Earthquake Reaearch in China  2018, Vol. 32 Issue (3): 355-366
Analysis of the Frequency Domain Water-level Deconvolution Method Based on Reservoir Airgun Source Data
You Xiuzhen, Li Jun, Lin Binhua, Huang Yandan, Wu Lihua, Guo Yang
Fujian Earthquake Agency, Fuzhou 350003, China
Abstract: Based on the 2016 airgun experimental data of the Fujian Nanyi reservoir, we adopted the frequency domain water-level deconvolution method and cross-correlation time delay detection technique to study the influence of level scaling factor and the background noise level of the station on deconvolution calculation results, and analyze the effect of deconvolution on eliminating the influence of the source caused by different air-gun pressures. The results show that:(1) When the level scaling factor is smaller, the signal to noise ratio of the waveform after the deconvolution is smaller, and when the level scaling factor is over smaller, the identification error of travel time is greater. (2) When the SNR of the station record is higher, the recognition accuracy of travel time is higher, the influence of SNR on the reference station record is far greater than the far station, when the SNR of the far station record is more than 10, the error of travel time is within 6ms, but when the SNR of the reference station record is 30, the travel time error may reach to 20ms. (3) When the airgun source difference is big, the frequency domain water-level deconvolution method has better effect on eliminating the source influence, but the method error may be introduced when the source difference is small.
Key words: Large volume airgun     Water-level deconvolution in frequency domain     Cross-correlation time delay     Green's function

INTRODUCTION

Since the 1960s, airgun source has been widely used in offshore oil exploration, and a wealth of valuable experience has been accumulated. As airgun source technology becomes more and more sophisticated, in order to make it useful in geophysical prospecting, researchers have developed a lower-frequency seismic source-large-volume airgun source, which draws more and more people's attention because of its high excitation energy, abundant low-frequency components, controllability, repeatability, low cost, less destructive effect and non-pollution nature. In recent years, domestic seismic scientists conducted a series of experiments on deep structure detection using large-volume airgun source, such as the experiment of a joint land-sea detection of the Fujian land area and the western part of the Taiwan Straits of China and the experiment of"Yangtze River Geoscience Project", and built earthquake signal transmitting seismic stations in Binchuan of Yunnan Province, Hutubi of Xinjiang and Zhangye City of Gansu Province, in order to monitor changes in the properties of underground media (Chen Yong et al., 2016; Wang Baoshan et al., 2016).

In reservoir airgun source experiments, due to small volumes of reservoirs, high-pressure bubbles produce violent vibrations in reservoirs, with long-term oscillating wavelets at the same time. As a result, airgun source signals excited do not repeat completely, which further affects the monitoring accuracy of changes of underground media. Because the Green's function can reflect the information of underground media in study areas, seismologists proposed a deconvolution method to obtain the approximate Green's function between airgun seismic source and its receiver stations in order to eliminate the influence of seismic source (Wang Baoshan et al., 2012; Luan Yi et al., 2016). Liu Zifeng et al. (2015) and Wei Yunyun et al. (2016) conducted deconvolution treatments to eliminate interferences from the change of seismic source before using airgun source to identify the variation of wave velocity of crustal media. Wang Baoshan et al. (2012), by comparing cross interference and cross correlation methods, believed that although the results of deconvolution have low SNR, it can well remove the influence of triggering environment. Zhai Qiushi et al. (2016) compared the effects of deconvolution in frequency and time domain, pointing out that frequency-domain deconvolution has advantages in computing efficiency, but the SNR is not as good as that in time domain.

Former research focuses on direct processing of data by deconvolution, or the comparison to the effects of other methods. However, there is little research on the problems with the frequency-domain water-level deconvolution method. In this paper, the frequency-domain water-level deconvolution method and cross-correlation time delay detection technique are adopted to study the influence of water-level scaling factors introduced by the deconvolution method, when different values are taken, on the calculation results, and the influence of background noise level of stations on the calculation results, and the effect of deconvolution on eliminating the influence of seismic sources is analyzed.

