Earthquake Research in China  2019, Vol. 33 Issue (4): 573-583     DOI: 10.19743/j.cnki.0891-4176.201904003
A Comparative Study on the Excitation of Large Volume Airgun Source with Different Combinations in Hutubi, Xinjiang, China
SU Jinbo1, WANG Qiong1, CHEN Hao2, WEI Yunyun1, ZHANG Wenxiu1, WANG Haitao3     
1. Earthquake Agency of Xinjiang Uygur Autonomous Region, Urumqi 830011, China;
2. The First Monitoring and Application Center, CEA, Tianjin 300180, China;
3. China Earthquake Networks Center, Beijing 100045, China
Abstract: In order to study the excitation of large-volume airgun source with different combinations in Hutubi,Xinjiang,China,we conducted a targeted experiment. The method of time-frequency analysis is used to study the signals recorded by a seismometer on the shore of the excited pool,and it is concluded that different gun combinations will lead to different frequency of bubble pulse signals. Besides,linear combination method is used to analyze the signal-to-noise ratios of signals excited by different gun combinations which was recorded by seismic stations around the airgun source. In order to improve the signal-to-noise ratios,it is more effective to increase the activation energy (the number of excited guns at the same time) than to stack the excited signals with smaller energy repeatedly.
Key words: Airgun source     Different gun combinations     Energy characteristic     Frequency characteristic     Signal-to-noise ratio    

INTRODUCTION

Airgun source, characterized by advantages of high energy, good repeatability, energy conservation and environmental protection, is the most widely used artificial seismic source in offshore oil exploration (Chen Yong et al., 2007; Wang Baoshan et al., 2016; Chen Yong et al., 2017). In recent years, seismologists have attempted to use large volume airgun source in inland areas to study the structure and variation of regional underground medium (Wang Baoshan et al., 2016). Since 2011, a number of large-volume airgun source signal transmitters have been built in Binchuan in Yunnan, Hutubi in Xinjiang and in Zhangye in Gansu to dynamically monitor the changes in the properties of regional underground medium (Wei Bin et al., 2016; Zhang Yuansheng et al., 2016; Wang Bin et al., 2016).

In order to detect the structure of deep medium, large volume airgun source is utilized in inland areas. Due to its low-frequency signals and high repeatability, non-modulated airgun array is mostly used for activation test. In theory, the energy and frequency components of signals excited by airgun are determined by the number of airguns in the airgun array. The Hutubi large volume airgun source is equipped with 6 airguns with a volume of 2, 000in3 and an artificially inverted cone-like water body activation pool (100m-diameter upper surface, 15m-diameter lower surface, and 15m deep). The main frequency of simultaneous activation of the non-modulated airgun array of 6 airguns is 2-6Hz, which generates energy equivalent to a natural earthquake of magnitude 0.9 (Yang Wei et al., 2013; Su Jinbo et al., 2016; Wei Bin et al., 2016). The question to be addressed is how the frequency components and energy release of airgun signals change with the quantity variation of airgun array. Thus, we conducted an experiment with different airgun numbers to analyze and further solve this problem using waveform data recorded by seismic stations.

1 THE EXPERIMENT AND DATA INTRODUCTION

Aiming at the problem mentioned above, a targeted experiment excited by airgun source was conducted from January 8, 2015 to January 14, 2015 in Hutubi, Xinjiang. Combinations of different number of airguns were excited continuously in a lower noise environment from night to early morning (Table 1).

Table 1 Experimental details

A total of 6 groups of experiments were conducted within 7 days, starting from all 6 guns being implemented, the number of guns was gradually decreased until the last single gun was fired. Each group of experiment is controlled to be excited when the pressure in each airgun is 15MPa. The excited times of activation of 6 group experiments are showed in Table 1.

Numerous seismic stations have been built around the Hutubi airgun source, forming a small seismic monitoring network (hereinafter referred to as the Hutubi seismic network). Some Xinjiang Digital Seismic Network stations around the airgun source can also receive signals, which can be used as research samples. In this study, the observed data from 11 seismic stations within 160km of the Hutubi airgun source are selected, among which integrated Guralp CMG-6TD short-period seismometer is used in Hutubi seismic network station, and BBVS-60 seismometer and EDAS_24IP data acquisition are used in Xinjiang Digital Seismic Network (Fig. 2). The research on the characteristics of airgun source is based on the data recorded by a seismometer on the shore of the Hutubi airgun source activation pool (Guralp CMG-40T seismometer, Q330s+ data acquisition, hereinafter referred to as reference station, station code ZD0, Fig. 1).

