Shifting Correlation Between Earthquakes and Electromagnetic Signals: A Case Study of the 2013 Minxian–Zhangxian M _{L} 6.5 (M _{W} 6.1) Earthquake in Gansu, China
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Abstract
The shifting correlation method (SCM) is proposed for statistical analysis of the correlation between earthquake sequences and electromagnetic signal sequences. In this method, the two different sequences were treated in units of 1 day. With the earthquake sequences fixed, the electromagnetic sequences were continuously shifted on the time axis, and the linear correlation coefficients between the two were calculated. In this way, the frequency and temporal distribution characteristics of potential seismic electromagnetic signals in the pre, co, and postseismic stages were analyzed. In the work discussed in this paper, we first verified the effectiveness of the SCM and found it could accurately identify indistinct related signals by use of sufficient samples of synthetic data. Then, as a case study, the method was used for analysis of electromagnetic monitoring data from the Minxian–Zhangxian M _{L} 6.5 (M _{W} 6.1) earthquake. The results showed: (1) there seems to be a strong correlation between earthquakes and electromagnetic signals at different frequency in the pre, co, and postseismic stages, with correlation coefficients in the range 0.4–0.7. The correlation was positive and negative before and after the earthquakes, respectively. (2) The electromagnetic signals related to the earthquakes might appear 23 days before and last for 10 days after the shocks. (3) To some extent, the occurrence time and frequency band of seismic electromagnetic signals are different at different stations. We inferred that the differences were related to resistivity, active tectonics, and seismogenic structure.
Keywords
Shifting correlation method (SCM) seismic electromagnetic signals (SEMS) Minxian–Zhangxian earthquake magnetotelluric1 Introduction
Seismic electromagnetic signals (SEMS) are electric, magnetic, and electromagnetic signals related to the genesis and occurrence of earthquakes and the structural recovery of seismogenic region. SEMS have been reported in a large amount of literature (Eftaxias et al. 2001, 2009; Fujinawa et al. 1998; Han et al. 2014; Hattori et al. 2012; Huang et al. 2011b; King 1983; Park et al. 1993; Zhang et al. 2011; Zhao et al. 2009). Abundant indoor and/or outdoor experiments and numerical simulations have been conducted to verify the existence of SEMS phenomena (Huang et al. 1998; Kuo et al. 2014; Zhao et al. 2009; Enomoto et al. 2012; Ren et al. 2012; Potirakis et al. 2012; Huang 2011a). For example, radiation of ultralowfrequency (ULF) electromagnetic signals was observed in the early, middle, and late stages of a rockfracture experiment (Hao et al. 2003). At the end of last century, the Greek physicists proposed the VAN method for earthquake monitoring on the basis of seismic electrical signals (SES). It was claimed this method could be used to predict earthquakes above magnitude 5 (Uyeda et al. 2009; Varotsos et al. 1991), which generated much interest (Huang 2005). Since the 1960s, China has established a nationwide network of earthquakemonitoring stations based on geoelectric resistivity, geoelectric fields, and electromagnetic waves. In recent years, in China, much research has been conducted on the development of a method for monitoring extremely lowfrequency electromagnetic radiation and an earthquake electromagnetic satellite (Zhao et al. 2007, 2012). The development of these monitoring techniques reflects the attention given to SEMSbased earthquake prediction methods by the scientific community.
To identify and extract SEMS effectively, such approaches as maximum entropy estimation (Liu et al. 2012; Fan et al. 2010), time–frequency analysis (Eftaxias et al. 2001), wavelet transform (Zhang et al. 2013; Xie et al. 2013; Han et al. 2011), and principlecomponent analysis (Uyeda et al. 2002; Han et al. 2009), have been used. The occurrence time, frequency band, and propagation path of SEMS have been studied (Fujinawa et al. 1998). However, most of these methods compare electromagnetic signals (or treated data) within a period of time of a single earthquake to seek earthquakerelated anomalies and analyze the potential SEMS characteristics. In fact, the SEMS may not be obviously abnormal signals because of lowintensity and/or mixing with the background field and interfering noise. This may be why no SEMS anomalies have been observed before and after some earthquakes, and why some abnormal electromagnetic signals cannot be related to the corresponding earthquakes (Orihara et al. 2012; Fan 2010; Han et al. 2014; Hattori et al. 2012). Although many methods have been used to investigate and extract SEMS on the basis of ground and/or ionosphere measurements, the correlation between earthquakes and electromagnetic signals is still difficult to quantify solely on the basis of electromagnetic anomalies before and after a single event, not to mention the general features of complex and inconstant SEMS. Therefore, although many studies in this field have been reported, the nature of SEMS remains elusive, not to mention the temporal–spatial distribution of SEMS and their variations.