1 OVERVIEW OF RESERVOIR AIRGUN EXPERIMENTS

In December 2016, the Fujian Earthquake Agency conducted active source detection in Nanjing Nanyi reservoir in Zhangzhou. In the experiment, large-volume airgun source system independently designed and assembled by the Fujian Earthquake Agency was adopted, and a combined array of 4 Bolt-1500LL airguns were used, with the volume of a single airgun of 2, 000in3 and total volume of the array of 8, 000in3. The gun array is 7m×7m in size, with a sinking depth of 12m and 9 times of fixed-point excitation for each working condition test. The experimental observation system is composed of land-sea arrays. The land array incorporates 88 seismic stations in Fujian, some seismic stations around Fujian (Guangdong, Jiangxi, Zhejiang, Hunan and Taiwan, China), 40 mobile stations for real-time transmission and 100 PDS(field mobile stations with non-real-time transmission). The sea array consists of 57 sets of grid arrays formed by OBS. In consideration of the clarity of the airgun signals records, shoreside seismic station L3583 with the epicentral distance of 200m is selected as a near-field reference station, seismic station NJJS with the epicentral distance of 18.53km and seismic station NJNK with the epicentral distance of 19.05km are selected as far-field stations (Fig. 1).

 Fig. 1 Excitation position of airgun in the Nanyi reservoir and distribution of experimental observation stations
2 METHODS AND PRINCIPLES 2.1 The Frequency-domain Water-level Scaling Factor Deconvolution Method

Seismic wave data contains source function, the Green's function between source and seismic instrument, instrument response and ground motion noise, which can be expressed as follows

 $u\left(t \right) = s\left(t \right) * g\left(t \right) * i\left(t \right) + n\left(t \right)$ (1)

where, u(t) is data recorded by seismic instruments, s(t) source time function, g(t) the Green's function, i(t) instrument response, n(t) noise.

We consider signals recorded by the near-field seismic station near air-gun sources as an approximate time function of the source. Because observation instruments are not changed during the experiment, the influence of instrument response is not considered, and the influence of noise is ignored. Records of far-field and near-field seismic stations are respectively treated with Fourier transform, and then are divided to get frequency-domain deconvolution.

 $G\left(\omega \right) = \frac{{U\left(\omega \right)}}{{S\left(\omega \right)}}$ (2)

where, G(ω) represents the frequency spectrum of the approximate Green's function, U(ω) frequency spectrum of airgun records from far-field seismic station, and S(ω) the frequency spectrum of air-gun records from near-field seismic stations. Since the denominator in equation(2) may appear to be zero or approaching zero, the division in the frequency domain is unstable. By using frequency-domain water-level scaling factor deconvolution method proposed by Helmberger et al. (1971), equation (2) is refined, which is described as below.

 $G\left(\omega \right) = \frac{{U\left(\omega \right){S^ * }\left(\omega \right)}}{{\max \left\{ {S\left(\omega \right){S^ * }\left(\omega \right), \max \left\{ {S\left(\omega \right){S^ * }\left(\omega \right)} \right\}c} \right\}}}$ (3)

where, S*(ω) is complex conjugate for S(ω), max represents operator for the maximum value, and c stands for water-level scaling factor.

2.2 The Cross-correlation Time Delay Detection Method

The cross-correlation time delay detection method is a proven technology which is widely used. The principle is to calculate the cross-correlation coefficient of two similar waveforms with different time delays, and the time delay corresponding to the maximum cross-correlation coefficient is the delay of the two waveforms. Cross-correlation time delay measurement is carried out at a sampling interval; however, the peak of the correlation function does not usually fall on the sampling point, but deviates from the sampling point, which can be solved by fitting to obtain time measurement of higher precision (Céspedes et al., 1995). Therefore, the parabola fitting method is used to reconstruct the correlation function, and the peak value of the new correlation function and its corresponding position are obtained (Fig. 2). The formula for calculating the time delay at position of peak value of correlation function before and after fitting is as below,