Fig. 1 Combinations of non-modulated airgun array in Hutubi

Fig. 2 Distribution map of research stations (STZ Station in the red box)
2 ENERGY AND FREQUENCY CHARACTERISTICS OF SIGNALS FROM DIFFERENT GUN COMBINATIONS 2.1 Energy Characteristics

The energy released by the airgun source comes from the instantaneous release of high-pressure gas, which can be calculated from the capacity and pressure of high-pressure gas (Ronen S. et al., 2012). The specific relationship is as follows:

$ E=P V \ln \left(P / P_{0}\right) $ (1)

where E represents energy released by airgun, V is the volume of high-pressure gas, P is the working pressure, P0 is the environment pressure. Since the Hutubi airgun seismic source is located at 10m depth underwater, P0 in equation (1) is 1 atmosphere. From equation (1), it can be concluded that when the number of simultaneously excited gunschanges, there is a linear relationship between the energy released and the number of guns, which is shown in Fig. 4.

Fig. 3 A comparison diagram of linear stacking of signals excited by a different number of airguns

Fig. 4 Comparison between theoretical and measured energy excited with different gun combinations

According to the experimental details in Table 1, the actual energy excited by different gun combinations is studied using signals recorded by the reference station which is close to the airgun source. Firstly, the airgun signals are intercepted from the continuous waveform data recorded by the reference stations using the exact time of airgun activation. Secondly, the airgun source signals excited by different gun combinations are linearly stacked according to the number of excited guns. Daily signals are averaged to reduce the influence such as pressure difference of each shot on subsequent analysis (Fig. 3). The root-mean-square value of signal amplitude 1-3s after stacking is then calculated, and the root-mean-square value represents the energy release of airgun signals (Su Jinbo et al., 2015). As shown in Fig. 4, the actual activation energy also presents an approximate linear relationship, and with the increase of the number of excited guns, the excited energy increases approximately linearly. This is consistent with the theoretical value. The result indicates that the airgun source has stable working condition in the experiment, and signals generated by different gun combinations can display their unique characteristics stably.

2.2 Frequency Characteristics

In order to compare the differences between signal frequencies excited by different gun combinations, signals obtained from linear stacking of different gun combinations in Fig. 4 are normalized according to the maximum amplitude of each signal, and the signals are analyzed in time-frequency domain (Fig. 5). As shown in Fig. 5, the frequencies of signals excited by different gun combinations are concentrated around 4Hz. With the increase of the number of simultaneously excited airguns, the frequency components of excited signals show a higher consistency in 0-1s (on the left of the dotted line in Fig. 5), and a greater difference in waveform frequency components appear after 1s (on the right of the dotted line in Fig. 5). To conclude, the main signal frequency increases with reduce of the simultaneously excited gun quantity.

Fig. 5 Analysis of signals excited with different gun combinations in time-frequency domain

Previous experiments show that the non-modulated airgun array with prominent bubble oscillation has rich low-frequency components, with long detection range and great depth, which is more suitable for deep regional structure detection in oceans and inland areas (Qiu Xuelin et al., 2007; Zhao Minghui et al., 2008; Chen Yong et al., 2007; Chen Meng, 2014; Luo Guichun et al., 2007). The Hutubi large volume airgun source is a non-modulated airgun array, which is located at 10m depth underwater, and the minimum distance between guns is 2m while the maximum distance is 8m (Fig. 1). When the gun is excited once, high pressure gas immediately enters into the water, forming a bubble that resembles a sphere. When the bubbles start to form and rise by oscillation (before 1s), the coupling between each airgun bubble is not obvious due to small radius of bubbles. As the bubbles oscillate and rise, the hydrostatic pressure decreases, the radius of bubbles gradually increases, and the bubbles gradually start to coupling with each other (after 1s). When the bubbles are violently coupled, all the bubbles in the airgun array can be considered as one large bubble. According to the research of Johnson D. T., (1994) on bubble oscillation period, the relation between bubble oscillation period T and bubble radius is shown below:

$ T=2 \pi r_{0} \sqrt{\frac{1}{3 \gamma p_{0}}} $ (2)

where r0 is the radius of bubble in a state of equilibrium, in m. γ is heat capacity ratio, which is 1.0 under isothermal condition. According to the research of Ziolkowski et al., γ=1.13 when its adiabatic (Ziolkowski A., 1970), p0 is hydrostatic pressure at the depth of bubbles, in Pa. When bubbles generated by activation of different gun combinations rise to the same depth, heat capacity ratio γ and hydrostatic pressure p0 are all equal, with the increase of the airgun quantity, the radius r0 of bubbles reaching a equilibrium state increase, the oscillation period T gets longer, and the oscillation frequency 1/T decreases (Hu Jiupeng et al., 2017). Therefore, when the bubbles generated by each gun in the airgun array begin to couple with each other to form a large circle, the signal frequency reduces with the increase of the gun number. This explains the difference in signal frequency between different gun combinations after 1s in Fig. 5. It should be noted that this model can only approximately explain the difference in frequency. However, it is not able to make quantitative calculation on the dynamic process and attenuation mechanism after the bubbles are coupled with each other. If further research regarding this kind of problems is needed, the model should be improved.

3 SNR DIFFERENCES OF SIGNALS EXCITED WITH DIFFERENT GUN COMBINATIONS

Compared with natural earthquakes, the energy of signals generated by airgun source is relatively weak. Due to signal attenuation, airgun signals are often drowned in noise and difficult to be recognized effectively when they are transmitted to remote receiving station. However, due to high repeatability of airgun signals, the signal-to-noise ratio can be improved by the stacking of multiple airgun signals received by stations. At present, a common stacking method is linear stacking, that is, a number of airgun source signals received by stations are directly stacked according to the activation time alignment, and then the average is obtained. The formula is shown below:

$ X(t) = \frac{1}{N}\sum\limits_{j = 1}^N {{x_j}} (t) $ (3)

where X(t) is signal after stacking, xj(t) is the signal of the jth activation, and N is the number of shots used for stacking. The advantage of linear stacking is that it do not cause obvious deviation of the original signal phase and decrease of the amplitude, which can ensure the authenticity of waveform (Wu Anxu et al., 2016).

In this study, airgun signals received by 11 stations in 160km around the Hutubi airgun source are selected for research (Fig. 2). 40 sets of signals are selected for linear stacking for each combination, and the stacked signals are filtered by 2-8Hz. The propagation of signals obtained is shown in Fig. 6, which exhibiting significantly increased signal-to-noise ratio of signals with the increase of the number of excited guns. Especially for the stations far away from the airgun source, the signals can be identified gradually with the increase of the number of guns simultaneously excited.

Fig. 6 Propagation of signals excited with different gun combinations received by stations with distance

The signal-to-noise ratio can be used as a ruler to evaluate the effect of activation of different gun combinations. According to the research of Silver P. G. et al., (2007), signal-to-noise ratio can be defined as below:

$ \mathrm{SNR}=\frac{\mathrm{RMS}_{\text {sigal }}}{\mathrm{RMS}_{\text {moise }}} $ (4)

where RMSsignal is the root-mean-square value of signal amplitude of signal energy, and RMSnoise is the root-mean-square value of signal amplitude of the background noise segment (Yamaoka K. et al., 2014). The relationship between SNR and times of stacking is shown below:

$ \mathrm{SNR}=\sqrt{N} \times \mathrm{SNR}_{0} $ (5)

where SNR0 represents the SNR of the original signal. It should be noted that background noise is affected by many factors, and there are differences in the background noise levels due to different positions of stations. The background noise level of the same station also varies in different time periods, but this kind of difference is much smaller than that between different stations. The background noise level is relatively stable for some particular fixed stations with good bases and low artificial noise around. Therefore, signals received by the STZ Station, 77km from the airgun source, are used to compare the activation effects of different gun combinations (station in the red box in Fig. 2).

Signals excited with different gun combinations and received by STZ Station are stackedbased on each time of activationin sequence according to different gun combinations (Fig. 7). Signals from 0.5s before the arrival of P-wave to 2s after the arrival of P-wave are selected as the signal segment, and signals from 0s to 1s prior to the arrival of P-wave are considered as the noise segment, and the SNR of each signal is calculated according to equation(4). The relation between the SNR of different gun combinations and the times of stacking is obtained (Fig. 8). As shown in Fig. 8, with the increase of times of stacking, the rise of the SNR decreases gradually, which is consistent with the theoretical relationship of equation (5).

