A033 Combination of Multi-component Streamer Pressure and Vertical Particle Velocity - Theory and Application to Data

Transcription

1 A33 Combination of Multi-component Streamer ressure and Vertical article Velocity - Theory and Application to Data.B.A. Caprioli* (Westerneco), A.K. Ödemir (Westerneco), A. Öbek (Schlumberger Cambridge Research), J.E. Kragh (Schlumberger Cambridge Research), D.J. van Manen (Westerneco),.A.F. Christie (Schlumberger Cambridge Research) & J.O.A. Robertsson (Schlumberger Cambridge Research) SUMMARY In this paper, we generalie the optimal deghosting () method used for deghosting over/under data to combine pressure () and vertical velocity () data recorded with a multi-component streamer to minimie the impact of the noise on the deghosted data. The approach uses pressure and velocity ghost models and the statistics of the residual noise to minimie, in a least-squares sense, the noise on the up-going/ deghosted wavefield. and the standard summation (SUM) combinations are applied to pressure and velocity data recorded in the North Sea. We show that both methods attenuate the receiver ghost, fill in information at the pressure notch frequencies and that has the least post-combination noise level. We also show pre- and post-stack vertical velocity data with encouraging signal-to-noise ratios. Finally, in order to further improve the deghosted data, we suggest a toolbox approach that takes advantage of both and SUM combinations and accounts for the varying signal-to-noise ratios observed on multi-component streamer data.

2 Introduction Experience has shown that seismic data acquired with a deep-towed streamer benefit from a lower noise environment by being further away from the sea surface, and from an increased low frequency response due to the sea surface receiver ghost. But, towing streamers deeper also places notches at lower frequency within the bandwidth of the data and, hence, limits the time resolution of the seismic wavelet. Several acquisition/processing techniques have been proposed to overcome the receiver ghost problem. Some examples involving two independent data components are: over/under towed streamers (Hill et al. 6), over/sparse-under 3D streamers (Kragh et al. 9) and the additional vertical velocity component where the pressure and the velocity measurements are combined to achieve deghosting (Long et al. 8). The latter approach must handle the typical high levels of flow and vibration noise in towed streamer velocity measurements. In this paper, we adapt the optimal deghosting () method used to deghost over/under data by Ödemir et al. (9) to the combination of the pressure and the vertical velocity recorded by a multi-component streamer. We also consider the standard summation (SUM) and discuss pros/cons of both combinations. Both approaches are then applied to real data. Wavefield decomposition: SUM Let and represent the frequency - (inline and crossline) wavenumber (ω, k x, k y ) transformed data of pressure and vertical particle velocity wavefields recorded at a depth H below the sea surface. The component has been scaled by the acoustic impedance in the water (ρc=density * water velocity). The deghosted up-going and down-going pressure wavefields U and D can be expressed as a function of the input data as (Amundsen 1993): U SUM ck, D. ck.5 5 (eq. 1) SUM where k =[(ω/c) -k x -k y ] 1/ is the angular vertical wavenumber. The dimensionless ratio ω/ck is the inverse obliquity factor required to balance the vertical component. Up-going events are recorded with the same polarity on and components. A straight summation of pressure and velocity data decomposes the wavefield into up- and down-going wavefields. A drawback of this approach is that any noise present on the input data ( or ) will directly leak into the deghosted results. Optimal deghosting: Discarding the direct arrival, the recorded, data with noise N, N can be modelled in terms of their respective flat sea ghost responses, and the unknown up-going wavefield U: N 1 r exp ik H U with (eq. ) N ck 1 r exp ik H For convenience, also includes the obliquity factor, r is the sea-surface reflection coefficient and i = -1. The solution that minimies, in a least-squares sense, the noise on the up-going wavefield (eq. ) is called Optimal Deghosting () (Ödemir and Öbek 8). In the special case of uncorrelated pressure and velocity noises with variances σ and σ, the solution is: * * U W W (eq. 3) where * denotes complex conjugate. is a three step process: (1) de-phase the and wavelet by correlation with their respective ghost operator and, thereby, also attenuate the spectral components with reduced signal levels due to the destructive ghost interference, () sum the de-phased components scaled by the corresponding noise variances σ, σ and (3) reshape the spectrum. Alternatively, one can rewrite eq. 3 to note that the contribution of individually deghosted solutions / and / is controlled by normalied deghosting weights W and W, which are a function of the theoretical signal-to-noise ratio (SNR) of the input components: /σ and /σ. For example, if

