2 Institute of Earthquake Science, China Earthquake Administration, Beijing 100036, China
China has the largest number of reservoirs in the world. Up to the end of 2011, China had 97, 246 reservoirs with reservoir capacity of 121.9 billion m^{3} (Sun Zhengang et al., 2013). China is also one of the reservoir earthquake-prone countries. Reservoir earthquakes have occurred in the earthquake-prone regions of Sichuan and Yunnan where a lot of high dams and large reservoir capacity cascade hydropower stations have been built. The issue of large reservoir induced earthquakes is drawing more attention from seismologists. After the Wenchuan earthquake, the Zipingpu reservoir and its special temoral and spatial relations with the earthquake have drawn a lot of attention (Lei Xinglin et al., 2008; Shemin et al., 2009; Ma Wentao et al., 2011; Deng et al., 2010; Lu Xian et al., 2010). Lei Xinglin et al. (2008) believes that the Zipingpu reservoir has a clear effect on the underground Longmenshan central fault and mountain front fault during its impoundment. Shemin et al. (2009) believes that the increase of Coulomb stress after the impoundment is sufficient to induce the earthquake. Ma Wentao et al. (2011) believes that there is a certain relationship in time and space between the Wenchuan earthquake and the Zipingpu reservoir. Deng et al. (2010) believes the M-t graph of the surrounding area of the Zipingpu reservoir shows no enhancement and the reservoir water cannot permeate to the Wenchuan earthquake focal depth of 14km. Lu Xian et al. (2010) believes that there is no relationship between the Dujiangyan earthquake swarm and the Zipingpu reservoir. Regardless of results, there is a consensus that reservoir impoundment has some effect on the underground medium, and the study of the reservoir region medium and stress field changes based on digital seismic data is an effective method. There is currently a lot of research on the relationships between reservoir water level changes and reservoir region earthquakes and between reservoir region medium changes and reservoir earthquakes (Zhou Bin et al., 2010; Wang Xian et al., 2013), but there is little research on the relationship between reservoir water level changes and reservoir medium variations. This paper uses continuous waveform data from the digital earthquake network at the Zipingpu reservoir and noise correlation technology to study the influence of the velocity of the reservoir underground medium by the loading and unloading of the reservoir water and its permeation, with a hope of further understanding the reservoir underground structure and state and its dynamic process.
1 GENERALITIES OF THE ZIPINGPU RESERVOIR AND THE EARTHQUAKE NETWORKThe Zipingpu reservoir is located at Maxi town, 9km northwestern of Dujiangyan, Sichuan, on the upper reaches of the Minjiang river. The reservoir is about 60km from the city of Chengdu and 6km in the shortest distance from the micro epicenter of the Wenchuan M_{S} 8.0 strong earthquake. Construction of the Zipingpu reservoir started on March 29, 2001, and was completed in December, 2006. The height of the dam is 156m and the total reservoir capacity is 11.12×10^{8}m^{3}. This paper uses the water level data provided by the Reservoir Seismic Research Institute of Sichuan Earthquake Administration to draw water level changes of the Zipingpu reservoir (Fig. 1). Fig. 1 shows that the reservoir started impoundment on September 30, 2005, and several days later, the water level rose rapidly to the dead water level of 817m. After the impoundment, the highest water level reached 875.18m. From September 30, 2005 to the end of 2007, the Zipingpu reservoir had 3 large scale impoundments and 2 disemboguements. On December 5, 2005 the water level reached 835.91m. On October 14, 2006, the water level reached the highest point of 875.18m. On December 12, 2007 the water level rose to 873.39m again.
The Zipingpu reservoir is located the middle section of the Longmenshan orogenic belt on the eastern edge of the Qinghai-Tibetan Plateau. The main stem fault divides the reservoir region and its adjacent areas into the Maowen tough shear zone, the central nappe structural belt, the detachment zone on the front edge of Longmanshan, the foreland extended deformation belt and the western Sichuan foreland basin. These five geological structural units are obviously different from each other in terms of material composition, structural layers and deformation modes. The body of the Zipingpu reservoir is located within the detachment zone on the front edge of Longmenshan near the central nappe structural belt and the foreland deformation belt (Zhou Bin et al., 2010). The underground water of the reservoir is made of two types: fissure-pore water of clastic rock and karst water of carbonate rock (Fig. 2). As is shown in Fig. 2, the main rocks in the reservoir region are carbonate rock in the southeast and clastic rock in the northeast with some parts being carbonate rock.
