The airgun source was first widely used in offshore oil exploration. Due to the controllable, repeatable and little destructive nature of the airgun source, as well as the determinedness of the excitation location andtiming, the limitation of the spatial and temporal distribution of the traditional natural source can be overcome. The method is used increasingly in geophysical exploration fields such as deep crustal structure and medium change monitoring (Luo Guichun et al., 2006; Wang Baoshan et al., 2016). Researchers at home and abroad have conducted some scientific experiments using airgun sources, such as the Los Angeles Regional Seismic Experiment ─ LARSE Program (Brocher T.M. et al., 1995), New Zealand South Island Seismic Exploration Experiment  SIGHT Project (Okaya D. et al., 2002), China's Joint Exploration Program in the Eastern Zone of the South China Sea (Qiu Xuelin, 2003), Joint LandSea Detection Experiments in Fujian and Taiwan Strait, Geosciences Yangtze River Planning Experiment and in airgun launching tests at earthquake stations in Binchuan of Yunnan, Hutubi of Xinjiang and Zhangye of Gansu.
In comparison to natural earthquakes, the energy of single shot excitation of artificial airgun source is limited. As the propagation distance increases, the signal will be covered by the background noise of the receiving station, and effective signal identification is difficult. Therefore, a large number of repeated excitations are required, and superimposed processing is performed to enhance the signaltonoise ratio of the airgun signal. When dealing with airgun signals for different research purposes, the superposition technique has developed into linear superposition (Wu Anxu et al., 2016), time domain and timefrequency domain phase weighted superposition (Stockwell R.G. et al, 1996; Schimmel M. et al, 1999, 2011), and the superposition of spectrum whitening (Lin Binhua et al., 2017; Jin Zhen et al., 2018). The linear superposition method does not change the original shape of the signal and preserves the true amplitude of the signal. The time domain phase weighted superposition can improve the signaltonoise ratio of the waveform, but the waveform after the superposition is distorted, and the phase offset and amplitude distortion appear in the timefrequency domain phase weighted superposition. The superposition of spectrum whitening weakens the signaltonoise ratio of the nearfield, but it improves the signaltonoise ratio of the farfield weak signal. The amplitude, however, is distorted.
The above superposition methods each have advantages and disadvantages. Except for linear superposition, the signal amplitude information obtained by other superposition methods has a certain degree of distortion. However, in practice, the amplitude information of the signal can provide researchers with more effective information, such as magnitude calculation, full waveform inversion, signal attenuation characteristics, etc. Therefore, while increasing the signaltonoise ratio, it is necessary to retain the amplitude information of the signal.
Although the linear superposition method does not change the true signal amplitude, it is rarely applied directly to airgun signal processing. This is because in actual observations, it is often accompanied by earthquakes, blasting, and recording shortterm kicks, etc. Airgun signals are weak, and these interferences may be tens of times or more than the airgun signal, which will make it difficult to eliminate the effects of interference signals after dozens or even hundreds of superpositions. If there is interference in a certain piece or in some records, the usability of the entire recorded information after superimposition is reduced or rendered completely unusable, which will undoubtedly cause great waste. In other words, the extraction of airgun signals should include the removal of the interference signal. For example, time domain normalization superposition and frequency domain whitening superposition are to improve thesignaltonoise ratio of the superposition result by reducing the weight of the interference signal. We once used the analysis of the noise spectrum to achieve the removal of the interference in the airgun signal. However, after the frequency domain analysis determines the abnormality, the entire record needs to be eliminated, and it is impossible to effectively judge whether the entire record has interference or partial interference. Jiang Shengzhao et al. (2017) proposed that automatic data screening could be realized based on the variation of noise level. This method can eliminate strong noise interference such as earthquakes, but similar to the noise spectrum method, as long as there is any interference in the waveform, the whole record will be removed. Therefore, it is the key and difficult point of airgun data processing to find out the interference degree of waveform and eliminate it effectively. In order to make full use of the important information of amplitude, this paper will start from the characteristics of the actual recorded data of the stations, and propose a linear superposition method based on probability to realize the automatic rejection of abnormal interference, and prove that the method has the advantage of removing interference and can obtain reliable amplitude information.
