Earthquake Reaearch in China  2019, Vol. 33 Issue (2): 336-353     DOI: 10.19743/j.cnki.0891-4176.201902007
Study on the Influence of Airgun Excitation Conditions on Airgun Signals and Travel Time Variation Measurements
XIANG Ya1, YANG Runhai2, WANG Bin2, ZHOU Yunyao1, LU Yongqing1, WU Huan1, QI Junwei1, PENG Jing1     
1. Key Laboratory of Earthquake Geodesy, Institute of Seismology, CEA, Wuhan 430071, China;
2. Yunnan Earthquake Agency, Kunming 650224, China
Abstract: Because of the different excitation conditions of the airgun source, there will be subtle differences in airgun signals. Travel time variation of airgun signals often mix into source information which can't fully reflect the evolution of the medium. This article uses the airgun signals from the Binchuan Transmitting Seismic Station to analyze the airgun signal's characteristics of phase and correlation. We conducted a comparative analysis of the effects of the pair difference method and the deconvolution method on eliminating the influence of the excitation conditions in travel time variation. The results show that:(1) The pressure pulse and its subsequent wave of airgun source wavelet are less affected by excitation conditions that we can use it to obtain high-precision excitation moments. (2) Deconvolution can improve the correlation of the airgun signal. (3) The pair difference method can't eliminate the influence of excitation conditions in travel time variation. Deconvolution can reduce excitation condition interference and the influence of the excitation condition in the travel time variation after deconvolution of the vertical signal is significantly reduced.
Key words: Airgun source     Pair difference     Deconvolution     Travel time variation     Correlation    

INTRODUCTION

The change of velocity of the underground medium can reflect the change of the physical state of the medium. Since the 1960s, geophysicists discovered that some earthquakes were accompanied by abnormal changes in seismic wave velocity (Savarensky E. F., 1968; Aggarwal Y. P. et al, 1973, 1975; Niu Fengli et al., 2008; Yang Runhai et al., 2011), which is one of the important means to study the evolution process of earthquakes. The airgun's source is less destructive and with higher temporal and spatial resolution, is suitable for 4-D seismological studies with time-varying information (Wang Weitao et al., 2017).

The airgun source receives a large amount of energy through the instantaneous release of high-pressure gas, and the repeatability is high (Chen Yong et al., 2016). In 2001, during the sea-land joint test in the northern part of the South China Sea, the airgun source was first applied to the detection of deep crustal structures (Qiu Xuelin et al., 2003, 2007), which laid the foundation for the development of airgun sources in the field of domestic seismology. In 2006, the Shangguanhu Reservoir experiment in Zunhua, Hebei Province verified the feasibility of airgun source stimulation in terrestrial waters (Chen Yong et al., 2007, 2008). In 2009, the Mapaoquan airgun experiment in Fangshan, Beijing, once again proved that the airgun source can be excited in small land water bodies (Wang Baoshan et al., 2010). Subsequently, the China Earthquake Administration successively carried out airgun continuous excitation experiments with a number of units including the Yunnan Earthquake Agency (Wang Bin et al., 2015; Zhang Yuansheng et al., 2016; Wei Bin et al., 2016; Chen Huifang et al., 2016) and obtained fruitful research results. The airgun source has become an important tool for detecting shallow media structures and space-time evolution of the continent (Wang Weitao et al., 2017).

The airgun wavelet is divided into a high frequency pressure pulse and a low frequency bubble pulse. The pressure pulse has large amplitude and high frequency, and can obtain high resolution in a small area scale. It is mainly used in seismic exploration fields such as the petroleum industry (Zhou Baohua et al., 1998a, 1998b). The bubble pulse frequency is low and the propagation distance is long. It is mainly applied to the crustal structure (Tian Xiaofeng et al., 2016; She Yuyang et al, 2018) and the media change related to earthquake gestation (Reasenberg P. et al., 1974; Liu Zifeng et al., 2015; Zhang Yuansheng et al. 2017). The scale of seismic signal velocity is usually very small (Wang Weitao et al., 2009; Yang Wei et al., 2010). It has extremely high requirements for the accuracy of the excitation event. Using the airgun signal to calculate the wave velocity variation of the medium is one of the more commonly used methods for studying medium changes. Since dv/v=-dt/t(dv and dt are seismic wave velocity changes and travel time changes, respectively, v and t are the original path seismic wave velocity and travel time), the wave velocity change dv is often reflected indirectly by calculating the travel time change dt. The calculation of the wave velocity of the airgun signal is affected by factors such as signal-to-noise ratio, calculation accuracy and source interference. After filtering and superimposition, the signal-to-noise ratio and calculation accuracy can be improved to some extent, but the influence of the source cannot be eliminated. Therefore, exploring a calculation method to remove the influence of the source is very important for the calculation of the wave velocity variation.