The digital earthquake remote monitoring network of the Zipingpu reservoir started to collect seismic information on August 16, 2004 and was accepted on June 27, 2005 (Hu Xianming et al., 2006). The network includes 7 digital remote monitoring stations, using short term earthquake instruments with a frequency bandwidth of 1-40Hz. The network also shares data from the Youzhaping station (YZP) of Sichuan Regional Digital Seismic Network. The 8 stations are evenly distributed around the reservoir with the average interval of 14km. Fig. 3 shows the distribution of the stations. Table 1 shows the stations and the instrument parameters.
This paper uses the continuous waveform data of vertical components from the Zipingpu earthquake network and YZP with the time range from January 1, 2005 to January 1, 2008. Fig. 4 shows the continuous records of the stations. The usable data days are 1003 and the longest continuous empty time is 27 days.
The principle of the measurement of the continuous changes of underground medium velocity in terms of ambient noise is the comparison between the empirical Green function (CCFs) and reference Green function (REF). CCFs represents the state of underground medium in a time period, while REF represents the background state of the underground medium. The calculation includes 4 steps: (1) calculate the noise cross-correlation function of different stations in different time periods, i.e. empirical Green function (CCFs), (2) obtain reference Green function (REF) and calculate the travel time delay between each CCFs and REF, (3) average the travel time delay of different time lag in the stations and use a simple model of seismic velocity homogeneity (Δ v/v =constant) (Lecocq et al., 2014) to represent the underground medium velocity changes.
The paper uses MSNoise for the data processing (Lecocq et al., 2014). This software, used in research on the Aukland volcanic area (Kasper, 2014) and the pre-earthquake and post-earthquake research (Berkeley Seismological Laboratory, 2014) has achieved reliable results.
3.1 Extract Empirical Green Functions CCFs from Noise Cross-correlation 3.1.1 Pretreatment of a Single StationThe research is about the fine velocity change of the reservoir underground medium, and the key is whether a stable and reliable CCFs can be obtained. First of all, we must obtain the pure ambient noise via pretreatment to ensure the quality of CCFs. The continuous waveform data of each station each day is collected into a file before the pretreatment which includes: de-meaning, taper, highpass and lowpass filtering, downsampling, temporal normalization and spectral whitening. Usually, waveform data has a nonzero average which will affect the data analysis. To normalize the data to suit the various standard equations, it is necessary to de-mean before the data analysis (Zheng Zhizhen, 1979). Besides in the data spectral domain processing such as FFT and filtering, if the ends of the data are not zero, there will be spectral domain illusion. In actual processing we need to taper the data so that the ends of the data will gradually turn to zero in the short time windows. The current study concerns the velocity change of the superficial medium of the reservoir, and attention is paid to the data of higher frequency, so we therefore select filtering parameters of 0.1-2.0Hz. To reduce the calculation work and storage volume, the data is downsampled to 10Hz. To reduce the seismic signal and instrumental anomalies and the influence of nonstable noise source in the vicinity of the stations, we normalize the data in time domain (Tukey, 1962). For a more even distribution of the signal energy in different frequencies, we perform spectral whitening of the data.
3.1.2 Extract Empirical Green Function by Cross-correlation CalculationThe idea of extracting underground structure information from ambient noise can be traced back to the 1950s and 1960s. Aki (1957) believed that surface wave dispersion in an underground structure could be extracted from ambient noise; Claerbout (1968) proposed to use ambient noise to restore the reflective response in one-dimension medium. The first successful application of the similar idea was in the research of solar seismology when time-distance curve was successfully extracted with the help of cross-correlation calculation of the solar surface noise (Duvall et al., 1993). After that, noise cross-correlation technology gained significant progress in the ultrasonics domain. Weaver et al. (2001) defined the cross-correlation features of random wave fields, that is, the computation of the earth elastic response via the extraction of the Green function from the divergent or random wave field. An example to prove this feature is the divergence field model in an elastomer.