For a specific earthquake, SEMS may arise during the seismogenic process, in the course of rock rupture during the coseismic moment, and during postseismic recovery of the seismogenic structure. By taking the time of occurrence of an earthquake as a reference point, the time axis can be divided into three stages, pre, co, and postseismic, in which SEMS may or may not exist. When multiple earthquakes occur successively, the SEMS in the three stages may overlap and be submerged by noise. Therefore, the specific characteristics of SEMS in the three stages cannot be determined with certainty by analyzing a single seismic event before the physical mechanisms of seismic electromagnetic radiation are clear. Recently, statistical study by superpose epoch analysis (SEA) has been used to investigate the relationship between earthquakes and geomagnetic variations. The results of statistical analysis preformed in Japan suggested there was no correlation between earthquakes and geomagnetic anomalies, and that ULF geomagnetic anomalies were probably more sensitive to earthquakes which were larger and closer to geomagnetic monitoring stations (Han et al. 2014; Hattori et al. 2012). As an alternative, in this paper, we introduce a new statistical method for study and investigation of the direct correlation between earthquakes and electromagnetic signals.
Earthquakes are caused by tectonic movement with similar dynamic processes. For all earthquakes, or all earthquakes of a specific type, the corresponding SEMS may share similar temporal distribution characteristics. This means we could choose several earthquakes for statistical analysis and extract the common features of SEMS. Correlation analysis is a basic statistical tool. For simultaneous recognition of pre, co, and postseismic SEMS, we propose use of the shifting correlation method (SCM) for SEMS and earthquake series. Continuous shifting of two sequences and calculation of correlation coefficients can result in a plot of correlation coefficients over the entire time axis. By shifting correlation analysis of electromagnetic signals of different frequency, a diagram based on the correlation coefficients can be obtained, and these diagrams clearly show the time–frequency distribution characteristics of SEMS.
In this study, we first introduce the basic principle of the shifting correlation method (SCM) and then verify the performance and functional characteristics of the SCM by use of synthetic data. Later, we discuss the application of the SCM to SEMS recognition by applying it to sequences of the mainafter shock of the Minxian–Zhangxian earthquake and electromagnetic monitoring data.
2 Basic Principle of SCM
The correlation coefficients between the two sequences, calculated by shifting correlation method, are not single value but a correlation coefficient sequence, i.e. the curve of variation of the correlation coefficient when the short sequence shifts to the left or right relative to the long sequence.
3 Effectiveness of the SCM Verified with Synthetic Data
As is apparent from Fig. 2b, the shifting correlation coefficients are calculated when the three short sequences are shifted relative to the long sequence M. Relative to the starting point of the shifting, the numbers of the shifted samples are denoted by positive and negative values on the horizontal axis when the short sequences are shifted right or left. It is apparent that strong correlation occurs at positions of 0, −20, and 10, respectively, on the three curves which coincides completely with the preset signals. This indicates that the SCM can accurately distinguish asynchronous correlation between two sequences. This in indicative preliminary validation of the effectiveness of the method.
The effectiveness of the SCM was validated by simulating the single correlation through the synthetic data as above. However, if we superimposed sequences E1, E2 and E3 in equal proportion in Fig. 2a, so a short sequence of equal length was synthesized, and then performed shifting correlation calculation with the corresponding long sequence, could the SCM distinguish the correlation at the three different positions simultaneously? Following this idea, further verification of the effectiveness of the SCM was conducted.
These calculations using synthetic data indicate that the SCM can clearly distinguish simple, hidden, and complex correlations between two sequences. The larger the sample size of the short sequence, the higher the resolution. This method can be used to investigate the correlation between two physical quantities and the correlation characteristics. As an example, the method was used to analyze the correlation between an earthquake and electromagnetic signals.