In 2011, the Yunnan Earthquake Agency built China's first airgun signal fixed launch pad in the Dayindian Reservoir of Binchuan County, Dali Bai Autonomous Prefecture, Yunnan Province. So far, many achievements have been made, but many problems remain to be studied. In order to carry out research on the effects of the change of the excitation conditions of the Binchuan airgun signal launcher on the airgun signal and the method of eliminating the source function, the Yunnan Earthquake Agency conducted a dense excitation experiment in February 2017. In this paper, the experimental data is used to analyze the phase and correlation characteristics of airgun signals under different excitation conditions. The travel time variation of airgun signals is calculated by different methods, and comparative analysis is carried out.

1 EXPERIMENTAL OVERVIEW AND DATA

The Dayindian Reservoir is a medium-sized reservoir integrating domestic water and agricultural irrigation. Due to the influence of water consumption and seasonal changes, the water level of the reservoir changes, and the airgun signal and its correlation coefficient will change accordingly (Luan Yi et al., 2016). Airgun signal wave velocity changes are often mixed into source information such as water level changes. The reservoir airgun array consists of four Bolt 1500LL airguns with a single airgun capacity of 2000in3. The square pontoon side of the fixed airgun array is 7m long. The conventional excitation conditions of the reservoir are sinking depth h=10m and working pressure p=15MPa. In 2012, it entered the conventional excitation and continued to this day. In order to carry out research experiments in the early stage of mobile airgun promotion and overcome the shortcomings of low water levels and the inability to be excited, the base of the launching station has drilled a well with diameter of 5m and depth of 20m. The small Bolt airgun with a single capacity of 250in3 is used in the well. In order to cooperate with the airgun excitation experimental observation and research, 40 mobile observation stations were re-established on the basis of the original observation station of the Yunnan Earthquake Agency. The mobile observatory seismometer is equipped with a 2s-100Hz CMG-40T seismometer manufactured by GURALP from the United Kingdom and a REFTEK-130B data collector produced by the US REFTEK company (Wang Baoshan et al., 2012). The commonly used reference station (CKT0) is placed in a swing room with a base distance of about 50m from the airgun array, and the signal is recorded as a source function. The sampling rate of CKT0 is 200Hz and 100Hz, and the sampling rate of other flow observing stations is 100Hz.

During the intensive excitation experiment in February, 2017, the water level of the Dayindian Reservoir was about 19m and that of the well was 15m. The QS-05 portable digital seismograph and the TAG-33M force-balanced strong seismometer were installed in the experiment. The portable seismometer sampling rate was 500Hz, and the strong seismic instrument sampling rate was 200Hz. Before the experiment, we numbered all the instruments and performed the consistency test. Except for the abnormality of the Z-(vertical) component signal of the instrument of sta37, the consistency of other instruments was good. The E (east-west) component and the N (south-north) component of the sta37 instrument correspond well with other instrument signals. The Z component signal is opposite in phase and negative phase to other instruments, so it is necessary to multiply the Z-component signal when processing the instrument data of sta37. Phase correction is performed with -1. The reference station in the experiment is the sta06 instrument placed on the bank of the reservoir. Sta06 is about 50m away from the airgun array and about 40m away from the well. In the early stages, portable digital earthquakes were arranged around the airgun source with a radius of 0.5km and 1.7km. The instrument (Fig. 1), in which the GPS was destroyed shortly after the installation of the sta23 instrument, no data was recorded. In the early stages of the experiment, the "control variable method" was used, that is, the reservoir and well excitation were carried out under the working pressures p=9MPa, 12MPa and 15MPa at the depths of sinking h=8m, 10m and 12m, respectively. During the reservoir excitation process, the floating stage was shifted 7m southward and 7m northward at h=10m and p=15MPa respectively. The initial excitation conditions are shown in Table 1. In the later stage, the intensive excitation under normal excitation conditions was mainly carried out, and a line was laid along the northeast direction, and strong earthquake meters and portable seismographs were set up for recording and observation.

