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AIRGUN SOURCE MODEL (AGORA): Its Application For Seismic Surveys Sound
Maps In The Dutch North Sea
H.Özkan Sertleka, Michael A. Ainslieb,c
a Behavioural Biology, Institute of Biology, University of Leiden, The Netherlands
bTNO, The Hague, The Netherlands
cISVR, University of Southampton, UK
Contact author:
H.Özkan Sertlek
Behavioural Biology, Institute of Biology Leiden, Leiden University, The Netherlands
osertlek@gmail.com
Abstract: Seismic exploration has the potential to make a significant contribution to the
soundscape of the North Sea. An airgun works by rapid release of air into water, forming a
large bubble, which then pulsates, radiating sound as the bubble successively compresses
and rarefies the surrounding water. An airgun array source signature model is described,
following Gilmore’s equation of motion, incorporating liquid compressibility, mass
diffusion, and thermal effects, and gas pressure laws. Predicted airgun signatures are
compared with measurements. The proposed source model, coupled with a propagation
model, can be used to generate anthropogenic and natural sound maps for. In this study we
focus specifically on sound maps associated with seismic surveys in the Dutch North Sea.
Keywords: Airgun array, source signature, sound mapping
INTRODUCTION
Sound maps can provide a useful insight about the distribution of sound over large regions.
Model predictions offer a practical means to fill gaps left where measurements are
unavailable [1]. Sound maps based on model predictions rely on the solution to two key
problems: the reliable modelling of sound propagation and of source characteristics. For
sound mapping, the solution of large scale broadband propagation problems is required. The
modelling of source properties requires an additional effort by understanding its working
principles and supporting the source level estimations by measurements. The sound
generated by airguns can be estimated by the solution of bubble motion problems by
including the effect of liquid compressibility, mass diffusion, thermal effects and
momentum. This results in a set of differential equations from various branches of physics.
In this paper, the calculation of airgun array signatures is investigated. A simulation tool
(AGORA) is developed. The calculated source signatures can be used to generate seismic
survey sound maps for anthropogenic and natural sources in the Dutch North Sea. The
model is an implementation of Ziolkowski’s approach [2,3] including mass and heat transfer
as described by Reference 4 and 5. It solves a differential equation system iteratively. First,
the bubble radius, bubble wall velocity, temperature and mass of the bubble are calculated.
These quantities are then used for the estimation of the radiated pressure from the airguns.
The signature of airgun array can be calculated as a sum of contributions from each single
airgun, with bubble interactions treated as a perturbation [3]. Results so obtained are
compared with measurements made available by the E&P Sound and Marine Life JIP
(henceforth abbreviated “JIP”). After the validation of the source model, the calculated
source signatures can be used as an input for seismic sound maps.
CALCULATION OF PRESSURE FROM SINGLE AIRGUN
The equation of motion can be represented by different equations from various approaches.
Gilmore’s equation which is based on the Kirkwood-Bethe approximation is investigated in
this paper [5],
where a is the bubble radius, is the bubble wall velocity, c is the sound speed in
the disturbed liquid, which can be calculated from the equation of state as
. Further, is the sound speed in water, and B and n are experimental
constants: n = 7 and B = 304 MPa for water. The parameter H is the specific enthalpy at the
bubble wall, which can be calculated similarly by using the equation of state [2] as
, where is the undisturbed hydrostatic
pressure , is the acceleration due to gravity, and is the depth
of airgun. The pressure is that at the bubble wall, which can be estimated using the
polytropic relation, ignoring the surface tension and the liquid viscosity, i.e.,
, where is the experimentally determined polytropic index. However, the
calculation of the pressure at bubble wall by a polytropic relation has several limitations for
nonlinear oscillations [6,7]. Instead of using the polytropic relation, can be written as
where is the surface tension and is the liquid’s shear
viscosity, is the specific gas constant, is the temperature of the air in the gas bubble,
is the mass of gas contained in the bubble and is the volume of the gas bubble. The
time derivative of H can be written
where
and
should be found to include mass and heat transfer [4,5]. The
derivative of volume can be simply written as
. The efficiency of the airgun
can be estimated by an empirical parameter , which characterises the remaining air in
the gun chamber after the airgun has fired[8]. The maximum value of the mass in the bubble
can be . The time derivative of mass can
where is the port-throttling constant which is related to the airgun-port area
(with dimension [L2]) , is the volume independent port-throttling constant (dimension
[L2-3
]), is a dimensionless power law exponent which is empirically determined from the
