Th ELI1 12 Joint Crossline Reconstruction and 3D Deghosting of Shallow Seismic Events from Multimeasurement Streamer Data

Transcription

1 Th ELI1 12 Joint Crossline Reconstruction and 3D Deghosting of Shallow Seismic Events from Multimeasurement Streamer Data Y.I. Kamil* (Schlumberger), M. Vassallo (Schlumberger), W. Brouwer (Schlumberger), D. Nichols (Schlumberger), M. Cowman (Schlumberger) & A. Özbek (Schlumberger) SUMMARY Generalized Matching Pursuit has been proven capable of achieving joint crossline interpolation and 3D receiver deghosting on severely aliased marine seismic measurements in real scenarios. In fact, theoretically GMP is capable of reconstructing the upgoing wave under aliasing of any order, as long as there is no spectral overlap between replicas of different events in the crossline wavenumber spectrum of the measured data. Therefore, severely undersampled shallow seismic reflections, with their highfrequency content and broad crossline spectrum, represent the greatest challenge for GMP. We propose an algorithm using moveout correction to reduce spatial aliasing and to improve the GMP performance in shallow seismic reflections. In addition, we propose a simple yet effective criterion to automatically activate the correction. We also show how 3D deghosting can still be performed. These concepts are illustrated using real data examples.

2 Introduction Towed-streamer marine seismic acquisition is typically characterized by fine sampling along the streamers (inline direction) and by coarse and possibly irregular sampling in the crossline direction. Consequently, the recorded wavefield can be strongly aliased in the crossline direction. Robertsson et al. (2008) introduced the concept of a multimeasurement streamer, measuring the particle velocity vector in addition to the pressure and showed that the value of a vector particle velocity measurement increases the crossline Nyquist wavenumber by a factor two and even, under certain conditions, up to a factor three. More recently, Özbek et al. (2010) described the joint reconstruction and deghosting problem and introduced the generalized matching pursuit (GMP) method. GMP is a data-dependent approach that exploits the anti-aliasing and the deghosting potential enabled by the additional measurements and relates all measured signals to the same 3D wavefield i.e., the upgoing wavefield. It has been shown that GMP can achieve joint interpolation and deghosting beyond the limit predicted by the multichannel sampling theorem (Papoulis, 1977). Theoretically, GMP is capable of reconstructing the upgoing wave under aliasing of any order, provided that no spectral overlap between replicas of different events affects the input in the crossline wavenumber domain (Vassallo et al., 2010). When proper mitigation strategies are in place, the likelihood of such overlap in the crossline wavenumber domain is normally low. However, the likelihood of overlap increases with the presence of high-order aliasing and a nonsparse crossline spectrum. Therefore, severely undersampled events such as shallow seismic reflections, having high frequency content and broad crossline spectrum (being curved events), represent the greatest challenge for GMP. Common measures used to improve the GMP performance in shallow seismic reflections are spatial-temporal windowing and the use of priors (Özbek et al., 2012). For near-offset shallow reflections, these may not be always sufficient to allow a correct reconstruction of the highest frequencies; hence, more effective solutions are needed. We introduce an algorithm using moveout correction to reduce spatial aliasing and further improve the GMP performance for shallow seismic reflections. We recall how the moveout correction can be applied to both the pressure data and its crossline gradient (Robertsson et al. 2008). In addition, we propose a simple yet effective criterion to automatically activate the correction without any intervention from the user. Finally, we show how 3D deghosting can still be performed. We illustrate these concepts using real data examples. Generalized Matching Pursuit in Shallow Reflection Data Moveout correction is often applied before interpolation to reduce spatial aliasing, as it simplifies those components of the wavefield that obey the model assumed by the moveout curve; however, this implies the risk of deteriorating the reconstruction of those events that do not obey such an assumption (Robertsson et al. 2008). As recent publications show, GMP applied on multimeasurement data does not, in general, need moveout correction to achieve accurate reconstruction under aliasing. However, in shallow seismic reflection data reconstruction, seismic events are strongly curved, and the order of aliasing is large at high frequencies. In these conditions, moveout correction can provide added robustness to GMP on a localized scale and enable more accurate reconstruction. Robertsson et al. (2008) shows that the moveout correction is compatible with multichannel interpolation using the pressure and its crossline gradient. In particular, the moveout-corrected pressure data is given by:, (1) where are the receiver inline and crossline coordinates, and is any moveout function. The crossline gradient of the moveout-corrected pressure can be obtained from:, (2)