Fig. 1 Location distribution of reservoir, temporary observatory and active source flow observatory 53268

Table 1 Experimental excitation conditions

In comparison to the single airgun in the well, the airgun array has the characteristics of high energy, low main frequency and long propagation distance. This paper mainly uses the reservoir excitation signal to analyze the correlation and travel time, and uses the pre-excitation experimental data recorded by the sta06 instrument (68 guns) to analyze the characteristics of excitation signals in reservoirs and wells under different excitation conditions. Due to the large error of some QS-05 portable digital seismograph GPS timing system, this paper uses the data recorded by the original mobile observation network to calculate and analyze the travel time variation.

2 CHARACTERISTICS AND CORRELATION ANALYSIS OF AIRGUN SIGNALS UNDER DIFFERENT EXCITATION CONDITIONS 2.1 Phase Characteristics of Airgun Signals

Due to the mechanical delay of the airgun console and other factors, the recorded excitation log is different from the actual firing time of the airgun. The recorded data and the excitation log are combined with the recorded data and excitation log from the reference station sta06, the Z components of the first reservoir and well excitation signals recorded by the sta06 are respectively taken as the template to obtain an accurate excitation time otime with the cross-correlation method (Zhang Yunpeng et al., 2017) on the basis of the otime excitation event waveform. In order to analyze the characteristics of the "airgun wavelet" under different excitation conditions, the signals under the same excitation conditions recorded by the sta06 are linearly superimposed, and the "airgun wavelet" corresponding to the excitation condition is represented by the superimposed signal, and under various excitation conditions. The signal is initially aligned and analyzed.

Taking the signal under the normal excitation condition (p=15MPa, h=10m) as an example, the frequency of the signal recorded in the reservoir and well recorded by sta06 is shown in Fig. 2, where: (a) is the reservoir excitation signal and its frequency characteristics, (b) is the excitation signal and its frequency characteristics in the well. The hydrophone installed near the air gun array can clearly record the airgun wavelet (Xia Ji, 2017). In the experiment, the reference station sta06 is located on the bedrock, and the epicenter distance is much larger than the bubble radius. Therefore, the sta06 record signal and near the airgun wavelet recorded by the field hydrophone is more complicated than the phase. The "airgun wavelet" recorded by sta06 includes high-frequency pressure pulses (30-70Hz) and low-frequency (2-6Hz) bubble pulses, and also includes some signal components between the two frequencies (8-30Hz). Hu Jiupeng et al. (2017) believe that this part of the signal may be formed by repeated reflections of wavelets caused by irregular water shapes. The excitation signal in the well is limited by the small energy of the single airgun and the insufficient bubble oscillation environment in the well. There is no obvious pressure pulse and bubble pulse phase like the reservoir excitation wavelet, the duration is shorter, the overall frequency is higher, and the frequency is lower focusing on 10-15Hz.

Fig. 2 The waveform and time frequency of the sta06 recording signal at working pressure of 15MPa and depth of 10m

Fig. 3 is the amplitude normalized signal excited by the same working depth h and the different working pressure p recorded by sta06. Combined with the pressure pulse and bubble pulse frequency and phase information of the signals in Fig. 2 and Fig. 3, when the same h, the change of p has little influence on the pressure pulse phase of the reservoir excitation signal, and has a great influence on the bubble pulse phase, and the bubble pulse oscillation period as the increase in p increases significantly. The excitation signal in the well has no obvious bubble pulse, but the first three positive phases with larger amplitude of the signal under the same h are less affected by p, and the latter part of the signal is sensitive to the change of p, showing the same as the reservoir excitation signal.

