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Shot-to-shot directional designature using near-field hydrophone data
Gordon Poole* and Chris Davison, CGG; Jake Deeds, Kevin Davies and Gary Hampson, Chevron
Summary
A method for shot-to-shot directional designature using
near-field hydrophone measurements is presented. The
algorithm is compared with traditional designature methods
and data examples are given on a variable depth streamer
dataset from the Norwegian North Sea.
Introduction
Far-field designature is a standard step in the marine
processing sequence which converts the source far-field
signature to a desired output. The conversion is made by
convolving the data by the derived shaping filter. Usually a
filter is derived to combine the operations of debubbling
and zero-phasing. This approach leaves the source ghost
notch in the spectrum of the data and produces a tight zero
phase wavelet. The far-field signature is often derived
using modeling software (e.g., Nucleus (PGS Seres AS) or
Gundalf (Oakwood computing associates Ltd)).
In the quest for broader bandwidth data it is necessary to
deghost the data on both source and receiver sides in order
to pursue the true subsurface reflectivity. For conventional
data, there is a limited diversity of the receiver ghost notch
frequencies which often prevents effective deghosting. For
this reason more sophisticated solutions have been
developed which include over-under streamers (Sønneland
et al, 1986), variable depth streamers (Soubaras, 2010), and
utilizing streamers incorporating geophones as well as
hydrophones (Carlson et al, 2007).
On the source side it has also been necessary to move
towards ghost removal. For conventional source data this
means shaping the far-field signature to a high bandwidth
zero phase pulse. More recently, broadband sources have
become available which use airguns at more than one depth
to diversify the source ghost (Hegna and Parkes, 2012).
Usually designature is applied as a 1D filter even though
the source response is not isotropic. To achieve the correct
broadband results for all angles, it is necessary to apply full
directional designature where the source signal at all take
off angles is corrected to the same zero phase wavelet.
In this paper we describe a method that uses near-field
hydrophone measurements to apply shot-to-shot directional
designature.
© 2013 SEG
SEG Houston 2013 Annual Meeting
Directional far-field derivation from near-field
hydrophone data
Near-field hydrophones have been used for many years.
Often positioned approximately 1m above and behind each
gun, the near-field hydrophones are usually used to check
for gun misfires and sub-array separation.
Ziolkowski et al (1982) proposed that near-field
hydrophones may also be used to derive far-field
signatures. Their method uses the near-field hydrophone
measurements to derive hypothetical isotropic point source
signatures termed notional signatures.
Although the
complex near-field includes many non-linear effects, the
near-field hydrophone measurements are modeled as a
linear combination of notional sources that includes
divergence, time delay, vessel motion and ghost effects. It
is also possible to add constraints into the notional source
derivation, e.g. by modeling cluster guns as two notional
sources with identical response. In addition the near-field
hydrophone and notional source positions may be varied
dynamically based on field measurements (e.g., rGPS and
acoustic bracing measurements).
Far-field signatures in any direction are produced by beamforming the notional sources whilst including the
appropriate directional ghost operator. The far-field
directional signatures may also be expressed in the
slowness (,px,py) or the frequency-wavenumber (f,kx,ky)
domains.
Near-field hydrophones require calibration using field
measurements (Ziolkowski and Johnston, 1997). The
calibration scalars may vary with frequency. In addition, it
may be necessary to compensate for differing impulse
responses between the near-field hydrophones and the
streamer hydrophones.
Designature operator derivation
If designature using the vertical far-field signature is
required, a single 1D filter is used. For directional
designature, a set of filters are used to account for all takeoff angles and azimuths of interest.
Conventionally every source element is towed at one depth.
This results in strong signal attenuation at the notch
frequencies. Under these circumstances full deghosting
amplifies any noise at these frequencies. As a result,
aggressive deghosting is either avoided entirely, by using a
phase only operator, or strong amplification is moderated
using some form of coloured damping. More recently,
DOI http://dx.doi.org/10.1190/segam2013-0550.1
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Shot-to-shot directional designature using near-field hydrophone data
using multi-level sources and receivers a fuller deghosting
is often possible with little or no damping.
Global directional designature
Although designature is commonly 1D, to properly
compensate for the directivity of the source, directional
designature is necessary. This improves resolution and
properly preserves AVO. This may be achieved by making
a plane wave decomposition of the data in the common
receiver domain. This transformation produces a different
trace for each source take-off angle which allows the
application of angularly dependent filters. Such schemes
have been applied in 2D in the -p domain (Van der Schans
and Ziolkowski, 1983) and in the f-k domain (Hubbard et
al, 1984). However, as the plane wave decomposition is a
weighted sum of traces from different shots, this approach
is only strictly valid if the directional signatures do not
change from shot-to-shot. As a consequence, it is often
assumed that the directional signatures remain constant
throughout the whole survey.
If least squares -p (Hampson, 1986) is used, the transform
for each temporal frequency is posed as an inverse
problem,
= ,
approach modifies the least squares -p formulation to
include a resignature operator, r. A resignature operator is
simply the inverse of the designature operator, r=1/g; it is a
signature that has been stabilized for inversion. By
formulating the problem in this way, a -p representation of
the data is formed so that reverse transformation and
resignature is performed in a single operation and it
matches the input data optimally in a least squares sense.