$\varphi \left( x, t \right)=\sum\limits_{n}{{}}{{a}_{n}}~{{u}_{n}}~\left( x \right)\text{ }{{e}^{i{{\omega }_{n}}~t}}$ | (1) |
where x is the position of the spot; t is the time; i is unit of imaginary number, a_{n} is a modal excitation function; u_{n} and ω_{n} are the earth intrinsic equation and intrinsic frequency. One of the important divergence field features is that modal amplitude is an irrelevant random variable.
$\langle {{a}_{n}}~a_{m}^{*}\rangle ={{\delta }_{nm}}~F\text{ }({{\omega }_{n}})$ | (2) |
where δ_{nm} is Kronecker function; F is the spectrum energy density. The cross terms in equation (2) disappeared in averaging, and therefore the co-relationship of x and y in the field is simplified as
$C\text{ }\left( x, y, \tau \right)=\sum\limits_{n}{{}}F\text{ }({{\omega }_{n}})\text{ }{{u}_{n}}~\left( x \right)\text{ }{{u}_{n}}~\left( y \right)\text{ }{{e}^{-i{{\omega }_{n}}~\tau }}$ | (3) |
where τ is time lag. The comparison reveals that equation (3) is only one amplitude factor F different from the real Green function of x and y. Therefore on the basis of long time relationships between the fields, two point Green function can be extracted from the divergence field, and this is the theoretic basis for noise imaging. Subsequently, the method has developed rapidly in the fields of ocean acoustic study (Roux et al., 2004) and seismology (Shapiro et al., 2004, 2005).
Mathematically, the cross-correlations of frequency domain and time domain are equivalent to each other. If the Fourier transform of the two series x (t) and y (t) are X (f) and Y (f) respectively, then the cross-correlation equation of the frequency domain is
$C\text{ }(f)=X*(f)\text{ }\times \text{ }Y\text{ }(f)$ | (4) |
where X*(f) is the complex conjugate of X*(f), and the Fourier inversion of C (f) is the cross-correlation c (t) of the time domain.
This paper divides up one day's data into 48 sections × 30min (50% superposition), conducts cross-correlation calculation of the data in each section of each station pair in the frequency domain, and superposes them to form the daily empirical Green function CCF. In the velocity measurement, there will be strong changes caused by weak correlativity between CCF and REF, and we thus set up moving-windows of 10, 30, 50 days respectively and superpose them to get CCFs so as to improve the correlation for a more reliable velocity change. Fig. 5 shows the energy interference graph of the 50-day superposed moving-windows of the empirical Green function extracted via the cross-correlation in the case of BAJ-GHS pair, as well as the correlation coefficient curve between CCFs and REF in moving-windows of different lengths. It can be found in Fig. 5 that there are obvious dithers of the cross-correlation coefficient in 10 day moving-window, and the cross-correlation coefficient curves in 30-day and 50-day moving-windows are smooth and show significant changes.
In order to study the influence of the reservoir water level on the medium velocity of different depths and analyze the effect of the water level pressure and permeation, we conducted three period calculations of 1-2s (0.5-1.0Hz), 2-4s (0.25-0.50Hz), and 4-8s (0.125-0.250Hz) respectively.
According to the characteristics of the Rayleigh surface wave (Fig. 6), the waves of the above three periods are sensitive to the media with depths of 0-2km, 1-4km, and 1-8km respectively.
There are two methods to obtain the reference Green function REF: the absolute superposition method and relative superposition method (Lecocq et al., 2014). As the changes of the underground medium velocity by the reservoir impoundment were not strong, we selected the superposition method, i.e. superpose all CCF to make REF. Fig. 7 shows the reference Green functions obtained from the 28 pairs of stations. Reverse superpositions are done for the convenience of display.
This paper calculates the relative travel time changes via moving-window cross-spectrum. The method was proposed by Ratdomopurbo et al. (1995) and was first used by Poupinet et al. (1984) in the research of the seismic velocity changes in earthquake pairs. The advantage of the method is the calculation is in the frequency domain and can determine the bandwidth of the signals concerned in the functions. Brenguier et al. (2008a, 2008b) used this method to study the relative seismic velocity changes of the underground medium of the Fournaise volcano in France and the relative seismic velocity changes of the underground medium along the San Andreas fault before and after the Parkfield M_{S} 6.0 earthquake in 2004. Clarke et al. (2011) described in detail the principle and procedures of the moving-window cross-spectrum method and proved the resolution and precision rates of the method in monitoring velocity changes.