Fig. 7 Successive stacking of signals excited with different gun combinations and received by STZ Station

Fig. 8 The SNR comparison of signals excited with different gun combinations and received by STZ Station with the increase of stacking times

According to the research of Li Xiaobin et al., when the signal-to-noise ratio is expressed in the form of dB, the relation between SNR of signals excited by different gun combinations and times of stacking can be expressed as below:

$ N=\left(\frac{\mathrm{SNR}_{X}}{\mathrm{SNR}_{Y}}\right)^{2} $ (6)

where, SNRX is the SNR of signals simultaneously excited by gun combination X, SNRY is the SNR of signals excited by gun combination Y, and N is the time of stacking (Li Xiaobin et al., 2016). According to linear relationship between the number of guns simultaneously excited and airgun energy as expressed in equation (1), the following formula can be obtained.

$ \mathrm{RMS}_{m}=m \cdot \mathrm{RMS}_{1} $ (7)

where, m is the number of simultaneously excited guns.

Assuming that the background noise level of stations is consistent during the research period, the following formula can be obtained by putting signal energy and noise energy information into equation(6):

$ n=\left(\frac{X \cdot \mathrm{RMS}_{1}}{\mathrm{RMS}_{\text {noise }}} \div \frac{Y \cdot \mathrm{RMS}_{1}}{\mathrm{RMS}_{\text {noise }}}\right)^{2}=\left(\frac{X}{Y}\right)^{2} $ (8)

where X·RMS1 is the energy of signals excited with gun combination X, Y·RMSY is the energy of signals excited with gun combination Y, and n represents the time of stacking. From equation (8), we can acquire the number of times of signal stacking required for other gun combinations to be theoretically equivalent to the SNR of signals excited by 6-gun combinations at one shot (Table 2). Signals obtained after theoretical times of stacking of actual signals excited by different gun combinations are shown in Fig. 9. It can be seen from Fig. 9 and Table 2 that after theoretical times of stacking, some differences appear in the SNR of signals excited by different gun combinations. The main reason for the difference is that in equation (8), Weve made the assumption that the noise level is relatively stable. However, in reality, the signal from background is complicated, hence cannot be fit perfectly into the scenarios in the assumptions.

Table 2 The number of times of signal stacking required for other gun combinations to be theoretically equivalent to the SNR of signals excited with 6-gun combinations at one shot and the SNR of signals after stacking

Fig. 9 Actual signals of different gun combinations obtained after theoretical times of stacking required being equivalent to the SNR of signals excited with 6-gun combinations at one shot
4 CONCLUSIONS

Based on the above analysis, we can draw the following conclusions:

(1) Signals excited by different gun combinations have a good consistency in frequency of 0-1s, the differences in signal frequency are mainly concentrated in the signals 1s after the activation of airguns. This is mainly because the bubbles generated by activation of airgun oscillate and rise in the water which further lead to the hydrostatic pressure gradually decreases, and the radius of bubbles gradually increases. When rising to a certain height, the bubbles gradually start to coupling with each other, forming a large bubble, and the radius of the bubbles increase with the increase of airgun quantity. In this period of time, according to the relation between bubble radius and oscillation period, the signal frequencies reduce with the increase of gun numbers in the airgun array(Xia Ji et al., 2016).

(2) The SNR of signals received by stations can be effectively improved by stacking. However, with the increase of the times of stacking, the SNR increases rapidly at first, but it tends to be stable gradually. This indicates that with the increase of stacking times, its effect on improving SNR attenuate to some extent. Therefore, according to the number of guns simultaneously excited and the actual situation of the background noise of stations in the research area, a reasonable experiment scheme can be developed and the times of activation can be controlled to obtain signals whose SNR meets the research requirements, which can avoid wasting of resources caused by a large number of experiments.

(3) To improve the SNR of stations with high background noise, a greater activation energy (the number of excited airguns simultaneously) is more effective than multiple stacking of signals with less energy. It can be seen from Table 2 that the SNR of signals excited by a single gun after 36 times of stacking is equivalent to the SNR of signals excited by 6 guns at one shot. When the times of stacking reach a certain number, its effect on improving SNR will weaken gradually. Therefore, when detecting medium structure in a large area, the number of guns in the airgun array should be increased as much as possible to achieve ideal results.