1 INTRODUCTION AND DATA SELECTION OF AIRGUN EXPERIMENTS IN FUJIAN RESERVOIRS 1.1 Overview of Reservoir ExperimentsSince 2014, the Fujian Earthquake Agency has successfully carried out active source detection experiments and accumulated a large amount of airgun observation data in the Jiemian Reservoir in Youxi, Sanming, the Mianhuatan Reservoir in Yongding, Longyan, the Shihuangfeng Reservoir in Wuping, Longyan, the Nanyi Reservoir in Nanjing, Zhangzhou, the Ansha Reservoir in Qingliu, Sanming, the Shanmei Reservoirs in Nan'an, Quanzhou, Shaxikou Reservoir in Nanping, and the Longmentan Reservoir in Dehua, Quanzhou. The experiment uses the largecapacity mobile airgun source system independently designed and assembled by the Fujian Earthquake Agency. An array made up of four 1500LL Bolt airguns was selected, with a single gun capacity of 2000in^{3} and the total capacity of the gun array was 8000in^{3}. In addition to the fixed network around the province and around Fujian, the experimental observation system also encrypts and distributes a number of mobile stations. Fig. 1 is a schematic diagram of the position of the fixedpoint excitation of the reservoir experiment and the distribution of the signal receiving network. The red pertangram represent the excitation positions of the reservoir airgun source in Fujian over the years. The blue dots and triangles represent fixed stations, and the green square points are mobile stations (in 2017).
This paper selects the airgun experimental data from the Ansha Reservoir and the Shanmei Reservoir in June, 2017 as the research object, and analyzes the consistency of the waveform obtained by the same receiving stations during the fixedpoint excitations to ensure the reliability of subsequent superposition results. We conducted the baseline correction of the airgun record with 28Hz bandpass filtering, selected the signal band, used the crosscorrelation method to calculate the correlation between different excitation signals and reference signals, and obtained the maximum correlation between each waveform and reference waveform. Fig. 2(a) and (b) are the waveform comparison diagrams and the maximum crosscorrelation coefficient of the 507 airgun signals received by the shore station L3551 of the Ansha Reservoir. The station is about 169m away from the airgun source. Fig. 2(c) and (d) are the waveform comparison diagram and the maximum crosscorrelation coefficient of the 501 airgun signals received by the shore station L3571 of the Shanmei Reservoir. The station is about 446m away from the airgun source. The results show that the maximum correlation coefficient of airgun signals is above 0.97, which indicates that the waveforms received by the fixedpoint repeated excitation in the Ansha Reservoir and Shanmei Reservoir are in good agreement, and the high consistency of the waveforms lays the foundation for the subsequent signal superposition processing.
It is assumed that the noise recorded by the station satisfies normal distribution and the mean value is zero. This is also the basic assumption that the direct linear superposition method can improve the signaltonoise ratio. At the same time, previous data has proven that the airgun signal is highly repetitive, and that a new signal with a stable amplitude plus noise that satisfies the normal distribution also satisfies the normal distribution, and also that the mean is the signal value and the variance and the noise are the same, which has been proven in probabilistic methodology and will not be discussed in detail here.
That is,
$ n(t)\tilde{\ }M\left({\mu, {\sigma ^2}} \right) $  (1) 
$ n(t) + f\tilde{\ }M\left({\mu + f, {\sigma ^2}} \right) $  (2) 
where n(t) is random noise; μ is the noise mean; σ^{2} is the variance; f is the signal value.
The amplitudes of the signals satisfying the normal distribution are symmetrically distributed at the center of the mean value. Under ideal conditions, the number theoretically smaller than the mean is equal to the number greater than the mean. As mentioned above, when the amplitude of the interference signal is much larger than the amplitude of the airgun signal, it will have a great impact on the analysis of the airgun signal. At the same time, more superposition may be needed to extract the airgun signal that meets the analysis requirements. Eliminating large interference is the key to airgun signal processing. In this paper, thesignals that satisfy the normal distribution are sorted according to the numerical value, and data with larger deviation from the mean value is removed (This part of the data has a larger amplitude, which is more likely to interfere, and has the greatest impact on the airgun signal). The data in the middle part are left. After the removal of the high and low data, the remaining data is added and averaged, which is a probability screening method (referred to as PR linear superposition). Its formula is expressed as
$ X(t) = \frac{1}{N}\sum\limits_{j = 1}^N {{x_j}} (t) $  (3) 
Among them, X(t) is the result of linear superposition; x_{j}(t) is the jth residual signal value; N is the number of superpositions.
