2. China University of Petroleum(East China), School of Geosciences, Qingdao 266580, Shandong, China;
3. Earthquake Agency of Chuxiong Prefecture, Yunnan Province, Chuxiong 675000, China;
4. 750 Test Range, China Shipbuilding Industry Company Limited, Kunming 650051, China;
5. Department of Numerical Control Application Technology, Chuxiong Technician College, Chuxiong 675000, Yunnan, China;
6. Western Yunnan Earthquake Prediction Study Area, China Earthquake Administration, Dali 671000, Yunnan, China
In the process of the active seismic source detection (Chen Yong et al., 2005; Wang Bin et al., 2015; Wang Baoshan et al., 2016), the airgun seismic sources need to be repeatedly excited to generate seismic waves many times over a long time. After the airgun is excited, the high-pressure air transmits the energy into the water, and then the water transmits the energy to the bottom to generate the seismic waves. Both of these transfer processes consume energy and cannot be transmitted 100%. In the assessment of the explosive energy radiation in water and its relationship to earthquakes, there have been some studies on the relationship between the explosive source equivalent and the earthquake magnitude (Savage B. et al., 2001; Song Pu et al., 2008; Yang Zhen et al., 2015), but there are fewer studies on energy radiation characteristics of the airgun seismic sources excited in the land reservoirs. Ronen S., (2002) assumes that the shock waves and the bubble pulsations are all the spherical waves, and calculates the energy of the shock wave and the bubble pulsation for the underwater wavelet signals as observed by Caldwell J. et al., (2000).
The airgun is a pulse seismic source, of which the excitation mechanism is similar to the explosion mechanism of the explosives in water. The explosion of explosives in water has some important applications in the military and other fields. Some theoretical and experimental studies have been carried out on it (Wang Bin et al., 2008; Zhang Aman et al., 2008). Cole R. H., (1948) proposed an empirical formula for the pulsation period and maximum radius of the bubbles of the TNT explosives in the water. Zhi Binwei et al. (2009) calculates the bubble period and the radius for the explosion in water of the 1217.6kg TNT equivalent explosive using the empirical formula, which is similar to Cole, PAMFLOW software, and the bubble calculation program based on the JWL state equation. Ma Kun et al. (2015) conducted experiments on the 0.125g, 0.5g, and 1g TNT equivalent explosives balls at different water depths, and corrected the Cole R. H.'s empirical formula coefficient(1948). These studies show that Cole R.H.'s empirical formula (1948) is applicable to the explosions with the TNT equivalent explosives ranging from gram to thousands of kilogram. In addition, there are also some simulation studies which use the AUTODYN, DYTRAN, ABAQUS and other commercial software or use self-programming programs to simulate the explosion of explosives in water (Zhang Zhijiang et al., 2007; Jia Xianzhen et al., 2015). In comparison with the numerical simulation, which has a large amount of computation and a lot of computation time, the empirical formulas summarized in the experiment have the advantages of small computation, shorter calculation time, and is convenient for the analysis of regularities. This paper synthesizes the theory and the empirical formula of explosion in the water, and studies the law of energy radiation of the airgun seismic sources excited in water, in order to provide some references for the theoretical research and the optimal use of the active seismic source detection.
1 METHOD AND PRINCIPLEThe data obtained in the excitation experiments of airgun seismic sources relating to the energy calculation include the air supply pressure, the shock wave amplitude, the first bubble amplitude, and the cycle of the first bubble. The airgun and the explosive excitation in water are instantaneous expansion sources. The calculation method of the explosive explosion in water can be used to calculate the excitation characteristics of the airgun seismic source. Most of the formulas for the explosive explosions in water are the empirical formulas. Therefore, this paper focuses on analyzing the law of the data changes.