Fig. 3 Comparison of the same sinking depth and different working pressure excitation signals in the reservoir and well (a) are signals at h=8m, 10m and 12m in the reservoir, respectively, (b) are signals in h=8m, 10m and 12m in the well, the black, blue, and red signals indicate p=9MPa, 12MP and 15MPa, respectively

Fig. 4 shows the airgun signals excited by the same p and different h recorded in sta06. It can be seen from Fig. 4 that the change of h not only affects the bubble pulse of the reservoir excitation signal, but also the slight change of the pressure pulse and its subsequent wave train and amplitude. The second half of the excitation signal in the well is greatly affected by h. The first three positive phases with larger amplitude also change with h.

Fig. 4 Comparison of excitation signals of the same pressure and different depths in the reservoir and well (a) are signals at p=9 MPa, 12 MPa and 15 MPa in the reservoir, and (b) are the signals at p=9MPa, 12MPa and 15MPa in the well. The black, blue, and red signals indicate h=8m, 10m and 12m, respectively

Fig. 5 shows the signals before and after the displacement of the airgun array recorded by sta06. When the airgun array generates displacement, the signal changes slightly, mainly in the amplitude of the pressure pulse and the phase of the subsequent wave train. The phase of the bubble pulse does not change much. The effect of displacement changes on the phase of the signal has a much smaller effect than the change in p and h.

Fig. 5 Comparison of different displacement excitation signals by the same pressure and depth Black, blue and red signals for s=0m, s=-7m (south shift) and s=+7m(north shift)
2.2 Airgun Signal Correlation Analysis

The signal-to-noise ratio of the excitation signal in the same epicenter is higher than that in the well. The correlation of the Z-component of the reservoir excitation signal with less time error and the lack of time-shifting is determined by 8 instruments such as sta12.

The cross-correlation function ρxy of the two energy finite signals x(t) and y(t) is defined as:

$ \rho_{x y}(\tau)=\int\limits_{-\infty}^{\infty} x(t) y^{*}(t-\tau) d t $ (1)

τ is the time delay, and y*(t-τ) is the complex conjugate of y(t-τ). The selected 68 gun original signals of each station are stacked as the reference signal of the station, and the single gun signal is cross-correlated with the reference signal to obtain the maximum cross correlation value. At the same time, other stations' signal perform a frequency domain water level deconvolution operation with sta06's signal (Helmberger D. et al, 1971; Zhai Qiushi et al., 2016; Wang Baoshan et al., 2018), get the approximate Green's function, and carry out the corresponding frequency band filtering to improve the signal-to-noise ratio after superposition and cross-correlation operations.

Fig. 6 shows the cross-correlation results before and after deconvolution of different station signals. The excitation conditions and corresponding serial numbers are shown in Table 1. Among them, the black solid circle is the cross-correlation value of the original signal under different excitation conditions, and the gray five-pointed star is the cross-correlation value of the post deconvolution signal. It can be seen from Fig. 6 that the cross-correlation values of the signals of different excitation conditions of the same station are quite different, and the correlation values of the signals are close under the same excitation conditions, and the change of the excitation conditions can be expressed by the correlation coefficient of the signals. The correlation coefficients of different station signals are not the same. The correlation coefficients of some station signals are very sensitive to the excitation conditions. For example, the signals of sta13, sta28 and sta30 can almost reflect the changes of all excitation conditions. The correlation coefficients of some station signals of different excitation conditions are not much different. For example, the 22-31 airgun pressure p is increased from 9MPa to 12MPa, but the correlation coefficients of the sta12, sta15 and sta22 signals are less different. According to the position of the station, it may be related to the media below the station and the station's azimuth. The overall correlation of the signal after deconvolution is improved, and the signal difference caused by the excitation condition is significantly reduced. The correlation coefficient of the signal of different excitation conditions before deconvolution fluctuates greatly, and the correlation coefficient of the signal after deconvolution is flat as a whole.

Fig. 6 Comparison of signal correlation coefficients before and after deconvolution

The correlation coefficient of the deconvolution signal of the sta12 is lower than that of the original signal, but the correlation coefficient of the whole signal after deconvolution is reduced. The correlation coefficient of other stations' deconvolution signals is significantly higher than that of the original signal, and the sta13 deconvolution signal is almost indistinguishable from the original signal. Deconvolution enhances the similarity of airgun signals and reduces the effects of excitation conditions on the signal.