Although the method cannot completely judge that the data with larger amplitude is interference, it can be seen from the normal distribution probability curve that the smaller the deviation from the mean value, the smaller the probability. The removal of the large value data is only the elimination of some data with low probability, and has little impact on the results. However, with this method, interference data can be well eliminated, especially for interference signals with large amplitudes.
2.2 Method ValidationTaking the station record of the YAAS of the seismic station in the airgun experiment of Ansha Reservoir as an example, the YAAS station is about 9km away from the airgun excitation point, and the Ansha Reservoir experiment is officially repeated 507 times, with each airgun excitation time as the standard, observation data at the same time in 507 recorded waveforms (that is, 507 data at any time) to verify the correctness of the probability hypothesis. The two red dots in Fig. 3 are the moments of randomly selected noise and effective signals, respectively. Fig. 4 is a frequency histogram of the noise and effective signal actually recorded by the YAAS station in the range of different amplitude values (the gray squares are noise, the white squares are the effective signals) and the normal distribution density function graph (the blue lines are noise and the red lines are valid signals). It can be seen from the Figure that both of them have a normal distribution characteristic, in which the mean value of the noise amplitude is about zero, and the mean value of the effective signal amplitude is about 280 count, which deviates from the zero value side. This indicates the amplitude characteristics of the airgun signal recorded by the actual repeated excitation is consistent with the above probability hypothesis and presents a normal distribution, indicating the validity of the hypothesis that the noise signal proposed in this paper satisfies the normal distribution.
The airgun's experimental observation data is collected, and the continuous waveforms of each station are intercepted one by one according to the airgun firing time. Each waveform is reserved for 20s before the gun control time, and the total length is 200s. The cut waveforms are subjected to baseline correction, 28Hz bandpass filtering, and tipping respectively. For the pretreated Nsegment repetitive excitation waveform (N is the number of excitations), the sampling point is taken as the step size, and the N recorded data at the same time (such as the Ansha Reservoir airgun experiment mentioned above, N is 507) are sorted by size, and a certain screening ratio is used to eliminate the data deviating from the mean value. If the screening ratio is 10%, the maximum and minimum 5% of the N data at the same time are eliminated, and then the remaining 90% of the data after the screening is averaged, that is, the probability of the time is selected to be linear (PR linear) superimposed results. After the similar processing is performed on the data corresponding to each moment, the superposition results of all the airgun excitation signals can be obtained. At this time, the number of excitations participating in the superposition at any time (i.e., different sampling points) is still the same, therefore, the method does not cause Waveform distortion. The selection of the screening ratio is related to the amount of interference. The selection of the screening ratio will be discussed later.
3 ANALYSIS OF CALCULATION RESULTS 3.1 Interference Removal EffectThe experimental data of airgun received by YAAS station are superposed linearly by PR. The station is about 9km away from the source. Because of the close epicenter distance, the singleshot signal is clearer. The processing results obtained in this paper are compared with the direct linear superpositions and the original single shot recording waveforms. The results are shown in Fig. 5. The airgun signal is consistent with the original single gun waveform and the direct linear superposition result after the linear superposition of PR, indicating the shape of the signal after the PR linear superposition and the amplitude are effectively retained. It can be seen from the 13s15s band that the noise is effectively suppressed after the single shot waveform is superimposed. In addition, in order to verify the effect of the PR linear superposition method to remove interference, the waveforms of the single shot before and after the interference removal are compared (Fig. 6). Fig. 6(a) shows the original waveform of 10 shots, in which the waveform interferences of No.1 and 2 are not obvious, and other guns have some interferences. Fig. 6(b) shows the singleshot waveform after the removal discussed in this paper recorded in Fig. 6(a). It can be seen that although No.1 and 2 have no obvious interference, the larger background noise is weakened, and the abnormal interferences of No.3 to 10 are all eliminated. It can be seen that the PR linear superposition can effectively preserve the true amplitude of the signal, and at the same time, the strong background noise and abnormal interference can be eliminated to improve the signaltonoise ratio of the waveform.