The power of the airgun seismic source is derived from high-pressure air. The initial energy of the airgun radiation can be calculated based on the volume and pressure of the high-pressure air (Ronen S., 2002), namely:
$ {E_0} = P \cdot V{\rm{ln}}\left({P/{P_{{\rm{atm}}}}} \right) $ | (1) |
where, E_{0} is the released energy (J), V is the volume of the high-pressure air (inch^{3}), P is the working pressure (psi) of the airgun, and P_{atm} is the environmental pressure (psi) on the water surface. In addition, the units of volume inch^{3} and pressure psi can be converted to m^{3} and Pa.
E_{0} is the total energy emitted by the airgun seismic source to the water, including the shock wave energy, the bubble energy, and the thermal energy loss during the radiation process. The unit of E_{0} is J, and the explosive heat of the TNT explosives is 4.2×10^{6}J/kg. The radiation energy of the airgun can be converted to the TNT equivalent (kg).
$ {W_0} = {E_0}/4.2 \times {10^6} $ | (2) |
Let the energy radiation of the airgun seismic source in water be E, then the energy radiation efficiency η of the airgun seismic source in water is as:
$ \eta = \frac{E}{{{E_0}}} \times 100\% $ | (3) |
The directionality of the shock wave and the bubble pulse wave excited by the airgun seismic source in water is ignored. Both waves are assumed as spherical waves. According to the correlation theory of acoustic energy, the radiation energy E_{P} of the airgun seismic source in water can be calculated based on the pressure P and the fluctuation period T received by the hydrophone with the distance R from the airgun seismic source.
$ {E_p} = 4\pi {R^2} \cdot \frac{{{P^2}}}{{\rho C}}{\rm{ }} \cdot T $ | (4) |
where, C is the sound speed in water (m/s), and 1460m/s is taken at room temperature, ρ is the water density (kg/m^{3}), and 1000kg/m^{3} is taken.
The shock wave pressure P_{s} and periodic T_{s} are substituted into formula (4) to calculate the shock wave energy E_{Ps}, and substituted into formula (3) to calculate the energy radiation efficiency η_{s} of the shock wave energy. The radiation bubble amplitude p_{b} and the periodic T_{b} of the airgun seismic source are substituted into formula (4) to calculate the bubble energy E_{Pb}.The energy radiation efficiency η_{b} of the bubble energy can be calculated by substituting the bubble energy into formula (3). The sum of these two radiation efficiency η_{sb} is the energy radiation efficiency of the airgun seismic source in water. The actual water energy radiation of the airgun seismic source is directional, so, this energy radiation efficiency calculation value is larger.
The integral formula for the shock wave energy E_{si} of the explosion in water (Zhou Lin et al., 2008) is as:
$ {E_{{\rm{si}}}} = \frac{{4\pi {R^2}}}{{\rho C}}\int_0^{6.7\theta } {{P^2}\left(t \right){\rm{d}}t} $ | (5) |
where, R is the distance from the measurement point to the explosion center (m), P(t) is the shock wave pressure (Pa) with the distance R from the explosion center at the momentt, C is the sound speed in water (m/s), θ is the time decay constant (s), which is the decay time for the pressure peak from the shock wave peak P_{m} to P_{m}/e.
The empirical formula of the bubble pulsation period T_{b} and the maximum radius R_{max} for the TNT explosives exploding underwater in infinite waters (Cole R.H., 1948) is as:
$ {T_{\rm{b}}} = 2.064\frac{{W_1^{1/3}}}{{{{\left({h + 10} \right)}^{5/6}}}} $ | (6) |
$ {R_{{\rm{max}}}} = 3.3825{\left({\frac{{{W_1}}}{{h + 10}}} \right)^{1/3}} $ | (7) |
where, W_{1} is the equivalent charge, which is TNT equivalent (kg), h (m) is the depth of the explosion in water, h is the depth of the airgun in this paper.