 $\delta = \frac{{\left({{y_0} - {y_2}} \right)\mathit{\Delta T}}}{{2\left({{y_0} + {y_2} - 2{y_1}} \right)}}$ (4)
 Fig. 2 Parabola fitted curve (The dot is the position of the maximum correlation coefficient after fitting, and the square points are positions corresponding to the adjacent sampling points of the peak value of correlation function before fitting)

where, y1 is the maximum correlation coefficient before fitting, y0 and y2 are respectively correlation coefficients corresponding to adjacent sampling points of the peak value of correlation function before fitting, and △T represents time interval of sampling

3 CALCULATION RESULTS

Take the A09 working condition test of Nanyi reservoir in December 2016 for example, the original waveform is segmented according to the firing time of the airgun, and then the vertical component records are preprocessed by removing mean value, 2Hz-8Hz filtering and normalization. Fig. 3 shows waveforms from reference station L3585 and far-field station NJNK after pretreatment. Because the working condition experiment is less than half an hour, during which there is no influential earthquake and water levels in the reservoir remains basically stable, thus underground media can be regarded as invariable. During the experiment, the floating loading platform with an airgun will deviate with the firing of the airgun, therefore, the staff of the Fujian Earthquake Agency fix the floating platform by means of hanging heavy objects and fastening with ropes, and according to monitoring results of GPS installed on the floating platform, the excitation position changes little, which is basically within 1m. We first analyze the effect of the processing order of deconvolution and superposition on results. Fig. 4 shows the calculation results of NJNK station. Cross correlation of approximate Green's functions calculated in different processing order is performed, and the peak value of cross-correlation coefficient is obtained, which is 0.999, indicating that the processing order of deconvolution and superposition has little influence on the final results, thus, superposition is followed by deconvolution calculation in data processing.

 Fig. 3 Waveforms from station L3583 and NJNK after pretreatment

 Fig. 4 Comparison of approximate Green's functions calculated in different processing order
3.1 The Influence of Water-level Scaling Factors

Water-level scaling factors are introduced into the frequency-domain water-level deconvolution method to obtain a reasonable threshold of water level, and when calculating, spectral amplitudes in the denominator less than the threshold are improved to the threshold level so as to improve the stability of deconvolution calculation results. To explore the influence of water-level scaling factor on the results of deconvolution, in the same circumstances, water-level scaling factors are set as 6 different values, 0.1, 0.01, 0.001, 0.0001, 0.00001 and 0.000001, to compare amplitude SNR of the Green's function after deconvolution, travel time difference of waveform of the Green's function relative to that before deconvolution and the peak value of cross-correlation coefficient of both. Amplitude SNR is the ratio of the maximum absolute value of effective signal amplitude to the mean square root of noise amplitude.