In order to further confirm the effectiveness of PR linear superposition to remove abnormal interference, this paper superimposes the received data of airgun experiments at each station of Ansha and Shanmei Reservoirs, normalizes the signals, and then sorts the results of each station by epicentral distance. The timedistance curve after superposition is obtained. The results are shown in Fig. 7 and Fig. 8. Fig. 7(a) and (b) are the time interval diagrams of the direct linear superposition and the PR linear superposition in the Ansha Reservoir respectively. Fig. 7(c) and (d) are the timedistance maps in the range of 165km to 195km in the epicentral distance of Fig. 7(a) and (b) respectively. Fig. 8(a) and (b) are the direct linear superposition and PR linear superposition at the Shanmei Reservoir respectively. Fig. 8(c) and (d) are the timedistance maps of Fig. 8(a) and (b) respectively in the epicenter distance range of 60km to 120km. By comparing the direct linear superposition and the PR linear superposition calculation results of the Ansha Reservoir, it can be seen that the sharpness of the PR linear superimposed signal is improved, and the tracking distance of the Pwave and the Swave is greater than the direct linear superimposed tracking distance. The tracking distances of the direct linear superimposed P and S waves are about 325km and 375km respectively, while the tracking distance of the PR linear superposition is increased to about 375km and 400 km. Although the PR linear superimposed tracking distance of the Shanmei Reservoir is similar to that of the direct linear superposition, it can be seen that the P and S waves traced by the PR linear superposition are similar to those at the Ansha Reservoir, and have higher definition than the direct linear superposition. In addition, the timedistance curves obtained at the two reservoirs are partially amplified. It can be clearly seen that the direct linear superposition has a certain suppression effect on random noise, but if there is strong noise and other large abnormal interference, it is subject to abnormal interference. The impact is more serious. These abnormal disturbances will seriously interfere with the analysis of the airgun signal, and the effective signal superimposed hundreds of times will be submerged. The PR linear superposition can remove the interference well. Therefore, it is concluded that the PR linear superposition method is simple, but the effect of removing the abnormal interference is remarkable.
The PR linear superposition effect is further verified by calculating the background noise level (noise standard deviation) of the superimposed waveform as a function of the number of superpositions. The airgun records of the L3507, QGQH and HAJF stations with 110km, 51km and 60km away respectively from the excitation point at the Shanmei Reservoir are selected. The interference of the L3507 station is large, and the interference of the QGQH station is slightly smaller than that of the airgun. The interference of the HAJF station is relatively weak. Fig. 9(a) are the direct linear superposition results of L3507, QGQH, and HAJF stations respectively from top to bottom. Fig. 9 (b) are the PR linear superposition results of L3507, QGQH, and HAJF stations respectively from top to bottom. Comparing the waveforms of the two superposition methods, whether the abnormal interference is strong or weak, PR linear superposition can effectively eliminate it, but it is more difficult to completely suppress random interference with direct linear superposition. In addition, the background noise levels of the three stations L3507, QGQH and HAJF are calculated based on the number of superposition times. The calculated band is 100s to 140s in the waveform diagram. The result is shown in Fig. 10. The L3507 station has a lot of interference in the first few shots. The noise levels of the direct linear superposition and the PR linear superposition show a decreasing trend with the increase in the number of superpositions, but there is still a significant difference between the two. When the PR linear superposition is superimposed 5 times, the noise level drops sharply, and then the trend tends to be smooth. The direct linear superposition noise level is also weakened, but its change is sluggish, and even after superimposing 500 times, the noise level is still greater than the PR linear superposition. Before the 79th superposition of QGQH and HAJF stations, the direct linear superposition is basically consistent with the trend of the PR linear superposition in noise level. This is because the recording waveform of the first 79 guns is ideal with no strong interference.The interference occurs at the 80th and 106th guns. After that, the noise level of the direct linear superposition appears to jump upwards, and then slowly falls back. The PR linear superposition, however, is completely unaffected by the interference, and continues to decrease and then turns to be stable. In general, PR linear superposition has significant advantages in removing interference.