According to the pulsation period T_{b} of the first bubble of the airgun seismic source, the TNT equivalent W_{1} of the airgun seismic source can be obtained from formula (8):
$ {W_1} = {\left[ {\frac{{{T_{\rm{b}}}{{\left({h + 10} \right)}^{5/6}}}}{{2.064}}} \right]^3} $ | (8) |
W_{1} and W_{0} are the initial TNT equivalents of the airgun seismic source and should theoretically be equal. Due to different material properties, the initial energy required for the airgun seismic source to produce the same frequency of explosion pulsation in water as the TNT explosives is different. This reflects the energy radiation efficiency of the airgun seismic source relative to the TNT explosives.
Let u be the bubble frequency coefficient of the high-pressure air for the airgun seismic source in water, of which the value is the ratio of W_{1} calculated by the wavelet of the airgun seismic source in water to the initial energy of the high-pressure air W_{0}. It reflects the energy radiation efficiency of the high-pressure air energy released into the water by the airgun seismic source, which changes with the change of the bubble cycle and frequency. The larger u, the higher the energy radiation efficiency of the airgun seismic source in water.
$ u = {W_1}/{W_0} $ | (9) |
The larger the pulsating bubbles in water, the greater the energy. The measurement of the bubble radius is more difficult in the actual engineering application of the airgun seismic source. Due to different material properties, it is roughly estimated that the airgun seismic source of the same TNT equivalent is smaller than the radius of the explosive pulsating bubble produced by the TNT explosives in water.
Let the initial TNT equivalent of the airgun seismic source be W_{1}, increasing the bubble radius coefficient α (0 < α < 1), then the maximum pulsating radius R_{max1} of the airgun seismic source bubble is as:
$ {R_{{\rm{max1}}}} = 3.3825{\left({\frac{{\alpha {W_1}}}{{h + 10}}} \right)^{1/3}} $ | (10) |
Let the initial TNT equivalent of the airgun seismic source be W_{0}, then the maximum pulsating radius R_{max0} of the airgun seismic source bubble is as:
$ {R_{{\rm{max0}}}} = 3.3825{\left({\frac{{\alpha {W_0}}}{{h + 10}}} \right)^{1/3}} $ | (11) |
The hydrophone observation experiment for the excitation wavelet of the airgun seismic source is carried out at the airgun seismic source base (Fig. 1) in the Dayindian Reservoir of Binchuan County, Dali Bai Nationality Autonomous Prefecture, Yunnan Province. A square floating platform has 4 airguns suspended below the center of each side at the depth of 10m. The tower crane on the shore is used to transport the experimental equipment and equipment such as airguns. American Bolt's Bolt 1500LL airgun is used (Fig. 2), of which the air chamber capacity is about 0.0328m^{3}, and the air chamber pressure adjustment range is about 6MPa to 15MPa. The wavelet observation in water uses the B & K8105 hydrophone of Danish B & K Company. The AD conversion uses the NI USB6251 collection card of American NI company.
The water body surge within a range of a few meters after the excitation of airgun is relatively large, so a linear test stand about 18m long and a semi-circular test stand with a diameter of 6m are designed and manufactured, and are sunk to the same depth as the airgun (Fig. 3). The hydrophone is installed on the test stand for the experiment. The two test stands are not used at the same time. The restraint of the test stand can improve the accuracy of the hydrophone relative to the airgun, and can also reduce the hydrophone movement when the water body surges. The hydrophone data for calculating the energy radiation efficiency is a short-term signal generated by the airgun. When the signal is received, the water body is less turbulent and can be considered as the hydrophone staying still.
Experiments were carried out with different air supply pressures and different airgun numbers. The data sampling rate is 100kHz. The axis of the airgun body is on the horizontal plane. The data of three measurement points are selected to calculate the energy radiation characteristics. The measuring point 1 is located at 3m directly below the airgun and the hydrophone is installed on the semi-circular test stand. The measurement point 1 and the measurement point 2 are in the same vertical surface. The measuring point 2 is located at 3m on the vertical line of the airgun axis in the horizontal plane and the hydrophone is installed on the semi-circular test stand. The measurement point 1 and the measurement point 2 are in the same vertical surface. The measuring point 3 is located at 3m of the extension line of the airgun axis and the hydrophone is installed on the linear test stand.