4 Case Study
Electromagnetic signals are regarded as among the most sensitive physical responses to earthquake (Zhao et al. 2007) but are vulnerable to interference from several sources. If SEMS indeed exist, they may be mixed with a variety of electromagnetic signals and noise, which makes it difficult to distinguish then. If the earthquake is correlated with the electromagnetic signals, the correlation can be recognized by the shifting correlation method, as indicated by the verification above.
If the existence of SEMS is manifest as a coseismic effect, the earthquake sequence may have a strong correlation with the electromagnetic sequences monitored synchronously; but if it is a pre or postseismic effect, the correlation between the two physical quantities cannot be observed unless the electromagnetic sequences are shifted relative to earthquake sequences, by a corresponding distance backward (left) or forward (right). Therefore, it is possible for us to extract the pre, co, and postseismic SEMS simultaneously when performing the SCM on electromagnetic signals the and earthquake sequence. On the basis of the results calculated we could further analyze the time–frequency feature of SEMS and its spatial distribution characteristics. It should be noted that the SCM is a statistical method based on several seismic events, not simply analysis of the correspondence between one or several seismic events with the anomalies in SEMS analysis.
4.1 General Information about the Minxian–Zhangxian Earthquake
4.2 Shifting Correlation Analysis
The shifting correlation method was used to analyze electromagnetic monitoring data from the Minxian–Zhangxian earthquake. The main procedures were:

first, the main shock and aftershock sequence of the earthquake was processed into a long sequence used for correlation analysis;

second, the electromagnetic monitoring data was processed into the short sequence; and

third, final treatment, calculation, and analysis of the shifting correlation coefficient between the two sequences.
Basic time and data information for electromagnetic monitoring of the Minxian–Zhangxian earthquake
Monitoring station  Epicenter distance (km)  Measured time (day)  Data lost  Data used for analysis (day) 

Majiagou (MJG)  10.4  23/7/2013–19/8/2013  2th–3th August  26 
Zhujiawan (ZJW)  11.3  25/7/2013–19/8/2013  30th July, 6th–7th August  23 
4.2.1 Earthquake Sequence Treatment
4.2.2 Treatment of Electromagnetic Monitoring Data
The robust time series processing software SSMT2000 provided by Phoenix was improved so the time series observed continuously could be divided into equal time intervals and the batch processing was performed automatically. In accordance with Meq sequence, the time series (Table 1) of the electromagnetic signal was also divided into time intervals of a day (LT 00:00 A.M–24:00 P.M.). SSMT2000 was then used to obtain the fullband (0.00055–320 Hz) electromagnetic spectrum. The treatment result for each day was output in the form of an EDI file. The EDI files of the power spectrum, after autoedit by MTEDITOR (software provided by Phoenix), were managed by MTPioneer software (Chen et al. 2004), and output as a diurnal curve of the power spectrum values with different frequencies (a total of forty frequency points). As a result, forty curves of electromagnetic response were obtained. For data missing from Table 1, cubic spline interpolation was performed to form a complete electromagnetic signal sequence at the different frequency points. Figure 6c shows the sequence of Ex at a frequency of 120 Hz at MJG station.
4.2.3 Calculation of Shifting Correlation Coefficients
By using the Meq sequence and electromagnetic signal sequence divided into time intervals of 1 day, the curve of the shifting correlation coefficient between the two physical quantities was calculated. During the shifting process, the number of days shifted was determined by the length of the electromagnetic signal sequence, m, after treatment, i.e. controlling the magnitude of n (in Fig. 1). To ensure satisfactory statistical analysis, the largest sample size was used when calculating the preseismic correlation, i.e. when the electromagnetic signal sequence shifts to the right, for MJG station. For example, m = 28, and the number of days shifted was marked by negative value, representing preseismic correlation. In this study, because the earthquake sequences before July 22 were not included into the calculation, the number of samples used for calculation of the correlation coefficient are reduced when the electromagnetic signal was shifted to the left relative to the Meq sequence. The number of left shifted days was marked by a positive value, representing postseismic correlation. Finally, we calculated the shifting correlation coefficients between fullband electromagnetic signals and the Meq sequence and obtained nephrograms of the time–frequency distribution of the correlation coefficients.