experiments, and , and are the pressure, mass and volume of remaining air
in the gun chamber. The time derivative of temperature
where
is the rate of heat transfer into the air bubble [4,5]. This rate can be written as
where is the temperature difference between the bubble and
surrounding water. The parameter is also an experimentally determined constant. The
buoyancy of the air bubbles changes the hydrostatic pressure because of the rise of the sea
surface. This affects the bubble period [5] and can be described by
. The
ideal gas law is not valid when the pressure in the gun chamber very high. For this situation,
a modified form of temperature can be used [4] to describe an effective temperature in the
air-gun chamber,
, where for air. The relevant
equations for the bubble motion, mass and heat transfer can be written as a differential
equation system, which can be solved by iterative methods [5,8] with the initial conditions:
, ,
and . The optimized empirical
parameters from reference [5] are used for the mass and heat transfer coefficients
.These
parameters should be selected carefully to increase the accuracy of the model results
depending on the environment and airgun properties. Then, the radiated pressure can be
expressed as a function of enthalpy, bubble wall velocity and bubble radius [4] as
. Where is the distance from the bubble centre to the
far field point. Pressure can be estimated by various approaches [2]. This equation is a first
order approximation, in which higher order terms in 1/r are neglected by assuming r is large.
Thus, this equation gives the pressure in the free field and is called the “notional signature”,
without the surface reflection, or “ghost” [2]. The reflections from sea surface and seabed
can be added from propagation theories separately. The sound pressure, including the
contribution from the surface ghost, is calculated using image theory as
where is the sea surface reflection coefficient, is the distance between gun and
receiver, is the distance between the surface image and receiver as shown by Fig.1, and
is time delay, calculated as
. The time domain source signature, , is
calculated as
where is the dip angle. For a single
airgun, the source signature only varies with dip () angle and does not vary with the
azimuth angle (). However, the airgun array pattern may also vary with azimuth angle
depending on the array geometry. The mean-square sound pressure spectral density level is
and energy source spectral density level is
where
is the Fourier transform of the
sound pressure and
is the frequency domain source
signature.
Figure 1. The contribution of surface ghost
SOURCE SIGNATURE OF AIRGUN ARRAYS
During a seismic survey, multiple airguns are used in an array to amplify the sound. Airguns
arrays have horizontal and vertical directivity patterns. The effect of interference with the
ghost is to direct the source energy more towards the seabed than in the horizontal direction.
Before modelling the directivity, the interaction between the different airguns should also
be taking into account. This can be done by adding a time dependent perturbation term to
the source signature of each individual airgun[3,5]. Hence, the bubble interactions can be
estimated by an effective hydrostatic pressure for the mth airgun as
where
and t’ is the retarded time. This equation affects
the enthalpy according to Tail’s equation. Thus, the bubble motion characteristic will be
changed. In the next steps of derivation, perturbed airgun signatures are used for the
calculation of directivity.
Figure 2. Vertical variation of energy source spectral density level at 0 degree (left) and
90 degree(right) azimuth angles. The frequency axis varies from 0 Hz to 150 Hz.
For each individual airgun signature, the time delays between airgun location and centre
point of array (described as origin point x = 0, y = 0, z = 0) are calculated. The distances
between the gun and the ghosts are
and , where
is a unit vector, and and are the azimuth and grazing
angles
. The positions of airguns and their surface images are
and . The time delays are summed to obtain the
frequency domain pressure with 3D directivity as [9]
where is the number of airguns in the airgun array, and is the frequency domain
notional source signature of the mth airgun. The exponential phase terms represent the time
delays in the horizontal plane In Figure 2, the vertical variation of energy source spectral
density level is shown at different dip angles.
COMPARISONS
Some comparisons are done for JIP measurements for Svein Vaage broadband airgun study
measurements. One selected as representative of the 30 available airgun shots is used in
these comparisons. The positions of receivers and airgun are shown in Figure 3. Three
receiver locations are (0 m, 0 m, 30 m), (0 m, 0 m, 100 m) and (10.8 m, 9.8 m, 15 m). The
airgun location is nominally (0 m, 0 m, 6 m). In the original measurement set-up, there are
many receiver points. However, these three positions are chosen for the comparisons. The
model is sensitive to small changes in the source depth. To estimate the location of the
source depth during the shot, the nulls in Lloyd mirror pattern are used as
Figure 3. The geometry of the measurements
In Figure 4, the comparisons between AGORA and JIP measurements are shown for
and firing pressure .