3 USING DECONVOLUTION AND PAIR DIFFERENCE METHOD TO CALCULATE THE CHANGE OF THE MEDIUM TRAVEL TIME

Deconvolution can eliminate the influence of the source to a certain extent and improve the similarity of the airgun signals. Wang Baoshan et al. (2018) proposed that the use of deconvolution signals for the travel time variation can reflect the change of the medium and calculate the change of the travel time of the airgun signals on the basis of the interference method of cross-correlation delay detection. However, the deconvolution operation process has low stability and reduces the signal-to-noise ratio of the signal. Huang Yilei et al. (2017) proposed the pair difference method to calculate the travel time variation without losing the signal-to-noise ratio of the signal. In this paper, the deconvolution and pair difference method are used to calculate the travel time variation of the same airgun signal, and the calculation results of the two methods are briefly compared and analyzed.

3.1 Cross-correlation Delay Detection

For the seismic signals x(t) and y(t), if the wave forms are highly similar and there is only a delay τ in time, the delay τ can be obtained by calculating the correlation coefficient function of the two signals. The calculation method of the delay correlation coefficient is:

$ {R_{xy}}(\tau) = \frac{{\int\limits_{t - \frac{T}{2}}^{t + \frac{T}{2}} x (t)y(t - \tau){\rm{d}}t}}{{\sqrt {\int\limits_{t - \frac{T}{2}}^{t + \frac{T}{2}} {{x^2}} (t){\rm{d}}t\int\limits_{t - \frac{T}{2}}^{t + \frac{T}{2}} {{y^2}} (t){\rm{d}}t} }} $ (2)

Where T is the length of the selected time window, and τ and t are the instantaneous times of the signal. The maximum value of the correlation coefficient Rxy(τs) corresponds to the time τs which is the time delay of the two signals.

3.2 Deconvolution Calculation of Travel Time Changes

The seismic signal x(t) recorded by the station is usually composed of the source function s(t), the instrument response function i(t), the Green's function g(t), and the noise function n(t):

$ x(t)=s(t) * g(t) * i(t)+n(t) $ (3)

"*" indicates convolution. In order to get the media time change, we need to remove s(t), i(t) and n(t) to get the Green's function g(t). In the actual processing, the noise function n(t) is difficult to completely eliminate, so it is ignored first. x(t) is removed from the instrument response function i(t) to obtain u(t), and then deconvolutes s(t) to obtain g(t).

The deconvolution process in the time domain is cumbersome. In this paper, the frequency domain level deconvolution method proposed by Helmberger D. et al., (1971) is used to transform the time domain signal by Fourier transform to obtain the seismic signal U(ω), the source function S(ω) and Green's function G(ω) in the frequency domain. According to the value of S(ω), selecting an appropriate level threshold α, increasing S(ω) smaller than the threshold to α, and then performing simple division to obtain G(ω). Then, G(ω) is inversely transformed by Fourier to obtain the approximate Green's function g(t) of the time domain. The calculation method is:

$ G(\omega)=\frac{U(\omega) S^{*}(\omega)}{max \left\{S(\omega) S^{*}(\omega), \alpha max \left\{S(\omega) S^{*}(\omega)\right\}\right\}} $ (4)

S*(ω) is a complex conjugate of S(ω). Then using the interferometric method based on cross-correlation delay detection (Wang Baoshan et al., 2008; Liu Zifeng et al., 2015), the signals to be tested are correlated with the template signals to obtain the time delay of each signal and the travel time variation trend of all signals.