First, we divide up the CCFs and REF into a number of superposed windows, then de-mean and taper them. Finally, we conduct the Fourier transform to obtain F_{cur} (f) and F_{ref} (f). Cross-spectrum X (f) is defined as
$X~(f)=~{{F}_{\text{ref}}}~(f)\times ~F_{\text{cur}}^{*}(f)$ | (5) |
where f is the frequency, and the asterisk stands for complex conjugacy. In frequency domain, the similarity of the two series is assessed via the correlation coefficient C (f) of the energy density. From equation (5), we can induce
$X~(f)=\left| X~(f) \right|e{{~}^{i}}^{\varphi }{{~}^{(}}{{~}^{f}}{{~}^{)}}$ | (6) |
where φ(f) is the unwrapping phase and has a linear ratio with the frequency f,
$\varphi j~=2~\text{ }\!\!\pi\!\!\text{ }\Delta ~t{{f}_{i~}}, ~\text{while }\!\!~\!\!\text{ }\ m=2~\text{ }\!\!\pi\!\!\text{ }\Delta ~t, \text{ }\!\!~\!\!\text{ then}\ ~{{\varphi }_{j}}~=m\cdot {{f}_{i}}$ | (7) |
For different frequencies f and phases φ, m can be obtained via weighted linear regression with corresponding residue e_{m} and weight w_{j}.
${{w}_{j}}~=\sqrt{\frac{c_{j}^{2}}{1-c_{j}^{2}}}\cdot \sqrt{\left| {{X}_{j}} \right|}$ | (8) |
where C_{j} is the correlation coefficient and X_{j} is the cross-spectrum. The advantage of the weight equation is that different weights can be obtained when the correlation coefficient serves as a constant and cross-spectrum energy changes. According to the relationship between Δ t and m, when m and e_{m} is divided by 2π, the travel time delay Δ t and its residue e _{Δt} corresponding to different time lags of the station pairs can be obtained.
3.3 Calculate the Changes of Average Relative Seismic VelocitySuppose the relative seismic velocity change Δ v/v is homogeneous in space, then it is an opposite number of relative travel time change Δ t/t, i.e. Δ v/v =-Δ t/t (Ratdomopurbo et al., 1995). Considering the interval of the stations, strength of the signal energy, correlation between CCFs and REF, the paper selects 8s-20s of the cross-correlation positive and negative lags and the parts are surface waves and coda waves. We averaged the travel time delay Δ t of the different time lags of the 28 pairs of stations as well as their corresponding residues e_{Δ t} and obtain the average travel time delays
$\overline{\Delta {{t}_{i}}~}=b{{t}_{i}}~$ | (9) |
$b=\frac{~\Sigma ~{{p}_{i}}({{t}_{i}}-\langle t\rangle )\overline{\Delta {{t}_{i}}}}{\sum {{p}_{i}}~{{({{t}_{i}}~-\langle t\rangle )}^{2}}}$ | (10) |
where p_{i} is the weight
${{p}_{i}}~=\frac{1}{{{\overline{{{e}_{\Delta t}}}}^{2}}}$ | (11) |
The variance corresponding to b is
$e_{b}^{2}=\frac{1}{\sum {{p}_{i}}~{{({{t}_{i}}~-\langle t\rangle )}^{2}}}$ | (12) |
and finally, we obtain the average relative seismic velocity
The time length of the study includes three large scale impoundments and two disemboguements of the Zipingpu reservoir. The empirical Green function CCFs of the 28 station pairs in the reservoir zone is extracted through noise cross-correlation. The case of the BAJ-GHS station pair in Fig. 5 reveals the cross-correlations between the station pairs. The example station pair crosses from the southwestern to the northeastern zone (Fig. 3) and is representative of the station pairs. Fig. 5 shows that the cross correlation coefficients between CCFs and REF are significantly low in the impoundments and disemboguements period, and there is some delay in time. This quantitatively represents the influence of the water level on the changes of reservoir underground medium velocity. This paper uses the results of cross-correlation and applies the moving-window cross-spectrum method to calculate the travel time delay of different time lags of the 28 pairs of stations in the three periods, which are 1s-2s (0.5-1.0Hz), 2s-4s (0.25-0.50Hz) and 4s-8s (0.125-0.250Hz) and corresponding to the depths of 0km-2km, 1km-4km and 1km-8km respectively. Finally we use the surface waves and coda waves to capture the changes of the average relative seismic velocity of the underground medium in the reservoir region (Fig. 8). It can be seen that the relative seismic velocity change of the reservoir underground medium does not exceed 0.1%. The reservoir water levels of impoundment and disemboguement influence the underground medium through the two functions of pressure and permeation. Biot (1956) believed that pore fluid can increase compression wave velocity and lower shear wave velocity. The reservoir region is composed mainly of carbonate rock with better permeation. The three periods in Fig. 8 show that the medium relative seismic velocity change in 2km corresponded by 1s-2s is largest with change amplitude of over 0.05%. This is because the permeation is stronger in the superficial layer under the same water level pressure.