3 CALCULATIONS OF UNDERWATER ENERGY RADIATION CHARACTERISTICS OF AIRGUN SOURCESFig. 4 is the seismic wavelet observed at the measurement point 1 which is 3m below the airgun by the B & K8105 hydrophone when one airgun is excited with 15MPa and 6MPa air supply pressure. The air chamber capacity of an airgun is 0.0328m^{3}, and let the bubble radius coefficient α be 0.25. The calculated results of the energy radiation characteristics are shown in Table 1. As shown in Table 1, the pulse duration, bubble period, and amplitude in the calculation process are automatically extracted and calculated by the program to avoid errors caused by manually reading of waveform data. When the air supply pressure is 15MPa, the airgun seismic source excitation energy is 253, 743J, which is equivalent to a M0.25 earthquake. When the air supply pressure is 6MPa, the airgun seismic source excitation energy is 834, 790J, which is equivalent to a M0.05 earthquake. When the air supply pressure is 15MPa and 6MPa, the E_{Ps} calculated by the spherical wave hypothesis is 3.6 and 17.0 times the E_{si} calculated by the integral, which indicates that the energy radiation efficiency calculated based on E_{Ps} and E_{Pb} is the upper limit of the energy radiation efficiency of the airgun seismic source in water (Ronen S., 2002).The bubble radius R_{max1} is slightly larger than R_{max0}. R_{max1} is calculated based on the observation data in water and can better reflect the characteristics in water. Therefore, the analysis mainly focuses on R_{max1} and let R_{max} be R_{max1}.
Fig. 5 is the energy radiation efficiency results for different air supply pressures at the measurement point 1 and the measurement point 2 when one airgun is excited. As shown in Fig. 5: ① The radiation efficiency of bubble energy increases with the increase of the air supply pressure. ② The radiation efficiency of the shock wave energy increases with the increase of the air supply pressure and then decreases. ③ The vertical downward energy radiation efficiency of the airgun seismic source is higher than the energy radiation efficiency in the horizontal direction. ④ As the air supply pressure increases, the bubble energy radiation efficiency will exceed the shock wave energy radiation efficiency. ⑤ The vertical downward energy radiation efficiency of the airgun seismic source is 9.4% when the air supply pressure is 15MPa.
The bubble pulse excited by the airgun is a damping oscillation with multiple cycles and has a long duration. The radiation efficiency increases with the increase of the air supply pressure. The vertical downward energy radiation efficiency is higher than the energy radiation efficiency on the horizontal direction. Therefore, the main energy that causes the earthquake after the airgun is excited is the vertical downward bubble energy.
The airgun source is a kind of jet sound source, but the acoustic efficiency calculation results that can be referred to are rarely reported. Presently, there is only the acoustic efficiency data of about 25% of airgun array seismic source in water, calculated roughly by Ronen S., (2002). Zhou Fan et al.(2012) calculated the sound efficiency of the rocket engine jet noise in air as 0.51% through experimental data. The acoustic efficiency in water is usually greater than the acoustic efficiency in air, and the bubble pulsation excited by airguns in water is a more efficient energy radiation process. Therefore, the maximum sound efficiency of 9.4% of airgun seismic source in water calculated in this paper is large, but it is reasonable.
Fig. 6 is the energy radiation efficiency results of different air supply pressures and airgun numbers at measurement point 3. As shown in Fig. 6: ① The bubble energy and shock wave energy radiation efficiency of one airgun increases first and then decreases as the supply pressure increases. ② The radiation efficiency of the shock wave energy is greater than that of the bubble energy. ③ The energy radiation efficiency of one airgun seismic source is about 1.9%.
