A033
Combination of Multi-component Streamer
Pressure and Vertical Particle Velocity - Theory
and Application to Data
P.B.A. Caprioli* (WesternGeco), A.K. Özdemir (WesternGeco), A. Özbek
(Schlumberger Cambridge Research), J.E. Kragh (Schlumberger
Cambridge Research), D.J. van Manen (WesternGeco), P.A.F. Christie
(Schlumberger Cambridge Research) & J.O.A. Robertsson (Schlumberger
Cambridge Research)
SUMMARY
In this paper, we generalize the optimal deghosting (ODG) method used for deghosting over/under data to
combine pressure (P) and vertical velocity (Z) data recorded with a multi-component streamer to minimize
the impact of the noise on the deghosted data. The ODG approach uses pressure and velocity ghost models
and the statistics of the residual noise to minimize, in a least-squares sense, the noise on the up-going/
deghosted wavefield. ODG and the standard PZ summation (PZSUM) 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 ODG 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 PZ deghosted data, we suggest a toolbox approach that takes
advantage of both ODG and PZSUM combinations and accounts for the varying signal-to-noise ratios
observed on multi-component streamer data.
74th EAGE Conference & Exhibition incorporating SPE EUROPEC 2012
Copenhagen, Denmark, 4-7 June 2012
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. 2006), over/sparse-under 3D streamers (Kragh et al. 2009) and the additional
vertical velocity component where the pressure and the velocity measurements are combined to
achieve deghosting (Long et al. 2008). 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 (ODG) method used to deghost over/under data by Özdemir et al. (2009) to the
combination of the pressure and the vertical velocity recorded by a multi-component streamer. We
also consider the standard PZ summation (PZSUM) and discuss pros/cons of both combinations. Both
approaches are then applied to real data.
Wavefield decomposition: PZSUM
Let P and Z represent the frequency - (inline and crossline) wavenumber (ω, kx, ky) transformed data
of pressure and vertical particle velocity wavefields recorded at a depth H below the sea surface. The
Z 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 PZSUM  0.5P   ck z Z ,
DPZSUM  0.5P   ck z Z 
(eq. 1)
where kz =[(ω/c)2-kx2-ky2]1/2 is the angular vertical wavenumber. The dimensionless ratio ω/ckz is the
inverse obliquity factor required to balance the vertical component. Up-going events are recorded
with the same polarity on P and Z 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 (P or Z) will directly leak into the deghosted results.
Optimal deghosting: ODG
Discarding the direct arrival, the recorded P, Z data with noise NP, NZ can be modelled in terms of
their respective flat sea ghost responses GP, GZ and the unknown up-going wavefield U:
P

 Z
 G 
N 
   P U    P 
 GZ 
N Z 
G P  1  r0 exp 2ik z H 
G Z  ck Z  1  r0 exp 2ik z H 
with 
(eq. 2)
For convenience, GZ also includes the obliquity factor, r0 is the sea-surface reflection coefficient and
i2= -1. The solution that minimizes, in a least-squares sense, the noise on the up-going wavefield (eq.
2) is called Optimal Deghosting (ODG) (Özdemir and Özbek 2008). In the special case of
uncorrelated pressure and velocity noises with variances σ2P and σ2Z, the ODG solution is:
G P*
U ODG 
 P2
GP
 P2
P
2

G Z*
 Z2
GZ
Z
2
 WP
P
Z
 WZ
GP
GZ
 Z2
(eq. 3)
where * denotes complex conjugate. ODG is a three step process: (1) de-phase the P and Z 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, (2) sum the de-phased
components scaled by the corresponding noise variances σ2P, σ2Z and (3) reshape the spectrum.
Alternatively, one can rewrite eq. 3 to note that the contribution of individually deghosted solutions
P/GP and Z/GZ is controlled by normalized deghosting weights WP and WZ, which are a function of the
theoretical signal-to-noise ratio (SNR) of the input components: |GP|2/σ2P and |GZ|2/σ2Z. For example, if
74th EAGE Conference & Exhibition incorporating SPE EUROPEC 2012
Copenhagen, Denmark, 4-7 June 2012
for some frequency band, the Z noise is much stronger than the P noise (σ2Z >σ2P), the contribution of
the Z 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 ODG method.