The new formulation may be stated as
=
,
where
( ,
)= ( ,
) ( ,
)
r(n,m) are the resignature operators for the mth slowness
and the nth shot in the receiver gather at frequency f. The
resulting model, pd, derived by least squares inversion, is a
frequency slice of the -p model of the data free from
source directionality effects. Figure 1 shows how with
standard -p a spike reverse transforms to a linear event in
the receiver domain. With the modified formulation, the
event is convolved with the resignature operators, which
vary from shot-to-shot and slowness.
where d is the N-length recorded data vector in the common
receiver domain, p is the M-length model vector in the
slowness domain and L is the NM matrix containing the
reverse f-p transform operator. The elements of L are given
by,
( , )=
Where f is the temporal frequency, hn is the offset of the nth
trace in the receiver gather, and sm is the slowness of the mth
p-trace. The model, p, is found by solving the system of
equations in a least squares sense using any suitable
algorithm.
The directional designature operators, g(m), are applied to p
and the inverse transform, L, is applied to return the result
to the common receiver domain. This method assumes that
the common receiver gather does not contain any spatially
aliased energy.
Shot-to-shot directional designature
As we have indicated, the conventional approach is limited
in that the -p transform mixes energy from different shots.
As a result, in the -p domain it is not possible to
distinguish between energy from different shots. If the
source signatures should change from shot-to-shot, the
distinction between signatures would be lost. The new
© 2013 SEG
SEG Houston 2013 Annual Meeting
Figure 1 – With standard -p, a spike (right) reverse transforms to
a linear event (top left), but with the new formulation it is also
resignatured with the relevant operator for that shot and slowness
(bottom left)
Inverse transformation of pd using the standard inverse
transform, L, returns the directionally designatured data to
the common receiver domain.
Equivalent formulations may be made using different
model spaces such as the f-k domain and the scheme may
be extended to 3D.
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Shot-to-shot directional designature using near-field hydrophone data
In order to apply shot-to-shot directional designature, it is
necessary to determine directional far-field signatures for
every shot. This is generally only possible using near-field
hydrophone data. The near-field data need careful quality
control and calibration before inversion for the notional
signatures. For each shot, beam-forming produces the
directional signatures. As a result, each sail line has a
volume of directional signatures which we may think of in
the temporal frequency domain as g(f,p,shot).
difference relates to a pre-stack NRMS of up to 0.15 and
can be seen to increase after the gun switch.
The results represent a nice uplift for broad bandwidth data
and obvious benefits for 4D repeatability.
Data example
Shot-to-shot directional designature is illustrated using a
marine variable depth streamer (BroadSeis profile) dataset
from the Norwegian North Sea using a conventional, single
level, source. The source consisted of 28 G-Guns with a
total volume of 4980 cubic inches. The example comes
from the acquisition of a single sail line during which the
source was modified to compensate for gun failure. This
consisted of disabling one gun from a cluster and enabling
an adjacent gun. The source configuration highlighting the
modification can be seen in Figure 2.
Figure 3 – Far-field signature comparison before (black) and after
(red) gun switch. a) full far-field, b) zoom, c) amplitude spectra, d)
phase spectrum of the cross-correlation between far-field
signatures
Conclusions
Figure 2 – Source layout highlighting gun switch
Directional far-field signatures were derived for every shot
on the sail-line. An example comparison of far-field
signatures before and after the gun switch along with
spectral comparison can be seen in Figure 3. The
designature operators were designed, stabilised and
inverted to find resignature operators. Designature was
applied using global directional operators and with shot-toshot directional operators for comparison.
Receiver gathers before designature, after global directional
designature and after shot-to-shot directional designature
are shown in Figure 4. An improved handling of low
frequency energy may be seen using the shot-to-shot
directional designature method. A common channel after
receiver deghosting can be seen with global and shot-toshot directional designature in Figure 5. An improved
designature result may be observed using the shot-to-shot
method by better handling residual bubble energy. The
© 2013 SEG
SEG Houston 2013 Annual Meeting
Near-field hydrophone measurements may be used to
derive directional far-field signatures on a shot-to-shot
basis. While conventional directional designature methods
are limited to global corrections, the method outlined above
allows dynamic shot-to-shot directional far-field
designature. This is useful to gain the full benefit of
broadband seismic acquisition and has obvious benefits for
4D repeatability.
Acknowledgements
The authors thank CGG and Chevron for permission to
publish this work. In addition the authors acknowledge
useful discussions with Yuan Ni and Cheikh Niang. The
help of the processing team, in particular Vincent Durussel,
Del Cook, and Vera Romano is appreciated. Data
examples are courtesy of Chevron, Petoro AS, Esso Norge
AS, and Idemitsu Petroleum Norge.
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Shot-to-shot directional designature using near-field hydrophone data
Time, ms
c)
a)
Zoom
Time, ms
d)
b)
Freq, Hz
Figure 2 – Far-field signature comparison before (black) and after
(red) gun switch. a) full far-field, b) zoom, c) amplitude spectra, d)
phase spectrum of the cross-correlation between far-field
Figure 4 – Receiver gather a) input, b) after global directional designature, c) after shot-to-shot
signatures directional designature, d) difference (b)-c))
Figure 5 – Common channel (7km offset) with receiver deghosting a) input, b) after global directional designature, c) difference (b)-d)), d) after shot-to-shot
directional designature
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http://dx.doi.org/10.1190/segam2013-0550.1
EDITED REFERENCES
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© 2013 SEG
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