Table 1 shows the amplitude SNRs of the Green's functions, travel-time differences and peak values of cross-correlation coefficients obtained with different water-level scaling factors for NJNK seismic station at A09 working condition, and Table 2 provides calculation results for NJJS and NJNK seismic station under A13 working condition. It can be seen from Table 1 and Table 2 that the amplitude SNRs of the Green's functions decrease with water-level scaling factor, travel-time differences of waveforms of the Green's functions relative to that before deconvolution vary, and peak values of cross-correlation coefficients calculated at different working conditions and stations also vary differently. Fig. 5 shows the deconvolution results with different water-level scaling factors for the NJNK station under A09 working conditions. It can be seen from Fig. 5 that the smaller the water-level scaling factor is, the more background noise there is, and when it is small to a certain value, effective signals are submerged in the background noise. Therefore, when using the frequency domain water-level deconvolution method, appropriate water-level scaling factors should be selected according to actual situations. It can also be seen from Fig. 5 that waveform after deconvolution has a relatively obvious travel-time change compared to that before deconvolution, which is about 0.3s; the reason may be that airgun triggered signals are mainly composed of pressure pulse generated by the air release of the airgun and bubble pulse produced by oscillations of bubbles in water. Pressure pulse is a kind of high frequency signal, with the main frequency ranging from tens to hundreds of hertz, which attenuates fast, and can hardly be recorded by far-field seismic stations, while a bubble pulse is a low-frequency signal, with a main frequency of 3Hz-8Hz, and ground motion caused by bubble pulse propagation is mainly recorded by far-field seismic stations.According to the records of OBS at the bottom of the reservoir beneath the floating platform of the airgun and the records of the hydrophone 2m above the airgun, bubble pulse is generated about 0.2s after pressure pulse, meanwhile, while doing the experiment, since the floating platform is relatively far away from the seismometer on the shore, about 200m, the recording of the seismometer cannot be completely equivalent to the time function of the source. According to records of the floating platform and seismometer on the shore and the speed at which waves travel through water (1.5km/s, because the distance between the airgun and the shoreside seismometer is only 200m, we believe that the waves propagate through water or the upper layer of shallow ground), we can see that it takes about 0.1s for pressure pulse generated by airgun to be transmitted to the seismometer on the shore, and about 0.3s for bubble pulse to be transmitted, that is, when records from shoreside seismometer with an epicentral distance of 200m are used as the approximate time function of the source, a time error of about 0.3s is also introduced, which may be the main reason why travel time of waveform after deconvolution changes by 0.3s in this study. This also indicates that it may not be completely applicable to use records from seismic station 200m away from the airgun source as the time function of the source. However, because observation data from the same station are used in this study, the subsequent analysis and conclusions are not affected.

 Fig. 5 Deconvolution results based on different water-level scaling factors for NJNK station under A09 working condition

Table 1 Comparison of amplitude SNRs of the Green's function, travel-time differences and peak values of cross-correlation coefficients calculated with different water-level scaling factors for NJNK seismic station under A09 working condition

Table 2 Comparison of amplitude SNRs of the Green's function, travel-time differences and peak values of cross-correlation coefficients calculated with different water-level scaling factors for NJJS and NJNK seismic stations under A13 working condition
3.2 The Influence of Background Noise on Results

Before using the frequency-domain water-level deconvolution method to monitor the changes of crustal media, it is necessary to understand influencing factors on the deconvolution calculation results. In this paper, the numerical simulation method is adopted to discuss the influence of background noise on deconvolution calculations by changing background noise level and water-level scaling factors for far-field or reference stations.

In previous studies, random white noise data is often used to simulate changes of noise. In fact, natural noises recorded by seismometers are not absolutely random white noise, but noises with certain changing rules over time and space; therefore, noise data recorded by seismic stations for half a month when the airgun is not fired is collected to simulate the influence of noise changes on analysis results. The collected noise data is extracted every 10min, treated with a baseline correction, 2Hz-8Hz filtering and two heads pinching out, to calculate the standard deviation of each extracted noise, and the results are shown in Fig. 6. It can be seen from Fig. 6 that the noise displays a regular change every day.

 Fig. 6 Daily variation of noise

Calculation steps are as follows: ① Noise data from records of far-field stations after pre-processing is replaced with 0, then extracted noise data is added to the airgun records of the station, and the generated new signals are regarded as records of far-field stations. ②The approximate Green's functions are obtained by deconvolution of new far-field station records and records of reference station (as previously mentioned, water-level scaling factor is 0.001). ③Deconvolution will introduce high-frequency noise, which needs to be filtered again. The frequency band range is 2.5Hz-6Hz. ④ Cross-correlation time delay method is used to calculate daily variations of travel-time error of P waveband (0.5s window length) of approximate Green's function obtained based on different water-level scaling factors with noise. ⑤ SNR recorded by far-field stations is changed, that is, amplitude of extracted noise is changed, to calculate daily variation of travel-time error of the Green's function with noise. ⑥ The reference station follows the same process.

