Case study of example of multiple attenuation for over/under streamer data
Karin Schalkwijk*, Clement Kostov, and Ed Kragh, SCR, Cambridge, U.K.
Introduction In towed streamer data, ghosts are difficult to separate from primaries, yet when left in the data, they broaden the seismic pulse, reduce bandwidth, and degrade imaging and time-lapse results (Laws and Kragh, 2002). Recently, significant advances in deghosting solutions for streamer data have been reported. Kragh et al. (2004) discuss a field test of simultaneous acquisition of data with a streamer at conventional depth of 5 m, and deeper streamers in an over/under configuration at 18 m and at 23 m. Kragh et al. (2004) demonstrate tight specifications for streamer positioning, lower noise levels on the deep streamers, and estimation of wave heights from ultra-low frequencies in the data. Stacks from the deghosted data are clearly superior when compared to the stacks from non-deghosted shallow streamer data. The over/under stacks show better low frequency signal content, flatter bandwidth and lower noise, in addition to the removal of the rough sea ghost. We note that the upgoing wavefield obtained from the over/under data (Kragh et al., 2004) meets some of the preprocessing requirements for prediction of free-surface multiples better than the data from the streamer towed at conventional depths; e.g. no receiver ghost, no direct arrival, lower swell noise levels. These properties of the upgoing wavefield should complement efforts on wavefield sampling as required for accurate 2D and 3D predictions of free-surface multiples, and generally improve preprocessing of the data for multiple prediction and inversion (Zhang and Weglein, 2005). In this paper, we review the expected benefits from over/under streamer data for 2D prediction of free-surface multiples. We test, illustrate, and discuss these expectations on the field dataset consisting of a shallow and a pair of over/under streamers (Kragh et al., 2004). The computation of an upgoing wavefield from the over/under data contributes to improvements in the attenuation of multiples and to an overall better image than the one obtained from the shallow streamer data. Theoretical background: amplitudes of first-order free-surface multiples We start with expressions for predicting free-surface multiples, after Berkhout and Verschuur (1997). The discretized impulse response of the medium with a free-surface at a particular temporal frequency ω is denoted as matrix X , while the impulse response of the medium without a free-surface is denoted as ∆X . Matrices S , D, R0 represent respectively source, receiver, and sea-surface operators. The relations between data and the corresponding impulse responses are P = D X S for a medium including a free surface. The term M 1 = XR0 X predicts first-order free-surface multiples in the impulse response with correct amplitudes. Accurate prediction of higher-order multiples requires a model based on M = ∆XR0 X . We assume now a 1D background medium, a flat sea surface, as well as point sources and point receivers. Then, the receiver matrix D is equal to the receiver-side ghost, while the source matrix S is the convolution of the source function and the source-side ghost. Specifically, matrix S is S (ω ) =
A(ω ) G ( z s ) , where A(ω ) is proportional to the source ikz
2 ik z z
function and the ghost operator is G ( z ) = (1 − r0e
) with depth z equal to the depth of the
source z s (Amundsen, 1993). The factor k z is a vertical wavenumber, referred to as an
EAGE 68th Conference & Exhibition — Vienna, Austria, 12 - 15 June 2006
obliquity factor and equal to
ω
c
cos(θ )
(Figure 1), where the angle θ is a take-off angle.
Note that in the case of a 1D background medium, take-off and incidence angles, as well as source and receiver wavenumbers, are equal to each other. An approximate model for first-order multiples M 1 may be computed by omitting the deghosting parts of the source and receiver operators, M 1 = Pik z r0 P . In processing practice, space coordinates. Here, we denote the matching filter as B (ω , k s , k r ) , where k s , kr are the wavenumbers associated with the shot and receiver coordinates. We consider now three processing scenarios and derive the corresponding matching filters (Table 1). Source-side deghosting Yes No No Receiver-side deghosting Yes Yes No First-order multiples M 1 the approximate model M 1 is scaled by a matching filter, usually a function of time and of
~
~
~
P
ik z r0 P A(ω ) ik z P r0 P A(ω )G ( z s ) ik z P r0 P A(ω )G ( z s )G ( zr )
B (ω ) for ~ approximate model M 1 1 B(ω ) = A(ω ) 1 B(ω , k s ) = A(ω )G ( zs ) 1 B(ω , k s , kr ) = A(ω )G ( z s )G ( zr )
Matching filters
Table 1: First-order multiples and matching filters for three common preprocessing cases. The complexity of the matching filter increases when deghosting is omitted from preprocessing. Figure 1 displays scaling factors |
kz k |, | z |, | k z |, | G ( z s ) |, | G ( z s )G ( zr ) | G ( z s )G ( zr ) G ( zs )
computed for a frequency of 20 Hz and source and receiver depths of 5 m. For this frequency, and, for these source and receiver depths, the ratio of the obliquity factor to the source-side ghost is nearly constant amplitude (curve 2 in Figure 1). However, the scaling factor for nondeghosted data includes two ghost terms in the denominator, and increases rapidly as the angle approaches 90º (curve 1 in Figure 1). The corresponding matching filter would also be rapidly varying with take-off and incidence angles. In practice, the matching filters compensate for several causes of mismatch between the data and the model, including ghost and rough sea effects (Figure 2). Other factors not discussed here are kinematic errors, amplitudes of high-order multiples, events in the data that are not part of the model (e.g., primaries, internal multiples), source and receiver array effects, and, noise in the data.