3 for some frequency band, the noise is much stronger than the noise (σ >σ ), the contribution of the component will be reduced. It can be shown that the SNR of the deghosted data is the algebraic sum of the SNR of the pressure and velocity data: the SNR is always improved by the method. A -D data example Multi-component streamer data were acquired in the North Sea with a conventional source array and a streamer of km length. The streamer was towed at a 5 m depth leading to notch frequencies at multiples of ~3 H, starting at H for and ~15 H for (normal incidence). Observer logs report a moderate swell (1- m significant wave height) and some seismic interference (SI). The water depth is around 9 m. The subsurface is organied in 3 structural/target units; the deepest is at s TWT. A real-time preprocessing sequence was applied to the data: bad trace detection/interpolation, orientation, coherent noise attenuation and unit conversion. In this instance, a 3 H low-cut was applied to the data. From now on, only the noise after noise attenuation i.e. the residual noise is considered. The water velocity was 148 m/s, the acoustic impedance 15. µbar/µm/s; we assumed r =1and k y =. A typical and shot record is displayed in Figure 1 (top). ood signal strength can be observed on both and components. The low frequency noise on is visible, but deep continuous reflections can be seen through the noise. Up- and down-going (ghost) events can be identified on and (e.g. at.78 s) with a TWT~33 msec. Some SI is observed, mostly on, suggesting near-horiontal propagation. In Figure 1 (bottom), deep and complementary notches can be observed on FK amplitude spectra computed in a window containing mainly signal (< 5s). The notches occur where expected. The and data are combined using equation 1 (wavefield decomposition) and equation 3 (optimal deghosting). For optimal deghosting, we assume that, after noise attenuation, the noise is uncorrelated, spatially incoherent and that σ, = σ, (ω). The statistics of the noise were estimated by averaging amplitude spectra computed in a window containing mainly noise (Figure a). As expected, the noise on is stronger than the noise on at low frequencies. Furthermore, it is notable that the noise levels are relatively consistent from shot to shot. The variations in the noise are due to coherent noise not excluded from the analysis window. The impact of the noise models on the deghosting filter is limited to the low frequencies. The normalied weights at normal incidence (Figure b) suggest that, for this tow depth, reverts to a pressureonly solution below ~ H (as σ >σ ). Above H, the contribution of both components is mostly governed by the ghost operators (as σ σ ). As expected, the pre-stack result is quieter at low frequencies compared to SUM; ghost events have been attenuated and notches are filled in by both combinations (Figure 1). re- and post-combination brute stacks are displayed in Figure 3. Again, produces the clearer stack, but all 3 target units are well defined on the straight SUM stack. This is a promising result given the fact that no further processing was applied. From the average amplitude spectra at unit (Figure 4), and notches are clearly visible and both SUM and spectra outline the envelope of the input and spectra. The fine details of the spectra reflect the contributions of the and data. SUM and signal spectra compare well except at the lowest frequencies where the noise impacts the SUM result. Figure 4 also shows the average spectrum computed in a noise window. As expected, the stack has the least residual noise. Discussion On closer examination, it can be seen that the average amplitude spectra of and SUM differ by a small amount at higher frequencies (1- db). This could be caused by inaccuracies in the ghost models (e.g. cable depth, flat sea assumption, -D processing). SUM is known to be independent or more robust to such perturbations. The greater sensitivity is the price for introducing an optimal weighting when the and noise levels diverge. While this is desirable when σ, σ differ significantly at low SNR (e.g. at low frequencies or/and late times), it might not be appropriate, given the extra ghost model sensitivities, when the SNR is high. Such sensitivities are also to be avoided for particular applications such as time-lapse. Furthermore, we observed data with a positive SNR. Average amplitude spectra of the stacked data suggest a ~db SNR at ~3H, ~H and ~5H on unit 1, and 3, respectively (Figure 5). However, because only the statistics of the noise impact the filter, the contribution of low frequency data is limited (Figure b), independently of the SNR of the input data. These remarks suggest that, in order to take the best of both combinations and to account for the varying SNRs on the input data, a time/frequency-dependent merge of and