Fig. 7 and Fig. 8 show the daily variation of travel-time identification error of P wavebands of the Green's function with the noise after adding noise and deconvolution for far-field station NJNK and reference station L3583 under A09 working conditions. Fig. 7(a) provides the calculation results obtained based on different water-level scaling factors when the SNR of airgun records from far-field stations is about 49, and Fig. 8(a) shows the calculation results obtained based on different water-level scaling factors when the SNR recorded by reference stations is about 50. It can be seen from Fig. 7(a) and Fig. 8(a) that when scaling factors are the same and the SNRs recorded by far-field and reference stations are not much different, the travel-time error calculated by the former is only a few milliseconds, while the travel-time error recognized by the latter is significantly greater than that of the former, thus we can see that SNR recorded by reference station has a much greater influence on the results than that recorded by far-field stations. In addition, the difference of water-level scaling factors has an impact on travel time of waveform after deconvolution calculation. When the value of water-level scaling factor is too small, travel-time error is big. This study only changes background noise level of seismic stations, air-gun signals are not changed, therefore, the variation of travel time of waveform of air-gun records with different SNRs after deconvolution calculations should be the same in theory, but the results show that the variation of travel time calculated with different SNRs is not the same (Fig. 7(b) and Fig. 8(b)), which indicates that background noise level of stations has a great influence on the results. The higher the airgun SNR is, the higher the accuracy of results. The variation trend of travel-time difference obtained from airgun records with different SNRs at far-field stations is consistent, indicating that all recognized errors are caused by noise. This requires a great deal of effort to eliminate noise effects in formal applications. When SNR recorded by far-field stations is greater than 10, the travel-time error is generally less than 6ms. For records with difference SNRs from reference station, because different SNRs will affect the approximate seismic source function, variation trend of travel time difference obtained shows poor consistency. Besides, SNR recorded by reference station has a greater influence on the identified results of travel time. For records with a SNR of about 30 from the reference station, the travel-time error may reach about 20ms, and for records with a SNR of even about 100 from the reference station, the travel-time error may reach several milliseconds. Moreover, there is no significant correlation between daily variation of travel-time error calculated with different water-level scaling factors and SNR records from seismic stations and daily variation of background noise.

 Fig. 7 Daily variation of P waveband travel-time error with noise after adding noise and deconvolution for far-field seismic stations (a)Different water-level scaling factor; (b) Different SNRs(water-level scaling factor is 0.001)

 Fig. 8 Daily variation of P waveband travel-time error with noise after adding noise and deconvolution for the reference station (a)Different water-level scaling factor; (b) Different SNRs (water-level scaling factor is 0.001)
3.3 The Effect of Eliminating the Source Influence

In order to test the effect of frequency-domain water-level scaling factor method on eliminating the influence of airgun source, deconvolution calculations of records from NJNK seismic station are conducted at working pressure of 1000, 1200, 1500, 1800 and 2000psi(water-level scaling factor is 0.001), and A09 working condition at gun pressure of 1000psi is used as a reference to compare the time delay of waveforms excited at different gun pressure before and after deconvolution.

Fig. 9(a) and Fig. 9(b) provide waveforms of airgun signals at different working pressures before and after deconvolution. Because of high repeatability of airgun source signals, the vertical lines are taken as reference to compare arrival time positions of peak values of all waveforms in waveband of initial seismic phase. It can be seen from Fig. 9 that as the gun pressure increases, there appear a certain differences in the arrival time at peak value positions of waveforms before deconvolution, which is obvious at gun pressure of 2000psi, while after deconvolution, the differences of arrival time at peak value positions of waveforms become small. Time window length is set to be 0.3s, step length 0.2s, to calculate cross-correlation time delay of different wave bands for signals excited at different gun pressure before and after deconvolution compared with that at A09 working condition (Fig. 10). The gun pressure difference between A09 and A10 is 200psi, the time delay of different wave bands of two waveforms before deconvolution is small, which is slightly larger after deconvolution, but both are less than 0.01s (that is, 1 sampling point). Wave band of initial seismic phase before and after deconvolution should be the second time window, time delay calculated in this wave band is the second dot in the time delay graph. The time delay after deconvolution is basically smaller than that before deconvolution, especially at A09 working condition, and the time delay before deconvolution reaches 2 sampling points at A13 working condition, which is significantly shortened after deconvolution. As a result, the frequency-domain water-level deconvolution method can effectively eliminate the influence of seismic sources with big differences.