The probabilityrelated linear superposition method is to remove the interference with a certain screening ratio and then superimpose the signals. We are going to analyze the relationship between the screening ratio and the background noise level from the actual records of some stations. Same as the calculation of the band of the noise level in Fig. 10, Fig. 11 shows the fluctuations of the background noise levels of the stations of L3551, QGQH, L3571, and L3507 with the screening ratio. L3551 has less interference, but the noise levels of the other three stations are relatively larger before screening. The results show that the noise levels of the four stations showed a decrease with the increase of the screening ratio, andthen the transition gradually increased. Some stations did not increase significantly. This shows that after a certain proportion of screening, the noise level is significantly reduced. The reduction in the noise level indicates that the interference of the waveform is eliminated. When the noise level is at a minimum, the interference is basically removed. Therefore, if it is possible to accurately judge the degree of interference of each segment of the waveform, we can accurately select the appropriate screening ratio to obtain the optimal interference removal. In fact, due to the differences in the recording quality of each station, the stations with more interference should have a larger ratio of screening, while the stations with less interference should have a smaller screening ratio, but this will bring more inconvenience to the calculation. In addition, from the calculation results of the selected stations, it can be seen that as the screening ratio increases, that is, the number of superpositions decreases, the noise level also increases, especially for stations with less interference, such as station L3551 in this paper. According to the law of large numbers in probability theory, as the number of repetitions approaches infinity, the arithmetic mean of the values converges almost abruptly to the expected value. By the same token, in the case where there is no special interference and the signal absolutely satisfies the normal distribution, the more the number of superpositions, the lower the noise level. In this method, a higher screening ratio is selected, that is, only a small number of samples are reserved for superposition. The result is farther from the true mean value. This also indicates that the method conforms to the law of large numbers in probability theory. Therefore, by selecting the appropriate screening ratio, i.e. the demand for the interference removal can be satisfied, and the effective signal can be retained as much as possible, the processing result with the highest signaltonoise ratio can be obtained. However, in practice, the frequency and amplitude of interference occur at different times. In order to make the algorithm more convenient, the appropriate screening ratio can be adopted according to the actual situation (such as the background noise level of the station, the interference frequency).
In this paper, based on the randomness of noise and the high repeatability of airgun signals, a probability screening linear superposition method is proposed, and the correctness of the probability hypothesis is proved by an example. Through the application of the actual observation signals of the airgun source in the Ansha Reservoir and the Shanmei Reservoir, the following conclusions are obtained:
(1) After the station data is linearly superimposed by PR, the amplitude of the signal is effectively preserved, and the interference removal effect is obvious, which indicates that the method can effectively preserve the true amplitude of the signal, effectively improve the signaltonoise ratio, and significantly reduce the effects of different types of interference such as earthquake events, short bursts and strong background noise. Compared with direct linear superposition, PR linear superposition shows obvious superiority in removing interference and phase tracking effect.
(2) The quality of the experimental data received by the observing station is uneven. According to the actual situation, the appropriate screening ratio can be selected so that the result can meet the demand of eliminating interference, and the effective signal can be retained as much as possible to obtain the processing result of the highest signal noise ratio. In practice, depending on the actual situation of the observed data (such as the background noise level of the station, the frequency of interference, etc.), different screening ratios are selected for different stations. At this time, the optimal superposition results can be obtained, but the number of superpositions of each station may not be the same. Integrate the data of all stations and adopt appropriate screening ratios (such as 10% selected in this paper) to uniformly screen out the observation data of all stations. Although this is not necessarily the case for a single station. The optimal result may also eliminate some of the normal data, so that the data has a slightly higher noise level due to less samples, but in general, the process is not only simple, but the number of times of superposition of each station is the same. The latter signal can also meet expectations.
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