ACKNOWLEDGEMENT

Thanks two reviewers for their valuable suggestions. Wang Baoshan, a research professor at the Institute of Geophysics, China Earthquake Administration, gave patient guidance to this research. Hu Jiupeng, an assistant research professor and Dr. Ji Zhanbo at the Institute of Geophysics, China Earthquake Administration, gave us great help in thinking about the ideas of the paper. Zhang Wenlai, senior engineer, Shi Yongjun, senior engineer, Yang Fuxi, senior engineer, and Jia Lu, assistant engineer, at the Earthquake Agency of Xinjiang Uygur Autonomous Region provided great support for airgun experiments. We extend our deepest thanks to them.

REFERENCES
Chen Meng. Exploring and Monitoring Regional-scale Subsurface Structure Using Un-tuned Large Volume Airgun Array[D]. Beijing: Institute of Geophysics, China Earthquake Administration, 2014 (in Chinese with English abstract).
Chen Yong, Zhang Xiankang, Qiu Xuelin, Ge Hongkui, Liu Baojin, Wang BaoshanChen Yong, Zhang Xiankang, Qiu Xuelin, Ge Hongkui, Liu Baojin, Wang Baoshan. A new way to generate seismic waves for continental crustal exploration[J]. Chinese Science Bulletin, 2007, 52(16): 2264-2268. DOI:10.1007/s11434-007-0247-4
Chen Yong, Wang Baoshan, Yao HuajianChen Yong, Wang Baoshan, Yao Huajian. Seismic airgun exploration of continental crust structures[J]. Science China Earth Sciences, 2017, 60(10): 1739-1751. DOI:10.1007/s11430-016-9096-6
Hu Jiupeng, Wang Baoshan, Chen YongHu Jiupeng, Wang Baoshan, Chen Yong. The influence of water shape on land airgun triggered signals[J]. Journal of Seismological Research, 2017, 40(4): 543-549 (in Chinese with English abstract).
Johnson D.T.Johnson D.T. Understanding air-gun bubble behavior[J]. Geophysics, 1994, 59(11): 1729-1734. DOI:10.1190/1.1443559
Li Xiaobin, Ye Beng, Yang Jun, Chen Meng, Jin Mingpei, Wang BaoshanLi Xiaobin, Ye Beng, Yang Jun, Chen Meng, Jin Mingpei, Wang Baoshan. Research on comparison of excitation efficiency of air guns with various combinations in water reservoir[J]. Journal of Seismological Research, 2016, 39(3): 458-465 (in Chinese with English abstract).
Luo Guichun, Ge Hongkui, Wang Baoshan, Hu Ping, Mu Hongwang, Chen YongLuo Guichun, Ge Hongkui, Wang Baoshan, Hu Ping, Mu Hongwang, Chen Yong. Fired models of air gun source[J]. Earthquake Research in China, 2007, 23(3): 225-232 (in Chinese with English abstract).
Qiu Xuelin, Chen Yong, Zhu Rixiang, Xu Huilong, Shi Xiaobin, Ye Chunming, Zhao Minghui, Xia ShaohongQiu Xuelin, Chen Yong, Zhu Rixiang, Xu Huilong, Shi Xiaobin, Ye Chunming, Zhao Minghui, Xia Shaohong. The application of large volume airgun sources to the onshore-offshore seismic surveys:implication of the experimental results in northern South China Sea[J]. Chinese Science Bulletin, 2007, 52(4): 553-560. DOI:10.1007/s11434-007-0051-1
Ronen S.Ronen S. Psi, pascal, bars, and decibels[J]. The Leading Edge, 2012, 21(1): 60-61.
Silver P. G., Daley T. M., Niu Fenglin, Majer E.L.Silver P. G., Daley T. M., Niu Fenglin, Majer E.L. Active source monitoring of cross-well seismic travel time for stress-induced changes[J]. Bulletin of the Seismological Society of America, 2007, 97(1B): 281-293. DOI:10.1785/0120060120
Su Jinbo, Wang Baoshan, Wang Haitao, Wang Qiong, Ji ZhanboSu Jinbo, Wang Baoshan, Wang Haitao, Wang Qiong, Ji Zhanbo. Research on characteristic of seismic attenuation in the northern Tianshan Area using seismic signal from airgun source[J]. Journal of Seismological Research, 2015, 38(4): 598-605 (in Chinese with English abstract).