5 Calculation Results and Analysis
5.1 MJG Station
After a series of treatments, the length of electromagnetic signal sequence and Meq sequence at MJG station was 28 and 67, respectively. In most previous studies, the SEMS probably arose within 2 or 3 weeks before the earthquakes (Zhang et al. 2011; Uyeda et al. 2002; Orihara et al. 2012; Hattori et al. 2012; Han et al. 2009, 2014), so to ensure sufficient sample size, the electromagnetic signal sequence was shifted to the left and right relative to the Meq sequence by a maximum of 15 and 25 days, respectively. In the former situation, when left shifted 15 days the number of samples for SCM calculation was 14. Thus, in Fig. 8, the strong correlation at 15 days after may be attributed to reduction of the amount of data available for calculation during the process of shifting to the left.
For the two anomaly regions with very prominent correlation at lowfrequency, 23 days before the earthquake and 11 days after the earthquake, the number of samples involved in the calculation was 28 and 19, respectively. The correlation coefficient at 0.01 Hz was 0.5 and 0.7, respectively. The lead time of the preseismic anomaly was approximately similar to that in studies of the Wenchuan, Lushan, and Izu Island earthquake by use of different methods (Uyeda et al. 2002; Ma et al. 2013; Fan et al. 2010). Moreover, the correlation of the highfrequency component was not significant, especially preseismically. This is in agreement with the results of Fan et al. (2010), Fujinawa et al. ( 1998 ) and Park et al. (1993) who performed studies on the frequency of electromagnetic anomalies.
It is apparent from the nephrogram that during the period from 22 days before to 10 days after the earthquake, the correlation coefficient was very small. There was almost no coseismic correlation. A weak correlation coefficient of approximately 0.38 appeared at high frequency approximately 1 day after the earthquake. Eftaxias et al. (2001) reported a failure to record the coseismic anomaly; in contrast, (Orihara et al. 2012; Contoyiannis et al. 2010; Tang et al. 2010) reported that they had observed coseismic electromagnetic signals. The missing coseismic signals are discussed in detail below.
5.2 ZJW Station
It is apparent that 20 days before the earthquake, a moderately strong correlation was observed. A significant correlation occurred at a relatively high frequency (approx. 15 Hz) six days before earthquake, with the correlation coefficient 0.67. Sixteen and six days before the earthquake, correlation appeared intermittently at high frequency, with the highest on 6 days before the earthquake. The anomaly in the lowfrequency was quite continuous from the coseismic stage to six days after the earthquake. Starting from seven days after, the correlation extended to the medium frequency until 11 days after earthquake. The correlation coefficient was 0.56 in the coseismic stage and increased to 0.65 five days after the earthquake. The continuous variation of correlation coefficient from the coseismic stage to 11 days after the earthquake may be indicative of postseismic stress adjustment. This result corroborates the hypothesis concerning the disappearance of the anomaly for the impending earthquake and that the postseismic anomaly does not disappear immediately (Tang et al. 1998; Eftaxias et al. 2001). It can be seen from Fig. 7f that the quality of lowfrequency data is still satisfactory at this station, which indicates the highreliability of this phenomenon. It should be also noted that strong correlation appeared at medium frequency at Ey approximately 14 days after. This might be for the same reason as the strong correlation 15 days after earthquake at MJG station—a reduction in the amount of data.
6 Discussion
6.1 Correlation Between EM Sequence and Random Sequences
6.2 Comparative Analysis of Two Stations
Analysis of the data at the two stations shows that the correlation nephrograms reveal the occurrence of similarities and differences. First, from the nephrograms there is no coseismic correlation in the highfrequency component at the two stations. We speculate that there are two different interpretations for the absence of coseismic highfrequency signals:
 1
Because of the excessively high frequency of coseismic electromagnetic radiation, the device fails to record the signals. In other reports, the frequency range of the coseismic electromagnetic anomaly is of kHz or MHz magnitude (Eftaxias et al. 2009). However, the highest frequency of the electromagnetic monitoring instrument we used in this article is 320 Hz (V52000, Phoenix), thus the highfrequency signals has not been recorded.