3 which is the sum of the moveout-corrected pressure gradient and the product of the moveoutcorrected time derivative of the pressure and the spatial derivative of the moveout function. Note that if we applied the moveout correction to the vertical gradient measurement, it is not straightforward to preserve the relation between (i.e., the ghost model). Therefore, although deghosting cannot be achieved after moveout correction, multichannel interpolation (MIMAP, Vassallo et al. 2010) using moveout-corrected pressure and crossline gradient as input is actually possible and can benefit of both the de-aliasing potential of multichannel reconstruction and the benefits obtained with the moveout correction. In Equations (1) and (2), different moveout correction functions can be accommodated. Although the normal moveout (NMO) is the most commonly used, it is well-known that conventional NMO is not 100% reversible and can lead to wavelet distortion. This is caused by the NMO stretch. To fully preserve the wavelet, a time-invariant approach is used in this work where each trace within a space time window is shifted back in time by a time shift :, where different can be considered. A simple example is given by:, (3) where is the receiver depth, is the source coordinates, is the propagation velocity in water, and is the effective depth from which a reference event is assumed to be reflected. Note that the velocity of water is used here to approximate the propagation velocity. This approximation is used to sufficiently reduce the curvature of shallow reflection events (in a given spacetime window) for MIMAP to obtain accurate reconstruction. Figure 1 shows a slice at 60 Hz of the frequency wavenumber transform of the moveout operator calculated over a realistic spread. This represents the transform of the ideal event that is collapsed into a pulse at by applying the moveout shift. Figure 1 Frequency slice (60Hz) of fk x k y spectrum of the moveout operator To apply the moveout operator only where it is needed without direct user intervention, an automatic activation criterion is required: the operator must be applied only when overlapping alias is expected within the signal bandwidth. Based on the expected curvature within each space-time window, the maximum unaliased frequency is calculated as shown in Figure 2. When this frequency lies within the seismic bandwidth, the moveout operator is activated. Figure 2 Diagram depicting a spacetime window (left) and its bandwidth (right). Sampling at generates spectral replicas of the signal cone at regular steps of. The green and yellow lines show the edges of the signal cone based on the slope of the curved events at the edges. The maximum unaliased frequency is compared with the maximum frequency of interest to determine if moveout is needed. As MIMAP can only reconstruct the total pressure wavefield, a successive step of the algorithm is required to achieve joint interpolation and 3D deghosting. Inverse moveout is applied to the interpolated data, and the total reconstructed pressure in addition to the crossline and vertical gradient

