting, SEG, Expanded Abstracts, 27, Hennenfent, G., and Herrmann F. J. [2008] Simply denoise: wavefield reconstruction via jittered undersampling: Geophysics, 73, V19-V28. Herrmann, F. J. [2010] Randomized sampling and sparsity: Getting more information from fewer samples: Geophysics, 75, VB173-VB187 Moldoveanu, N. [2008] Circular geometry for wide-azimuth towed-streamer surveys, 70 th Annual Conference and Exhibition, Expanded Abstracts, Moldoveanu, N. and Kapoor J. [2009] What is the next step after WAZ for exploration in the Gulf of Mexico: 79 th Annual international Meeting, SEG, Expanded Abstracts, 28, Neelamani, R., Krohn C., Krebs, J., Romberg, J., Deffenbaugh, M., and Anderson, J. [2010] Efficient seismic forward modeling using simultaneous sources and sparsity: Geophysics,75, VB15-VB27. Seni S., Robinson S., Denis M. and Sauzedde P. [2009] Dukhan 3D: An ultra high density, full wide azimuth seismic survey for the future: International Petroleum Technology Conference, IPTC Zhou C., Schuster G., Quasi-random migration of 3D field data: 79 th Annual international Meeting, SEG, Expanded Abstracts, 14,