 2
The highfrequency signals in the observed frequency range are absorbed by crustal media. The seismic electromagnetic signals may come from two sources: some electromagnetic signals are released through the hypocenter and transmitted by the earth medium, whereas others are transmitted by the waveguide between the ionosphere and earth (Fujinawa et al. 1998). The monitoring stations, which were within 12 km of the swarm of earthquakes, were located near the epicenter in this study. No surface ruptures were caused by this shock (Zheng et al. 2013). Therefore, we infer that most of observed SEMS may directly come from the hypocenter through the earth medium, the highfrequency SEMS may be absorbed by the crust, as suggested by Eftaxias et al. (2001). At ZJW station, highly correlated SEMS appeared below a frequency of 0.001 Hz, and the ribbonlike signals lasted 10 days after the shock. To some extent, this phenomenon seems to indicate regularity in seismogenic and postseismic activity.
Second, although the distance of the two stations from the epicenter almost the same, statistical significance arose on different days and for different frequencies. The reasons for the different results at MJG and ZJW are:

because the number of samples in the electromagnetic sequence is limited, the result is vulnerable to local noise, and cannot reflect the time–frequency characteristics of SEMS steadily, which may lead to differences at the two stations; or

the distance between the epicenter and the two stations is only 12 km, but the apparent resistivity curves (Fig. 7) and the results from onedimensional magnetotelluric inversions showed their deep resistivity structures are quite different (the results as seen in the attachment). The resistivity at MJG is significantly lower than that at ZJW. Moreover, previous studies have suggested that different deep structure may result in different recording of SEMS (Varotsos et al. 1991; Hattori et al. 2012; Huang et al. 2010); different distributions of tectonic deformation fields, stress and strain field, and active tectonics may also affect the results.
Because this study focuses mainly on the theory and realization of the SCM, further studies of the exact reason for the above phenomenon will be conducted in the future.
7 Conclusions
The shifting correlation method (SCM) is proposed for analysis of the correlation between earthquakes and electromagnetic signals. We assumed that seismic electromagnetic signals (SEMS) could exist in the pre, co, and postseismic stages. After continuous shifting of one sequence, the correlation coefficients between the two physical quantities were calculated. Thus, we could seek information about SEMS along the entire time axis (the position with high correlation) with the time of occurrence of the earthquakes as the origin. Synthetic data were first used to estimate the efficacy of the SCM for recognition of signals with asynchronous correlation. SCM was then used for analysis of electromagnetic monitoring data from the Minxian–Zhangxian earthquake, to obtain the preliminary temporal–frequency distribution characteristics of SEMS.
From the synthetic study we found that SCM could suppress noise to some extent. The larger the sample size involved in SCM, the more effectively the noise was minimized and the higher the resolution of the correlating signals. Thus, SCM is very suitable for treatment and analysis of longterm monitoring data obtained by use of seismic station networks. Moreover, as was apparent from the analytical procedure, SCM is not confined to correlation analysis between earthquake and electromagnetic signals. It is also suitable for correlation analysis of other precursory physical quantities.
The results of a case study of the Minxian–Zhangxian earthquake corroborate the belief that SEMS precede earthquakes. In the frequency range involved in this study, SEMS may appear within 23 days before the shock, and disappear 5 days before the shock. Strongly correlated SEMS appear at low frequency in the coseismic and postseismic stages, and may disappear 10 days after the earthquake. We also found that the time of occurrence of SEMS varied for the different stations and the frequency band of SEMS was also different at different stages. However, the case study had some limitations, for example the limited number of samples of observed electromagnetic data and we only considered linear correlation between earthquakes and electromagnetic signals. Nonlinear correlation with sufficient samples is worthy of study.
In general, a new method has been proposed for investigation of the relationship between earthquakes and electromagnetic signals, and some results are in agreement with those from previous studies. The relationship between SEMS characteristics, position of monitoring stations, active tectonics, and seismic rupture are worthwhile being further profound studied.
Notes
Acknowledgments
The authors thank two anonymous reviewers for their constructive comments on the original manuscript. The authors also thank Liu Ming, who contributed to the field work, and Fang Lihua, associated professor from the Institute of Geophysics, CEA, who provided the original mainafter shocks catalogue for this paper. This research was supported by the Special Fund for Basic Scientific Research of the Chinese National Nonprofit Institutes (grant no. IGCEA1306) and the Natural Science Foundation of China (grant no. 41174058).
Supplementary material
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