 Fig. 9 Comparison of waveforms of airgun signals before and after deconvolution at different working pressure

 Fig. 10 Time delay of waveforms of airgun signals excited at different gun pressure before and after deconvolution compared with that at A09 working condition for NJNK seismic station
4 CONCLUSION AND DISCUSSION

In this paper, data from airgun experiments in Nanyi reservoir of Fujian in 2016 is taken as research objects, the effects of water-level scaling factors and background noise of seismic stations on deconvolution results are analyzed to study the effect of deconvolution method on eliminating the influence of seismic source, and the following conclusions and understandings are drawn.

(1) Water-level scaling factors affects the SNR and travel time of waveforms after deconvolution. The smaller the water-level scaling factor is, the lower the waveform SNR is, and when the value of water-level scaling factor is too small, travel-time difference is big. In practical applications, appropriate water-level scaling factors should be selected after analysis.

(2) Background noise of seismic stations has influence on the results of deconvolution calculations. The higher the airgun SNR is, the higher accuracy the results show. When SNR recorded by far-field stations is greater than 10, the travel-time error is generally less than 6ms. For records with a SNR of about 30 from the reference station, the travel-time error may reach about 20ms, and for records with a SNR of even about 100 from the reference station, the travel-time error may reach several milliseconds.

(3) Source effect caused by different working pressure can be eliminated by using frequency-domain water-level scaling factor deconvolution method, and the effectiveness of this method in removing source effect is verified. This method has a good effect on removing source effect when the source difference is big, but it may introduce method error when source difference is small.

In this paper, factors influencing the calculation results of frequency-domain water-level deconvolution and the effect of deconvolution method on eliminating the influence of seismic sources are preliminarily analyzed, and the results can provide references for the application of deconvolution method to the monitoring of crustal media changes with airgun.

REFERENCES
 Céspedes I., Huang Y., Ophir J. Methods for estimation of subsample time delays of digitized echo signals[J]. Ultrasonic Imaging, 1995, 17: 142–171 . DOI:10.1177/016173469501700204. Chen Yong, Wang Baoshan. Preface to the special issue on advances in seismic exploration and monitoring with active sources in China[J]. Earthquake Research in China, 2016, 30(3): 281–283 . Helmberger D., Wiggins R R.A. Upper mantle structure of mid-western United States[J]. J Geophys Res, 1971, 76(14): 3229–3245 . DOI:10.1029/JB076i014p03229. Liu Zifeng, Su Youjin, Wang Baoshan, et al. Study on analysis method of travel time variations of seismic wave of active source in Binchuan[J]. Journal of Seismological Research, 2015, 38(4): 591–597 (in Chinese with English abstract). Luan Yi, Yang Hongfeng, Wang Baoshan. Processing of waveform data of large-volume air-gun sources (1): Yunnan Binchuan[J]. Earthquake Research in China, 2016, 32(2): 305–318 (in Chinese with English abstract). Wang Baoshan, Ge Hongkui, Wang Bin, et al. 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 Baoshan, Yang Wei, Wang Weitao et al. Un-blur the Signature of Large Volume Airgun Excited in a Reservoir with Deconvolution [C]. In: The Geophysical Society of China(Editor).Abstract Proc. 28th Annual Conference of the Geophysical Society of China [G]. Beijing: China Academic Journals (CD Edition) Electronic Publishing House Co., Ltd., 2012 (in Chinese with English abstract). Wei Yunyun, Wang Haitao, Su Jinpo, et al. A preliminary study on the abnormal variation of reflection traveltimes of airgun sources before two moderate-strong earthquakes in Xinjiang[J]. Earthquake Research in China, 2016, 32(2): 270–281 (in Chinese with English abstract). Zhai Qiushi, Yao Huajian, et al. Study on the deconvolution method and processing flow of airgun source data[J]. Earthquake Research in China, 2016, 30(3): 394–404 .