The four airguns are on the four sides of the 7m-long square. The hydrophone is located on one side, and the transmission distance of the seismic source wavelet generated by the remaining airguns is not 3m, and the superposition of the four airguns at this point is complex. Therefore, this paper mainly analyzes the energy radiation characteristics of one airgun.
Fig. 7 is the maximum radius calculation results of the first expansion bubble at measurement point 3 with different air supply pressures and airgun numbers. Among them, two airguns and four airguns have equivalent bubble radii. That is, the combined effect of multiple bubbles is used as the calculation result of one bubble. The larger the bubble radius, the greater the energy. As shown in Fig. 7: ① the bubble radius increases with the increase of the air supply pressure; ② when the air supply pressure is less than 12MPa, the bubble radius of one airgun and two airguns is similar, and the bubble radius of four guns is significantly larger than that of one airgun and two airguns, indicating that the airgun seismic source pressure wave with a horizontal propagation distance of 8m is approximately independent of each other and the effect of each other is smaller and the effect of superposition enhancement is weak. After the air supply pressure is greater than 12MPa, the two airguns have a larger bubble radius than one airgun, and the difference increases with the increase of the air pressure. In addition, the distance between the hydrophone and the nearest two airguns is about 3-5m in a four airguns excitation. Therefore, the pressure wave of the airgun seismic source with a horizontal propagation distance of 5m can be superimposed and enhanced; ③ the larger the air supply pressure of the airgun, the farther the pressure wave of the airgun seismic source is superimposed, and more obvious the superposition effect at the same distance.
The "Vertical Plane" and "Horizontal Plane" curves of Fig. 8 are calculated as the maximum radius of the first expansion bubbles of the B & K8105 hydrophone data at the measurement point 1 and the measurement point 2, respectively. As shown in Fig. 8, these two curves basically coincide. The maximum radius of the first expansion bubble is determined by the airgun depth h and W_{1}, and W_{1} represents the energy emitted by the airgun into the water. The depth of the airgun remained unchanged during the experiment. Therefore, the rough coincidence of the two curves indicates that the horizontal direction of the airgun with different air supply pressures is basically the same as the vertical downward energy radiation.
Fig. 9 is a photo showing the airgun seismic source excitation process in water. The depth of the airgun is 10m, and the chain connecting the airgun is about 2m. The chain is suspended under a square shelf with a side length of about 7m. The camera is placed at a depth of 7m in water. Obviously, the camera is about 1m from the shelf and about 3m from the airgun. The width of the steel facing the camera is about 0.1m. The excitation time of Fig. 9 is about the maximum radius of the first expansion bubble in water, and the maximum radius of the bubble corresponds to the width of the three shelves. Therefore, according to the proportional relationship of the triangle, the radius of the bubble is 9 times the width of the shelf, that is 9×0.1=0.9m, which is closer to the previous calculation of 0.89m. This is the reason why let the bubble radius coefficient α be 0.25 in this paper.
Fig. 10 (a) is the calculation result of the bubble frequency coefficient for different air supply pressures and airgun numbers at measuring point 3. As shown in Fig. 10 (a), the bubble frequency coefficient of one airgun is significantly greater than that of two airguns and four airguns. This paper mainly analyzes the frequency coefficient of bubbles of one gun. Fig. 10 (b) is the calculation result of the bubble frequency coefficient of one airgun for different air supply pressure at three measurement points. As shown in Fig. 10 (b), the values of the three curves are close, and the mean of the measurement points 1, 2 and 3 are 2.31, 2.42 and 2.37, respectively. The mean of these three curves is 2.36. Therefore, let the bubble frequency coefficient of the high-pressure air emitted from the airgun seismic source in the water be 2.36, that is, the airgun seismic source of 1kg TNT equivalent is the same as the bubble pulse frequency of the explosion in water produced by 2.36kg of TNT explosives.
At present, the airgun seismic source wavelet calculation is mostly a theoretical simulation based on the theory of the free bubble oscillation, from which the bubble pulsation cycle excited by the airgun can be obtained. However, there is little research on the calculation of airgun excitation bubble radius, and there are not many empirical formulas for calculating airgun excitation bubble pulsation period and maximum radius.