Su Jinbo, Wang Qiong, Wang Haitao, Shi Yongjun, Chen Xiangjun, Feng Lei, Chen HaoSu Jinbo, Wang Qiong, Wang Haitao, Shi Yongjun, Chen Xiangjun, Feng Lei, Chen Hao. Research on large volume airgun source signal reception in Hutubi, Xinjiang using seismic network data[J]. Earthquake Research in China, 2016, 30(3): 326-332.
Wang Baoshan, Ge Hongkui, Wang Bin, Wang Haitao, Zhang Yuansheng, Cai Huiteng, Chen YongWang Baoshan, Ge Hongkui, Wang Bin, Wang Haitao, Zhang Yuansheng, Cai Huiteng, Chen Yong. Practices and advances in exploring the subsurface structure and its temporal evolution with repeatable artificial sources[J]. Earthquake Research in China, 2016, 30(3): 284-297.
Wang Bin, Li Xiaobin, Liu Zifeng, Yang Jun, Yang Runhai, Wang Baoshan, Yang WeiWang Bin, Li Xiaobin, Liu Zifeng, Yang Jun, Yang Runhai, Wang Baoshan, Yang Wei. The source and observation system of Binchuan earthquake signal transmitting seismic station and its preliminary observation results[J]. Earthquake Research in China, 2016, 30(3): 316-325.
Wei Bin, Su Jinbo, Wang Haitao, Zheng Liming, Wang Qiong, Zhang Wenlai, Yuan Shun, Wei Yunyun, Chen HaoWei Bin, Su Jinbo, Wang Haitao, Zheng Liming, Wang Qiong, Zhang Wenlai, Yuan Shun, Wei Yunyun, Chen Hao. Site selection and construction of Hutubi airgun source signal transmitting seismic station and its characteristic of source[J]. Earthquake Research in China, 2016, 32(2): 222-230 (in Chinese with English abstract).
Wu Anxu, Ye Beng, Li Hong, Li Yun, Zheng Yiwen, Zhang Hongyan, Li YanWu Anxu, Ye Beng, Li Hong, Li Yun, Zheng Yiwen, Zhang Hongyan, Li Yan. The preliminary analysis of reliability on weak signal extraction for air-gun source surveys[J]. Earthquake Research in China, 2016, 32(2): 319-330 (in Chinese with English abstract).
Xia Ji, Jin Xing, Cai Huiteng, Xu JiajunXia Ji, Jin Xing, Cai Huiteng, Xu Jiajun. The time-frequency characteristic of large volume air-gun source wavelet and its influencing factors[J]. Earthquake Research in China, 2016, 32(2): 249-260 (in Chinese with English abstract).
Yamaoka K., Miyamachi H., Watanabe T., Kunitomo T., Michishita T., Ikuta R., Iguchi M.Yamaoka K., Miyamachi H., Watanabe T., Kunitomo T., Michishita T., Ikuta R., Iguchi M. Active monitoring at an active volcano:amplitude-distance dependence of ACROSS at Sakurajima Volcano, Japan[J]. Earth, Planets and Space, 2014, 66(1): 32.
Yang Wei, Wang Baoshan, Ge Hongkui, Wang Weitao, Chen YongYang Wei, Wang Baoshan, Ge Hongkui, Wang Weitao, Chen Yong. The active monitoring system with large volume airgun source and experiment[J]. Earthquake Research in China, 2013, 29(4): 399-410 (in Chinese with English abstract).
Zhang Yuansheng, Guo Xiao, Qin Manzhong, Liu Xuzhou, Wei Congxin, Shen Xuzhang, Yan WenhuaZhang Yuansheng, Guo Xiao, Qin Manzhong, Liu Xuzhou, Wei Congxin, Shen Xuzhang, Yan Wenhua. The construction of active source repeated monitoring in the Qilian Mountain, Gansu Province[J]. Earthquake Research in China, 2016, 30(3): 333-341.
Zhao Minghui, Qiu Xuelin, Xia Shaohong, Wang Ping, Xu Huilong, Ye Chunming, Kang YingZhao Minghui, Qiu Xuelin, Xia Shaohong, Wang Ping, Xu Huilong, Ye Chunming, Kang Ying. Large volume air-gun sources and its seismic waveform characters[J]. Chinese Journal of Geophysics, 2008, 51(2): 558-565 (in Chinese with English abstract).
Ziolkowski A.Ziolkowski A. A method for calculating the output pressure waveform from an air gun[J]. Geophysical Journal of the Royal Astronomical Society, 1970, 21(2): 137-161. DOI:10.1111/j.1365-246X.1970.tb01773.x