4 SUM solutions is desirable. We are currently exploring this idea. As an example, using below the frequencies listed previously and SUM above, an -SUM merge can be implemented pre-stack using NMO correction and time windows corresponding to each unit. For the deepest window (unit 3 and below) the data contributes via between ~-5H (Figure b) and via SUM above ~5 H. The -SUM merge results are illustrated in Figures 1, 3 and 4. More involved solutions are discussed by Ödemir et al. (). Conclusion The new optimal deghosted () solution for combination cancels the receiver ghost and guarantees minimied residual noise. The straight SUM result is encouraging and shows potential for improvement as no further noise attenuation has been applied to the data. To further improve the deghosted data, we suggest a toolbox approach that takes advantage of both and SUM combinations and accounts for the varying signal-to-noise ratios observed on multi-component streamer data. References Amundsen, L. [1993] Wavenumber-based Filtering of Marine oint Source Data. eophysics, 58, NO. 9. Hill, D., Combee, L., and Bacon, J. [6] Over/under acquisition and data processing: the next quantum leap in seismic technology? First Break, 4 (6) Kragh, E., Svendsen. M., oto, R, Curtis, T., Morgan,., Kapedia, D. and Busanello, J. [9] A Method for Efficient Broadband Marine Acquisition and rocessing, 71st EAE Conference and Exhibition, Extended Abstracts. Long, A., Mellors, D., Allen, T. and McIntyre, A. [8] A calibrated dual-sensor streamer investigation of deep target signal resolution and penetration on the NW Shelf of Australia. 78 th Annual International Meeting, SE, Expanded Abstracts, B6. Ödemir, K. and Öbek,, A. [8] Method for optimal wavefield separation. WO (A). Ödemir, K., Öbek, A., Caprioli,., Robertsson, J. and Kragh, E. [9] The optimal deghosting algorithm for broadband data combination, 79th SE Annual International Meeting, Expanded Abstracts, 8, Ödemir, K., Kjellesvig, B., Caprioli,., Christie,. and Kragh, E. [] Robust Deghosting in the resence of Model Uncertainties. US953787A. SUM MERE R 5m S 151 V 5m S 151 SUM 5m S 151 5m S 151 HYB R 5m 5m S S FREQUENCY [H] FREQUENCY [H] FREQUENCY [H] FREQUENCY [H] FREQUENCY [H] FREQUENCY [H] SUM MERE [1/m] Figure 1: (top),, SUM, and merged -SUM combined shot gather (T 1.5 gain) and (bottom) their FK amplitude spectra (same ). Note the good agreement between the loci of and notches shown in black and the actual receiver ghost notch in the data. After combination notches are filled in; SUM and results are similar; the solution is quieter at the low frequencies. The arrows point to an event, its ghost (note the polarity differences on and ) and the attenuation of the ghost. An -SUM merge example is also shown. -4-5

5 & NORMALIED DEHOSTIN WEIHTS σr (f) σv (f) Average FREQUENCY (H) FREQUENCY (H) Figure a: Statistics of the residual noise on and for all the shots (thin lines) and the line average (thick lines). σ(ω), σ(ω) are estimated by averaging (within and across shots) amplitude spectra computed on the last seconds of ~8 s shots prior to combination. Noise energy with dips < km/s is excluded from the analysis. Noise profiles intersect around 3-4 H and tend to converge as frequency increases. Figure b: Normalied deghosting weights W(ω) and W(ω) related to the line average noise levels (black curves in Figure a) at normal incidence (kx=). The impact of the noise on the filter is mainly limited to the frequencies below H. The thin lines show W(ω) and W(ω) in the special case σ= σ. Unit 1 SUM fullband Unit 3 Unit F < H SUM F > H F < 5 H SUM F > 5 H 6.km SUM MERE Figure 3: Brute stacks of,, SUM, and merged -SUM data (T gain). Signal- and noise-dominant windows used for spectra analysis start at.17,.8, 1.45 and 6s (not shown); all windows are.5s long and include a same large range of CMs. -SUM merge details are indicated. SUM MERE STACK 9 8 Unit Unit Unit 3 3 Noise FREQUENCY (H) Figure 4: Average amplitude spectra computed in unit and in the noise window on all brute stacks. All combined data have been scaled by prior to spectral analysis. The combined data outline the envelope of the spectra of the input data. As expected, has the least post-combination noise. By design, the spectra of the SUM merge (black) follows the and SUM curves FREQUENCY (H) Figure 5: Average amplitude spectra of brute stack data (nd panel in Figure 3) computed in the 3 signal and noise windows. The low frequency noise is clear, but a positive SNR can be observed on all signal units: arrows represent a SNR of db. The spectra for unit and the noise are the same as in Figure 4. 74th EAE Conference & Exhibition incorporating SE EUROEC 1