3.3 Pair Difference Method to Calculate Travel Time Changes

The pair difference method is proposed to maximize the signal-to-noise ratio of the signals. Huang Yilei et al. (2017) believe that the source function s(t) and the seismic signal x(t) contain the same source change information. The interference method is used to directly calculate the travel time changes of x(t) and s(t), respectively, and then use the travel time variation dtx of x(t) minus the travel time variation dts of s(t) to remove the influence of the source and obtain the transit time change dt of the medium. The process is as follows:

$ \mathrm{d} t=\mathrm{d} t_{x}-\mathrm{d} t_{s} $ (5)
3.4 Data Processing and Calculation Results

Due to the GPS timing error of some instruments in the intensive excitation experiment, in order to eliminate the interference of the instrument itself, we use the signal of the Binchuan mobile observing network to calculate the travel time variation. Zhang Yunpeng et al. (2017) analyzed the GPS errors of several reference stations at the transmitting base, all of which are within dozens of μs, far smaller than the dozens of ms of the travel time change. There is no obvious time shift in the data of the selected mobile stations. It is considered that the GPS of the selected stations is accurate. It can be seen from the foregoing that the pressure pulse and its subsequent wave train are less affected by the excitation conditions, and the band-pass filtering of the Z-component signal of the 200 Hz channel recording at the CKT0 is performed at 8-70Hz, with p=15MPa, h=10m, and with no displacement, the signal pressure pulse and its subsequent wave train are excited to obtain the excitation time. At the same time, station 53268 with less interference (the epicenter distance is 6km, as shown in Fig. 1) is selected to calculate the travel time change. In the calculation of the travel time variation of the signals at the station 53268, the time-frequency analysis of the signals recorded at the station 53268 is first performed and filtered according to the frequency range of the airgun signals. The mean and linear drift of the CKT0 signal are removed, and then the CKT0 signals are deconvolved using the processed 53268 signals. The time delay detection of the cross-correlation is used to calculate the travel time changes of the 53268 signals and CKT0 signals before and after deconvolution. The pair difference travel time variation is obtained by the subtractions of the travel time changes of the CKT0 signals from the travel time changes of the 53268 signals before the deconvolution.

Fig. 7 shows the 53268 signals before and after the deconvolution. The first three signals are the templates by stacking all the signals before the 53268 deconvolution. The last three signals are the templates of all the Green's function after the deconvolution (dec). According to the epicenter distance and the velocity structure of the Binchuan area (Chen Siwen et al., 2016), the red line window is P-wave, and the blue line window is S-wave.

Fig. 7 Schematic diagram of P-wave and S-wave phases before and after the deconvolution of the 53268 signals

In this paper, the travel time variation of the P-wave and S-wave before and after the deconvolution of the signals at the 53268 is calculated. At the same time, according to the time-frequency characteristics of "airgun wavelet" in Fig. 2, the CKT0 signals are divided into pressure pulse and bubble pulse, and their travel time changes are calculated separately, as shown in Fig. 8 as the experimental excitation condition change and the travel time variation result. The P-wave and the S-wave dt trend of the signals before the deconvolution are consistent. The working pressure p decreases, dt decreases (dv increases), and vice versa. dt is positively correlated with p change. The sinking depth h becomes shallower, dt increases (dv decreases), and vice versa. dt is negatively correlated with h change.When the displacement s changes, dt fluctuates, but the change trend is not obvious enough for p and h. It may be because p and h after s change are consistent with p and h of the template signal, and the signal changes are small. When the excitation moment is obtained by the correlation, the travel time difference caused by s is greatly reduced. The change trend of the bubble pulse dt is consistent with the trend of the dt change of P-wave and S-wave before the deconvolution at the 53268. The change trend of the pressure pulse E-component dt is consistent with the bubble pulse change, but the value is significantly smaller than the bubble pulse dt. Compared with the E-component, the N-, Z-components of the pressure pulse have stable travel time and there is no obvious change as in the E-component of the pressure pulse.

Fig. 8 Calculation results of excitation conditions and travel time changes

The results of the pair difference method show that the travel time difference between the body wave and the bubble pulse is greater than the travel time difference between the body wave and the pressure pulse. Except for the large travel time variation fluctuation between the E-component of the P-wave and the bubble pulse, the other pair difference method results all show the change in the excitation conditions. The pair difference method does not eliminate the influence of the excitation condition. The results of the deconvolution travel time variation show that the E-component dt is related to the change of excitation condition. The N-component of dt is affected by the excitation condition except for some periods (about 60 shots), but most other periods are independent of the change of the excitation condition. The Z-component of dt is irrelevant to the excitation conditions. The pair difference method cannot eliminate the influence of the excitation condition, and the deconvolution cannot completely eliminate the excitation condition either. But the deconvolution effect is obviously better than the pair difference method, and the Z-component dt cannot see the influence of the excitation condition.