4.1 First Impoundment and DisemboguementFig. 8 shows that before the first large scale impoundment on September 30, 2005, there is no obvious relationship between the water level and the relative seismic velocity change. Within 10 days after the impoundment, the water level rose rapidly from 760.36m to 835.91m. The medium relative seismic velocities at the three depths for the three periods dropped rapidly, showing that the reservoir water pressure was the main cause of the change of the relative seismic velocities, and the infiltration only affected the superficial layer medium within 2km. After that, the reservoir started to disembogue and the relative seismic velocity rose gradually.
4.2 Second Impoundment and DisemboguementThe second impoundment started on August 15, 2006. The water level rose to the highest point of 875.18m on October 14, 2006. The medium relative seismic velocity at the three depths lowered afterwards and there was an obvious time delay. The relative seismic velocities corresponding to 1s-2s and 2s-4s also decreased to the minimum at the same time, while that of 4s-8s reached to the minimum nearly one month later. This shows that the permeation became the main factor affecting the change of relative seismic velocity under the same reservoir water pressure, and it could influence the fault at the depth of 4km. During the second disemboguement, there was some delay for the changes of relative seismic velocity at the three depths, but almost at the same time it rose to the maximum. This shows that the permeation at the time already influenced the fault at a depth of 8km.
4.3 Third ImpoundmentThe third impoundment had a water level rise of 873.39m on December 12, 2007, and the relative seismic velocities at the three periods almost dropped to the minimum at the same time, which shows a high consistency with the water level changes. The cross correlation coefficients were -0.81, -0.66, -0.76 respectively (Fig. 9). By this time the reservoir water pressure and permeation had a joint effect on the medium relative seismic velocity changes and the water had infiltrated to the fault as deep as below 8km.
In summary, this paper analyzes the three impoundments and two disemboguements of the Zipingpu reservoir, discusses the main factors affecting the seismic velocity changes in different periods, and traces the water permeation in the medium at different depths. The results show that before the large scale impoundment of the Zipingpu reservoir, there was no obvious correlation between the relative seismic velocity change and the water level change, but during the later impoundments and disemboguements, there was obvious negative correlation between them, that is, when the water level rose, the relative seismic velocity dropped and when the water level dropped, the relative seismic velocity rose. The analysis reveals that pressure was the main factor for the medium relative seismic velocity changes in the first impoundment. In the later 2 impoundments, permeation became the main factor. At the highest point of the second impoundment, the permeation affected the fault as deep as 4km, and at the lowest point of the second disemboguement, the permeation affected the fault as deep as 8km.
Lu Xian et al. (2010) found in the study of the relationship between the reservoir water level and the seismic frequencies in the zone that during the three water level rising months of September 2005, September 2006 and September 2007, the seismic frequencies also rose and the majority of the focal depths concentrated on 5km. According to the present research, the relative seismic velocities corresponding to the three months dropped rapidly from zero. Therefore, the study of continuous changes of the relative seismic velocity of the underground superficial medium can be the basis for reservoir earthquake prediction, and has a great significance.
ACKNOWLEDGMENTThe large amount of continuous waveform and reservoir data were provided by the Sichuan earthquake administration.Dr.Ma Yanlu, Dr.Yang Zhigao, research professorer Zhou Longquan, research professor Du Fang, senior engineer Dai Shigui, senior engineer Xie Ronghua and senior engineer Han Jin gave us a lot of support and encouragement in this research. We owe our greatest gratitude to all of them. We are also thankful for the valuable advice from the peer previewers.
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