Figure 4. Comparisons of sound pressure (left panels) and mean-square sound pressure
spectral density level (right panels) of airgun at different distances
(the distances between airgun and receiver location is 16.9 m, 23.6 m and 93.6 m) and
elevations. The source depth is 6.36 m and the firing pressure is 13.8 MPa (2000 psi).
050 100 150 200 250 300
-15
-10
-5
0
5
10
15
Time [ms]
Pressure [kPa]
D1=16.95 m,horizontal distance=14.58 m,zr=15 m
Measurement
AGORA
0200 400 600 800 1000
80
100
120
140
160
Frequency (Hz)
Lf (dB re 1Pa2 s/ Hz )
D1=16.9508 m, horizontal distance=14.5836 m, zr=15m
Measurement
AGORA
050 100 150 200 250 300
-10
0
10
Time [ms]
Pressure [kPa]
D1=16.9508 m, horizontal distance=14.5836 m, zr=15m
Measurement
AGORA
0200 400 600 800 1000
100
110
120
130
140
150
160
170
Frequency (Hz)
Lf (dB re 1Pa2 s/ Hz )
D1=16.9508 m, horizontal distance=14.5836 m, zr=15m
Measurement
AGORA
050 100 150 200 250 300
-15
-10
-5
0
5
10
15
Time [ms]
Pressure [kPa]
D1=23.64 m, horizontal distance=0 m, zr=30m
Measurement
AGORA
0200 400 600 800 1000
80
100
120
140
160
Frequency (Hz)
Lf (dB re 1Pa2 s/ Hz )
D1=23.64 m, horizontal distance=0 m, zr=30m
Measurement
AGORA
050 100 150 200 250 300
-10
-5
0
5
10
Time [ms]
Pressure [kPa]
D1=23.64 m, horizontal distance=0 m, zr=30m
Measurement
AGORA
0200 400 600 800 1000
105
115
125
135
145
155
165
175
Frequency (Hz)
Lf (dB re 1Pa2 s/ Hz )
D1=23.64 m, horizontal distance=0 m, zr=30m
Measurement
AGORA
050 100 150 200 250 300
-3
2
3
Time [ms]
Pressure [kPa]
D1=93.64 m, horizontal distance=0 m, zr=100m
Measurement
AGORA
0200 400 600 800 1000
90
100
110
120
130
140
150
160
Frequency (Hz)
Lf (dB re 1Pa2 s/ Hz )
D1=93.64 m,horizontal distance=0 m,zr=100m
Measurement
AGORA
050 100 150 200 250 300
-3
2
3
Time [ms]
Pressure [kPa]
D1=93.64 m, horizontal distance=0 m, zr=100m
Measurement
AGORA
0200 400 600 800 1000
90
100
110
120
130
140
150
160
Frequency (Hz)
Lf (dB re 1Pa2 s/ Hz )
D1=93.64 m,horizontal distance=0 m,zr=100m
Measurement
AGORA
On the other hand, the source signatures can be calculated from different long ranges. R0
denotes the distance between dipole centre (0 m, 0 m ,0 m) and measurement location. For
these calculations, the measurements at (0 m, 0 m, 100 m) and (10.8 m, 9.8 m, 15 m)
coordinates are used. The first measurement is at 100 m beneath of the airgun with 0 degree
dip angle. The distance of second measurement at R0=20.9 m with dip angle.
The measurement and calculated results are shown in Figure 5.
Figure 5. The comparisons for the source signature and energy source spectral density
level . The measured and calculated source signatures for R0=20.92 m (dip angle is
54.4 degree) and R0=100 m (dip angle is 0 degree)
The empirical calibration coefficients of mass and heat transfer are not optimized for this
dataset. Thus, better agreement may be obtained by optimizing these parameters for JIP
dataset. AGORA assumes that the surface is flat. Realistically, the sea surface is not flat,
resulting in rough surface scattering. All these uncertainties can lead to differences between
the model and measurement results. By using calculated signatures, annually averaged
seismic survey maps of the Dutch North Sea are generated at the center frequencies of 1/3
octave bands. These maps are shown for 3D seismic surveys of 2007 in Fig. 6. Propagation
loss is calculated by a hybrid method based on normal modes and flux theory [10].