4 DISCUSSION AND CONCLUSION 4.1 Discussion

In this paper, the characteristics of the "airgun wavelet" waveform under different excitation conditions are analyzed by using the Binchuan airgun source intensive excitation experimental data. The results show that the effect of the depth of sinking on the phase of the pressure pulse and its subsequent wave train is greater than the influence of the working pressure on it. Bubble pulses are sensitive to changes in sinking depth and working pressure. The change of "airgun wavelet" is related to the difference of the bubble pressure, bubble radius and water body pressure excited in different sinking depths and under different working pressures (Xia Ji, 2017). At the same time, according to the signal characteristics of different sinking depths, the phase change may also be related to the difference in the boundary reflection distance of the reservoir bottom and the water surface. When the airgun array is displaced, the overall signal change is small. After the amplitude is normalized, the phase and amplitude of the signals moving southward are basically the same with those of the pre-displacement signal. The signals moving north, compared with the pre-displacement signals, have subtle changes in the amplitudes of the pressure pulse and its subsequent wave train, but the other amplitudes and phases are basically the same. The depths of different positions in the bottom of the Dayindian Reservoir are different (Wang Bin et al., 2015, 2016). Therefore, the signal difference before and after the displacement may be related to the difference between the distance between the airgun arrays and the water bottoms in different positions and the distance between of the airgun arrays and the CKT0 station.

The influence of the deconvolution operation on the correlation of airgun signals is analyzed. The results show that deconvolution can reduce the signal difference caused by the excitation conditions and further improve the correlation of airgun signals. In this paper, wave filtering is done before and after the deconvolution process. In order to investigate whether the correlation of the signal after the deconvolution is caused by filtering, we select the signals of the sta12, sta13 and sta15 in the above analysis, filter after the spectrum respectively. We calculate the correlation of the signals before and after the filtering and after the deconvolution as shown in Fig. 9. The results show that the correlation between the sta13 and sta15 signals after the filtering is improved, but much lower than the correlation coefficient of the signals after the deconvolution. Except for the 55th gun signal the correlation of the sta12 signals after the filtering is improved, but the other signals are not much improved compared with the original signals, and most of the signal correlation coefficients are smaller than the correlation of the deconvolved signal. Therefore, deconvolution can improve the similarity of the signal, and this improvement is not completely caused by the noise reduction process such as filtering before deconvolution.

Fig. 9 Comparison of signal correlations before and after filtering and deconvolution The black dotted line, gray dotted line and gray solid line indicate the correlation coefficient of the original signal, filtered signal and deconvolved signal, respectively

Based on cross-correlation delay detection and interferometry, we discuss whether the difference between the pair difference method and the deconvolution method can eliminate the interference of the excitation condition in the calculation of travel time change. The results show that the difference between the pair difference method and the deconvolution cannot completely eliminate the excitation condition influence, but the effect of excitation conditions after deconvolution is significantly reduced. We perform multivariate regression analysis of all travel time changes dt and excitation conditions as shown in Fig. 10. In the figure, "P-pr", "P-bu" and "S-pr" respectively represent P-wave and pressure pulse, P-wave and bubble pulse and the difference dt between the S-wave and the pressure pulse. In the paper, the difference between the P-wave dt and the bubble pulse dt of the 53268 signal component E and the excitation condition change trend (Fig. 10(a)) is large and the multivariate regression results have the lowest correlation. The correlation coefficient between other pair difference method result and the regression results of the excitation condition is high, and the regression curve has the same shape. The overall displacement has the least influence on dt. We average the results of the multivariate fitting of the pair difference method other than the result of "P-bu"(FIg. 10(a)), and obtain the multiple linear regression equations of the travel time variation dt and the sinking depth h, the working pressure p and the displacement s:

Fig. 10 Comparison of travel time changes and multivariate regression fitting results The red solid line is a multivariate regression fit and the black dotted line is the travel time change. "P-pr" and "P-bu" are the difference between the P-wave and the pressure pulse "pr" and the bubble pulse "bu", respectively, and "R2" is correlation coefficient of the multivariate regression fit, the same with S-wave. "P.dec", "S.dec" are the P-wave and S-wave of the Green Function
$ \mathrm{d} t=(-2.2-3.1 h+2.5 p+0.24 s) \times 10^{-3} $ (6)

The fitting results show that dt is inversely proportional to h, and is proportional to p and s, and the influence of h is greater than the influence of p, and the influence of s is the smallest, which is consistent with the phase information of the "airgun wavelet" recorded by the sta06. The relationship between the travel time variation and the excitation conditions obtained in this paper is different from the conclusions obtained by Zhou Qingyun and Chen Junlei (2018), which mainly reflects in the influence of h on the travel time. By comparison, we found that Zhou Qingyun and Chen Junlei (2018) performed band-pass filtering on the CKT0 signal at the frequency of the bubble pulse before intercepting the data, that is, using the bubble pulse to obtain the excitation time. Therefore, it can be inferred that the selection of the template signal during the data interception also has a certain influence on the change of travel time. Besides the higher correlation between the dt of the E-component and the excitation condition Fig. 10(d), Fig. 10(h), the deconvolution calculation results also show that the dt of the N-component is greatly affected by s, which may be related to the north-south movement of the airgun array, and others have a low correlation with the excitation conditions. The Z-component dt is completely unrelated to the excitation conditions, but the overall fluctuation is large, which may be related to the fact that the excitation conditions change too radically and the airgun signal penetration depth of 53268 is shallow and the atmospheric pressure is relatively large. In reality, h and p are relatively fixed or slow, and the calculation results of the predecessors indicate that such large fluctuations will not occur in the short term (Liu Zifeng et al., 2015). The 47-56 gun signal has a relatively stable change in travel time. The main reason is that these airgun signals have the deepest sinking depth and the highest working pressure, so the airgun array has the highest energy (Xia Ji, 2017) and the highest signal-to-noise ratio. The results of multivariate regression further indicate that the pair difference method cannot remove the travel time change.

The deconvolution cannot be completely removed, but the deconvolution can improve the correlation of the signals and greatly reduce the excitation condition interference, especially in the vertical components.

4.2 Conclusion

In this paper, the phase and correlation characteristics of airgun signals under different excitation conditions in Binchuan are analyzed. The effects of the pair difference between the excitation and the deconvolution method are compared. The following conclusions are drawn:

(1) The pressure pulse is less affected by the excitation condition and can be applied to obtain the excitation moment of the event.

(2) The influence of the sinking depth on the phase and travel time of the airgun signals is slightly greater than the change of the working air pressure. The influence of the displacement change can be eliminated by the cross correlation or deconvolution in the vertical signals, but it is difficult to completely eliminate in the horizontal signals. The airgun array should have the consistent excitation condition as much as possible during the excitation.

(3) The change of excitation condition can be expressed by the correlation coefficient of the signals. Deconvolution significantly reduces the signal difference caused by the excitation condition and improves the correlation of the signals.

(4) When the pair difference method is used to calculate the travel time change, the influence of the excitation condition in the travel time variation cannot be eliminated. Although the deconvolution method cannot completely remove the influence of the excitation condition, the travel time variation after the deconvolution is significantly reduced by the excitation condition, especially in the vertical components.

The calculation of travel time variation has important reference value for the space-time evolution of medium. In actual conditions, the excitation conditions are relatively fixed or slow to change. When the airgun is excited, the consistency of the excitation conditions of the source should be kept to the maximum to ensure the calculation accuracy of the time-varying changes. Based on the good feasibility of deconvolution to eliminate the influence of excitation conditions, the travel time variation of the vertical component Green's function can be used as the reference object of medium change.

ACKNOWLEDGEMENT

The authors would like to thank Professor Wang Baoshan from the University of Science and Technology of China for the cross-correlation delay detection program and the data interception program provided by the researcher Wang Weitao from the Institute of Geophysics of the China Earthquake Administration. Thanks to the data provided by the "Active Source Innovation Team" of the Yunnan Earthquake Agency, and to the reviewer for the revised comments.

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