A 2-D data example
Multi-component streamer data were acquired in the North Sea with a conventional source array and a
streamer of 2 km length. The streamer was towed at a 25 m depth leading to notch frequencies at
multiples of ~30 Hz, starting at 0 Hz for P and ~15 Hz for Z (normal incidence). Observer logs report
a moderate swell (1-2 m significant wave height) and some seismic interference (SI). The water depth
is around 90 m. The subsurface is organized in 3 structural/target units; the deepest is at 1.5-2.4s
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 Hz 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 1480 m/s, the acoustic impedance 15.2 µBar/µm/s; we assumed
r0=1and ky=0. A typical P and Z shot record is displayed in Figure 1 (top). Good signal strength can
be observed on both P and Z components. The low frequency noise on Z is visible, but deep
continuous reflections can be seen ‘through’ the noise. Up- and down-going (ghost) events can be
identified on P and Z (e.g. at 0.78 s) with a TWT~33 msec. Some SI is observed, mostly on P,
suggesting near-horizontal 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 P and Z 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 σ2P,Z = σ2P,Z (ω). The statistics
of the noise were estimated by averaging amplitude spectra computed in a window containing mainly
noise (Figure 2a). As expected, the noise on Z is stronger than the noise on P at low frequencies.
Furthermore, it is notable that the Z noise levels are relatively consistent from shot to shot. The
variations in the P noise are due to coherent noise not excluded from the analysis window. The impact
of the noise models on the ODG deghosting filter is limited to the low frequencies. The normalized
weights at normal incidence (Figure 2b) suggest that, for this tow depth, ODG reverts to a pressureonly solution below ~20 Hz (as σ2Z>σ2P). Above 20 Hz, the contribution of both components is mostly
governed by the ghost operators (as σ2Z ≈σ2P). As expected, the pre-stack ODG result is quieter at low
frequencies compared to PZSUM; ghost events have been attenuated and notches are filled in by both
combinations (Figure 1). Pre- and post-combination brute stacks are displayed in Figure 3. Again,
ODG produces the clearer stack, but all 3 target units are well defined on the straight PZSUM stack.
This is a promising result given the fact that no further processing was applied. From the average
amplitude spectra at unit 2 (Figure 4), P and Z notches are clearly visible and both PZSUM and ODG
spectra outline the envelope of the input P and Z spectra. The fine details of the spectra reflect the
contributions of the P and Z data. PZSUM and ODG signal spectra compare well except at the lowest
frequencies where the Z noise impacts the PZSUM result. Figure 4 also shows the average spectrum
computed in a noise window. As expected, the ODG stack has the least residual noise.
Discussion
On closer examination, it can be seen that the average amplitude spectra of ODG and PZSUM differ
by a small amount at higher frequencies (1-2 dB). This could be caused by inaccuracies in the ghost
models (e.g. cable depth, flat sea assumption, 2-D processing). PZSUM is known to be independent or
more robust to such perturbations. The greater sensitivity is the price for introducing an optimal
weighting when the P and Z noise levels diverge. While this is desirable when σ2P, σ2Z 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 Z data with a positive SNR.
Average amplitude spectra of the stacked Z data suggest a ~20dB SNR at ~3Hz, ~20Hz and ~25Hz on
unit 1, 2 and 3, respectively (Figure 5). However, because only the statistics of the noise impact the
ODG filter, the contribution of low frequency Z data is limited (Figure 2b), 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 ODG and
74th EAGE Conference & Exhibition incorporating SPE EUROPEC 2012
Copenhagen, Denmark, 4-7 June 2012
PZSUM solutions is desirable. We are currently exploring this idea. As an example, using ODG
below the frequencies listed previously and PZSUM above, an ODG-PZSUM 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 Z data contributes via ODG between ~20-25Hz (Figure 2b)
and via PZSUM above ~25 Hz. The ODG-PZSUM merge results are illustrated in Figures 1, 3 and 4.
More involved solutions are discussed by Özdemir et al. (2010).
Conclusion
The new optimal deghosted (ODG) solution for PZ combination cancels the receiver ghost and
guarantees minimized residual noise. The straight PZSUM result is encouraging and shows potential
for improvement as no further noise attenuation has been applied to the data. To further improve the
PZ deghosted data, we suggest a toolbox approach that takes advantage of both ODG and PZSUM
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 Point Source Data. Geophysics, 58, NO. 9.
Hill, D., Combee, L., and Bacon, J. [2006] Over/under acquisition and data processing: the next quantum leap in
seismic technology? First Break, 24 (6) 81-96.