For example, Chen Haolin et al. (2003) discussed several major international airgun single gun theoretical models based on the theory of the free bubble oscillation and proposed a simulation method for airgun waves. Li Xuxuan et al. (2012) use Nucleus software developed by PGS Company based on the bubble free oscillation theory to perform numerical simulations of airgun source waves.
Based on the experimental data, the empirical formulas for calculating the pulsation period and maximum radius of the airgun excitation bubble are obtained by modifying the empirical formulas of explosive explosion in water. That is, the bubble frequency coefficient 2.36 and the bubble radius coefficient 0.25 are added to the empirical formula of the explosive explosion in water. The high-pressure air TNT equivalent of the airgun seismic source is taken as the input parameter, the coefficient for the bubble radius R_{max} is 0.25×2.36=0.59. Therefore, the empirical formulas of the bubble pulsation period T_{b} and the maximum radius R_{max} of one airgun seismic source excited in the water are as below:
$ {T_{\rm{b}}} = 2.064\frac{{{{\left({2.36{W_0}} \right)}^{1/3}}}}{{{{\left({h + 10} \right)}^{5/6}}}} $ | (12) |
$ {R_{{\rm{max}}}} = 3.3825{\left({\frac{{0.59{W_0}}}{{h + 10}}} \right)^{1/3}} $ | (13) |
Taking an airgun with an air supply pressure of 15MPa at a depth of 10m as an example, the bubble period calculated from the hydrophone wavelet data is 0.1926s. The radius of the bubble calculated from the underwater camera data is approximately 0.9m. The high-pressure air TNT equivalent of the airgun is 0.6kg. Then, the bubble period of 0.1909s and the bubble radius of 0.88m can be calculated from formula (12) and formula (13).
4 CONCLUSIONThe energy radiation efficiency and the bubble radius of the high-pressure air released by the airgun seismic source in water are calculated based on its wavelet data in water. By adding the bubble frequency coefficient and bubble radius coefficient to the empirical formulas of the explosive explosion in water, the empirical formulas for calculating the period and maximum radius of the airgun seismic source excitation bubble pulsation in water are obtained. The results show that: ① The vertical downward energy radiation efficiency is higher than that of horizontal direction. ② The main energy that causes the earthquake after the airgun excitation is the vertical downward bubble energy. ③ The shock wave energy radiation efficiency increases first and then decreases with the increase of the air supply pressure. ④ The vertical downward bubble energy radiation efficiency increases with the increase of the air supply pressure. With the increase of the air supply pressure, the vertical downward bubble energy radiation efficiency will exceed the radiation efficiency of the shock wave energy. ⑤ The vertical energy radiation efficiency of the airgun seismic source is 9.4% when the air supply pressure is 15MPa. ⑥ The energy conversion efficiency is different in all directions, which indicates that the shock wave and the bubble pulse wave of the airgun seismic source radiation are not spherical waves. ⑦ The higher of the air supply pressure, the farther of the distance for the superposition and enhancement of the pressure wave of the airgun seismic source, the more obvious the superposition effect at the same distance. ⑧ The horizontal and vertical direction energy radiation of the airgun with different air supply pressures is same basically. The energy radiation of the air gun with different air supply pressures is basically the same in horizontal direction and vertical downward direction. The research results of this paper can provide reference for the theoretical research, optimal use, energy saving and emission reduction, as well as seismic protection of the structures in water.
ACKNOWLEDGEMENTSWe are grateful to Institute of Geophysics, CEA, Yunnan Earthquake Agency, Western Yunnan Earthquake Prediction Study Area, CEA for their strong support and help to this study. We would also like to thank our colleagues Wang Yongtao, Ye Beng, Song Zhifeng, Lu Xiaolin, Mao Depei, Pu Weisheng and Dong Juan for their help.
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