4 measurements are passed as inputs to GMP. With the high order aliasing at high curvature resolved, the GMP algorithm can use the information of in addition to and for deghosting purposes. Note that in addition to the 3D deghosting capability, GMP provides refined interpolation to the MIMAP output. Matching the measured gradients mitigates the risk of complex events being eventually compromised by the use of the simple moveout model. Results We illustrate the shallow reconstruction of reflection data using GMP on data acquired in the North Sea. The data were acquired using 8 3-km-long multimeasurement streamers with a nominal cable separation of 100 m. The depth of cables was 17 m. The seabed depth was around 120 m, and the shortest inline offset was 150 m. At 100 m crossline cable spacing, first order alias is already possible at 7.5 Hz. Wavefields were reconstructed by GMP in the common shot domain on a 6.25-m 6.25-m isometrically sampled grid Figure 3 Crossline gather of the reconstructed total pressure and a zoomed section of the data. The data is reconstructed using GMP without moveout correction Figure 4 Crossline gather of the reconstructed total pressure and a zoomed-in section of the data. The data is reconstructed using GMP with moveout correction for the shallow reconstruction (above 0.73 sec in the zoomed section). 0.7 Figure 3 shows the near-offset total pressure wavefield computed using GMP without moveout and sorted in crossline. Reconstruction errors and interpolation noise are seen in the reconstructed shallow (highly curved) events, especially at high frequency. Much better quality can be seen after around 0.7 sec. Figure 4 shows the GMP performance after applying the presented algorithm in the shallow sections. The improvements in the reconstruction are evident. Figure 5 compares the frequencycrossline wavenumber amplitude spectrum for the input pressure data and the total pressure wavefield after reconstruction. Column A shows the input pressure data at 100-m spacing. Column B shows the reconstructed total pressure using GMP without activating the moveout correction step. Column C shows the reconstructed total pressure using MIMAP and moveout to enhance the reconstruction of the shallow section of the data. As expected, the input pressure suffers from severe aliasing before reconstruction using GMP (Fig 5.A). This is due to the broad crossline spectrum of the shallow reflected events. As a result, considerable spectral overlap between replicas of different events affects the input data. Significant dealiasing is achieved by conventional use of GMP (Fig 5.B), nevertheless the crossline spectrum of the GMP result using moveout in the shallow section looks significantly improved up to approximately 125 Hz. Although GMP is a data dependent technique and its results

5 in different scenarios may vary, the achieved reconstruction quality in this experiment is remarkable and very promising. A detailed study of the performance of the proposed algorithm run on a wider scale and compared with reference actual measurements can be seen in Letki and Spjuth (2014). Figure 5: f-k y amplitude spectrum for (A) input pressure, (B) total reconstructed pressure using GMP without moveout correction, and (C) total reconstructed pressure using GMP with moveout correction step Conclusions GMP applied on multimeasurement data does not, in general, need moveout correction to achieve accurate crossline receiver reconstruction and 3D deghosting under severe aliasing. However, under certain conditions, various factors combine to challenge the GMP wavefield reconstruction. For example, where the seismic events have strong curvature, such as with shallow reflection data, and the wavelet contains energy up to high frequencies corresponding to very high-order crossline aliasing. In these situations, an automatic algorithm based on MIMAP reconstruction on moveout corrected data can provide further robustness to GMP. We describe such algorithm, its activation criteria, its risks, and their mitigation. Results are shown on dataset from the North Sea show high-quality reconstruction at very short offsets up to frequencies of approximately 125 Hz. Acknowledgments This work involved many people: here, we would like to thank Robert Bloor, Peter Watterson, Chris Cunnell and Ralf Ferber for many useful discussions. We acknowledge the great contributions from Shipra Mahat, Rishi Ramsumair, Catalina Llano Ocampo and Bill Armstrong. We thank Schlumberger for permission to publish this talk. References Letki, L.P., Spjuth, C. [2014] Quantification of wavefield reconstruction quality from multisensor streamer data using a witness streamer experiment. EAGE Conference and Exhibition, submitted. Özbek, A., Vassallo, M., Özdemir, K., van-manen D.J. and Eggenberger, K. [2010] Crossline wavefield reconstruction from multicomponent streamer data: Part 2 Joint interpolation and 3-D up/down separation by generalized matching pursuit. Geophysics, 57, WB69 WB85. Özbek, A., Vassallo, K., Eggenberger, K., van-manen D.J., Özdemir, K. and Curtis, T. [2012] On the role of priors in generalized matching pursuit to reconstruct wavefields from multicomponent streamer data. EAGE Conference and Exhibition, B021. Papoulis, A. [1977] Generalized sampling expansion. IEEE Transactions on Circuits and Systems, 24, no. 11, Robertsson, J., Moore, I., Vassallo, M., Özdemir, A.K., van Manen, D-J. and Özbek, A. [2008] On the use of multicomponent streamer recordings for reconstruction ofpressure wavefields in the crossline direction. Geophysics, 73, A45 A49. Vassallo, M., Özbek, A., Özdemir, K. and Eggenberger, K. [2010] Crossline wavefield reconstruction from multicomponent streamer data: Part 1 Interpolation by matching pursuit using pressure and its crossline gradient. Geophysics, 75, WB53 WB67.