Figure 6. Annually averaged seismic survey sound maps of the North Sea for 2007 at the
center frequencies of 1/3 octave band from 30 Hz to 3 kHz. The receiver depth is 1 m. The
green lines show the Dutch coastline and the Dutch EEZ outline
050 100 150 200 250
-250
-150
-50
50
150
250
Retarded Time (t-r/c) [ms]
Source Signature [k*Pa*m]
Range=100 m
Measurement
AGORA
0200 400 600 800 1000
120
140
160
180
200
Frequency (Hz)
SLE (dB re 1Pa2m2 s/ Hz )
Range=100 m
Measurement
AGORA
050 100 150 200 250
-250
-150
-50
50
150
250
Retarded Time (t-r/c) [ms]
Source Signature [k*Pa*m]
Range=100 m
Measurement
AGORA
0200 400 600 800 1000
120
140
160
180
200
Frequency (Hz)
SLE (dB re 1Pa2m2 s/ Hz )
Range=100 m
Measurement
AGORA
050 100 150 200 250
-250
-150
-50
50
150
250
Retarded Time (t-r/c) [ms]
Source Signature [kPa*m]
Range=20.9208 m
Measurement
AGORA
0200 400 600 800 1000
120
140
160
180
200
Frequency (Hz)
SLE (dB re 1Pa2m2 s/ Hz )
Range=20.9208 m
Measurement
AGORA
050 100 150 200 250
-250
-150
-50
50
150
250
Retarded Time (t-r/c) [ms]
Source Signature [kPa*m]
Range=20.9208 m
Measurement
AGORA
0200 400 600 800 1000
120
140
160
180
200
Frequency (Hz)
SLE (dB re 1Pa2m2 s/ Hz )
Range=20.9208 m
Measurement
AGORA
0100 200
400
500
600
700
800
y distance [km]
90 95 100 105 110 115 120 125 130 135
63 Hz
125 Hz
1 kHz
30 Hz to
3 kHz
CONCLUSIONS
Calculation of airgun source signatures and their comparisons with E&P Sound and Marine
Life JIP measurements are shown in this paper. A Matlab script (AGORA) is developed to
solve the set of differential equations for the bubble motion and visualize airgun array
signatures. Good agreement is obtained between the JIP measurements and the airgun model
described in the present paper. The choice of exact source and receiver locations,
environmental parameters, mass and heat transfer coefficients can affect the accuracy of the
calculated results. Thus, these parameters should be selected carefully. After these
validation tests, the calculated source energy spectral densities can be used for the
calculation of seismic survey sound maps.
ACKNOWLEDGEMENTS
The authors thank Alex MacGillivray for his willingness to answer our questions about his
MSc thesis during the development of this model, and Robert Laws for many discussions
about airgun source modelling. The measurements of single airgun data are supplied by the
Joint Industry Programme on Sound and Marine Life. H. Özkan Sertlek’s PhD is supported
by NWO-ZKO grant ‘Effects of underwater noise on fish and marine mammals in the North
Sea’.
REFERENCES
[1] D Mennitt, K Sherrill, K Fristrup, The Journal of the Acoustical Society of America 135
(5), 2746-2764
[2] Ziolkowski, A., 1970, A method for calculating the output pressure waveform from an
air-gun: Geophys. J. R. Astr. Soc., 21, 137 – 161.
[3] Ziolkowski, A., .Parks, G., Hatton L., and Haugland, T.,1982, The signature of an air-
gun array: Computation from near-field measurements including interactions:
Geophysics, 47(10), 1413- 1421.
[4] Laws R.M. et al.,1990,Computer modeling of clustered air guns: First Break, 18(9),
331–338.
[5] MacGillivray A.O.,2006,An acoustic study of seismic airgun noise in Queen Charlotte
Basin, MSc Thesis.
[6] Prosperetti A.,1984,Bubble phenomena in sound fields:Part one,Ultrasonics (22),69-77
[7] Prosperetti A. et al,1988,Nonlinear bubble dynamics,J. Acoust.Soc.Am.83(2),502-514
[8] LI Guo-Fa et al,2010, Modeling air gun signatures in marine seismic exploration
considering multiple physical factors, Applied Geophysics, Vol.7, No.2 , P. 158 – 165
[9] Duren R E, 1988, A theory for marine source arrays, Geophysics 53 650–8
[10] Sertlek H.O. and Ainslie M.A., Range dependent propagation equations and
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