Kragh, E., Svendsen. M., Goto, R, Curtis, T., Morgan, G., Kapedia, D. and Busanello, J. [2009] A Method for
Efficient Broadband Marine Acquisition and Processing, 71st EAGE Conference and Exhibition, Extended
Abstracts.
Long, A., Mellors, D., Allen, T. and McIntyre, A. [2008] A calibrated dual-sensor streamer investigation of
deep target signal resolution and penetration on the NW Shelf of Australia. 78th Annual International Meeting,
SEG, Expanded Abstracts, B026.
Özdemir, K. and Özbek,, A. [2008] Method for optimal wavefield separation. WO2008134177(A2).
Özdemir, K., Özbek, A., Caprioli, P., Robertsson, J. and Kragh, E. [2009] The optimal deghosting algorithm for
broadband data combination, 79th SEG Annual International Meeting, Expanded Abstracts, 28, 147-151.
Özdemir, K., Kjellesvig, B., Caprioli, P., Christie, P. and Kragh, E. [2010] Robust Deghosting in the Presence of
Model Uncertainties. US2010953787A.
P
Z
VZ 25m SP 1501
ODG
SUM 25m SP 1501
MERGE
ODG 25m SP 1501
HYBPR
25m
25m
SPSP
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PR 25m SP 1501
SUM
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-0.06 -0.06 -0.04 -0.04 -0.02-0.02
0 0
0.02
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WAVENUMBER
WAVENUMBER
[1/m][1/m]
0.04
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-50
Figure 1: (top) P, Z, SUM, ODG and merged ODG-SUM combined shot gather (T1.5 gain) and (bottom) their FK amplitude spectra (same
dB scale). Note the good agreement between the loci of P and Z notches shown in black and the actual receiver ghost notch in the data. After
combination notches are filled in; SUM and ODG results are similar; the ODG solution is quieter at the low frequencies. The arrows point to
an event, its ghost (note the polarity differences on P and Z) and the attenuation of the ghost. An ODG-SUM merge example is also shown.
74th EAGE Conference & Exhibition incorporating SPE EUROPEC 2012
Copenhagen, Denmark, 4-7 June 2012
P & Z NORMALIZED DEGHOSTING WEIGHTS
0
σ2PR (f)
σ2VZ (f)
Average
-10
dB scale
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Figure 2a: Statistics of the residual noise on P and Z for all the
shots (thin lines) and the line average (thick lines). σ2P(ω), σ2Z(ω)
are estimated by averaging (within and across shots) amplitude
spectra computed on the 2 last seconds of ~8 s shots prior to
combination. Noise energy with dips < 2 km/s is excluded from
the analysis. Noise profiles intersect around 30-40 Hz and tend to
converge as frequency increases.
Figure 2b: Normalized deghosting weights WP(ω) and WZ(ω) related
to the line average noise levels (black curves in Figure 2a) at normal
incidence (kx=0). The impact of the noise on the ODG filter is mainly
limited to the frequencies below 20 Hz. The thin lines show WP(ω)
and WZ(ω) in the special case σ2P= σ2Z.
Unit 1
SUM fullband
Unit 3
Unit 2
ODG F < 20 Hz
SUM F > 20 Hz
ODG F < 25 Hz
SUM F > 25 Hz
P
6.2km
Z
SUM
ODG
MERGE
2
Figure 3: Brute stacks of P, Z, SUM, ODG and merged ODG-SUM data (T gain). Signal- and noise-dominant windows used for spectra
analysis start at 0.17, 0.8, 1.45 and 6s (not shown); all windows are 0.5s long and include a same large range of CMPs. ODG-SUM merge
details are indicated.
P
Z
ODG
SUM
MERGE
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FREQUENCY (Hz)
Figure 4: Average amplitude spectra computed in unit 2 and in the
noise window on all brute stacks. All combined data have been
scaled by 2 prior to spectral analysis. The combined data outline the
envelope of the spectra of the input data. As expected, ODG has the
least post-combination noise. By design, the spectra of the ODGSUM merge (black) follows the ODG and SUM curves.
0
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FREQUENCY (Hz)
Figure 5: Average amplitude spectra of brute stack Z data (2nd 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 20 dB. The spectra for unit 2
and the noise are the same as in Figure 4.
74th EAGE Conference & Exhibition incorporating SPE EUROPEC 2012
Copenhagen, Denmark, 4-7 June 2012