Figure 1. From top to bottom: (1) ratio of Figure 2. a) Shot gather computed by finiteobliquity factor to source and receiver ghosts difference modeling over an elastic 1D kz medium and including effects of a rough sea | | ; (2) ratio of obliquity factor and surface. b) Model of free-surface multiples G ( z s )G ( z r ) ~ one ghost; (3) normalized obliquity factor M 1 computed from data including ghosts. | k z (θ ) | / | k z (0) | ; (4) Amplitude-versus- Events a and b are first-order free-surface angle factor (AVA) | G (z s ) | for a receiver-side multiples (note differences in amplitudes ghost; (5) AVA factor | G ( z s ) | 2 for source and increasing with offset), while event c is a second-order multiple (note amplitude receiver ghosts. differences even at small offsets). Case study data examples In the case of over/under streamers, by measuring the vertical gradient of pressure, it is possible to perform an up/down separation on streamer data. The upgoing wavefield is then “receiver-side deghosted”. Poststack, the deghosted data (Figure 3b) show improvements over the non-deghosted data (Figure 3a). The signal-to-noise ratio is improved, the reflectors show better continuity and the wavelet is more compressed because of receiver-side ghost removal. In this part of the section, the sea floor is nearly horizontal at 120 m depth (160 msec two-way traveltime). After application of pre-stack surface related multiple attenuation (SRME), the deghosted stack again shows improvements with respect to the non-deghosted stack (Figure 4b), even after amplitude balancing the non-deghosted stack (Figure 4a) in order to remove the bandwidth differences. However, improvements in multiple attenuation are not as readily identifiable on the stack itself. Discussion Theoretically, the compensation of ghost and rough sea effects allows a more accurate prediction of the amplitudes of multiples, hence, a more reliable subtraction of the multiples from the data. In tests on a field dataset consisting of shallow and over/under streamers (Kragh et al., 2004), we note that receiver-side deghosting and lower noise levels on the over/under data contribute to an improvement of the stack. However, improvements in multiple attenuation itself on the over/under receiver-side deghosted data are not as readily identified as expected. The detailed interpretation and comparison of the multiple attenuation results is still in progress.
EAGE 68th Conference & Exhibition — Vienna, Austria, 12 - 15 June 2006
a)
b)
Figure 3. a) Stack from the data recorded with shallow (5 m) cable. b) Stack from the data recorded with the pair of over/under streamers (18 m and 23 m) receiver-side deghosted and shifted to simulate acquisition at 5-m depth.
a)
b)
Figure 4. a) Attenuation of free-surface multiples (by SRME method) and stack from the data recorded with shallow (5 m) cable. Note that the frequency spectrum was matched to the deghosted data. b) Attenuation of free-surface multiples (by SRME method applied after receiver-side deghosting) and stack from the data recorded with the pair of over/under cables. References Amundsen, L. [1993] Wavenumber-based filtering of marine point-source data. Geophysics, 58, 1335-1348. Berkhout, A.J. and Verschuur, D.J. [1997] Estimation of multiple scattering by iterative inversion, Part I: theoretical considerations. Geophysics, 62, 1586-1595. Kragh, E., Robertsson, J.O.A., Amundsen L., Rosten, T., Davies, T., Zerouk, K. and Strudley, A. [2004] Rough sea deghosting using wave heights derived from low frequency pressure recordings. 66th Meeting, European Association of Geoscientists and Engineers, H024. Laws, R. and Kragh, E. [2002] Rough seas and time-lapse seismic., Geophysical Prospecting, 50, 195-208. Zhang, J. and Weglein, A.B. [2005] Extinction theorem deghosting method using towed streamer pressure data: Analysis of the receiver array e.ect on deghosting and subsequent free surface multiple removal. 75th Meeting, Society of Exploration Geophysicists, Expanded Abstract, 2095-2098.