2. Jiangsu Earthquake Agency, Nanjing 210014, China
According to the China Earthquake Networks Center, an earthquake measuring 6.1 in magnitude (hereinafter referred to as the Yingjiang M_{S}6.1 earthquake) hit Yingjiang County of Yunnan Province (25.00°N, 97.80°E) at 09:20 a.m. on May 30, 2014, and an earthquake measuring 6.5 in magnitude (hereinafter referred to as the Ludian M_{S}6.5 earthquake) took place in Ludian County, Zhaotong City in Yunnan Province (27.10°N, 103.30°E) at 04:30 p.m. on August 3, 2014 (Zhao Xu et al., 2014; Wang Weilai et al., 2014). Before the two earthquakes, the geomagnetic stations in southwestern China (the research area) showed remarkable abnormal changes.In this paper, the spatial correlation method of geomagnetic vertical component diurnal variation is used to extract the above abnormal changes, and the spatial-temporal characteristics are studied in detail.
Earth's magnetic field is mainly composed of the main magnetic field, the varying magnetic field and crustal magnetic anomaly, of which, the main magnetic field and varying magnetic field are uniform in certain space scopes, and their changes are basically synchronous, that is, they are correlated in space. Crustal magnetic anomaly refers to local magnetic anomaly. Its correlation with the magnetic field outside the anomalous body is low, and people can observe the earth's magnetic field in and out of the anomalous body simultaneously and obtain information of the anomalous body by correlation calculations (Xu Wenyao, 2003, 2009; Li Hongyu et al., 2013). It is generally believed that the geomagnetic vertical component is most closely related to the underground medium, and diurnal variation of the geomagnetic vertical component is prone to distortion before earthquakes, therefore, many scholars use diurnal variation of the geomagnetic vertical component as the object of calculation, and use the correlation coefficient to quantitatively measure the degree of correlation of vertical components between different geomagnetic stations, and then to extract quantitatively geomagnetic anomalies.In North China, the geomagnetic total field is approximate to the vertical component, so the anomalies can be extracted by calculating the spatial correlation of diurnal variation of the total field. Lin Mei et al. (1982) processed and analyzed the daily value of vertical components recorded by geomagnetic stations in Yunnan in an hourly rate from 1976 to 1979, which is the earliest documented record of Chinese seismologists using the spatial correlation method of geomagnetic diurnal variation to process geomagnetic data and extract anomalies (Lin Mei et al., 1982). Later, Feng Zhisheng, Zhang Xiuxia, Wang Yali and Qiu Guilan et al. studied successively the spatial correlation characteristics of geomagnetic diurnal variation in Jiangsu, Gansu, Qinghai and Sichuan, and obtained some typical earthquake cases such as the Cangshan M_{S}5.3 earthquake in Shandong on September 20, 1995 and the South Yellow Sea M_{S}6.1 earthquake on November 9, 1996 (Feng Zhisheng et al., 1998; Zhang Xiuxia et al., 2008; Wang Yali et al., 2010; Qiu Guilan et al., 2014).
1 ANALYTICAL METHODS AND DATA SELECTION 1.1 Method Principle and Primary Arithmetic Steps(1) Spatial correlation analysis of geomagnetic diurnal variation (Feng Zhisheng et al., 2005):
Let Z_{A} and Z_{B} be the vertical components of geomagnetic field at A and B stations, and they are linearly dependent, that is
$ {Z_{{\rm{B}}i}} = b{Z_{{\rm{A}}i}} + a $ | (1) |
(i=1, 2, ……N, N is the window length for calculating correlation coefficient)
where,
$ b = \frac{{{L_{{\rm{BB}}}}}}{{{L_{{\rm{AA}}}}}};a = \frac{{\mathop \sum \limits_{i = 1}^N {Z_{{\rm{B}}i}}}}{N} - b\frac{{\mathop \sum \limits_{i = 1}^N {Z_{{\rm{A}}i}}}}{N} $ | (2) |
the correlation coefficient is:
$ R = \frac{{{L_{{\rm{AB}}}}}}{{{{({L_{{\rm{AA}}}} \cdot {L_{{\rm{BB}}}})}^{1/2}}}} $ | (3) |
standard deviation:
$ \sigma = {[\frac{{{{\left({1 - R} \right)}^2}{L_{{\rm{BB}}}}}}{{N - 2}}]^{1/2}} $ | (4) |
where,
$ {L_{{\rm{AB}}}} = \mathop \sum \limits_{i = 1}^N ({Z_{{\rm{A}}i}} \cdot {Z_{{\rm{B}}i}}) - \frac{1}{N}\left[ {\mathop \sum \limits_{i = 1}^N {Z_{{\rm{A}}i}}\mathop \sum \limits_{i = 1}^N {Z_{{\rm{B}}i}}} \right] $ |
(2) The phase of geomagnetic diurnal variation depends on local time, specifically, the time delay of the phase with longitude is 4 minutes/degree. The difference in longitude has little effect on the calculation of the spatial correlation coefficient of diurnal variation of the geomagnetic vertical component at two stations with a small longitude difference, however, as the difference of longitude between the calculated station and reference station increases, this effect will probably overwhelm related changes caused by diurnal variation distortion (Feng Zhisheng et al., 2005). To solve this problem, the time delay technique is adopted in this paper to eliminate the influence of diurnal variation phase differences caused by different longitudes of stations on correlation calculations. Examples are illustrated here. Fig. 1 shows the spatial correlation coefficient curves of the geomagnetic vertical component between Nanshan station and Xinyi station before and after time delay processing. The curve before time delay processing shows only a sharp fall on April 12, 2016, but this abnormal change is not significant, while the curve after the time delay treatment shows a significant decrease from April 7 to 19, 2016.
(3) The results obtained by the spatial correlation method of the geomagnetic diurnal variation are all of great noise. Fig. 1 shows the spatial correlation coefficient curves of the geomagnetic vertical component between Nanshan station and Xinyi station. In this paper, the moving average method is used to filter the spatial correlation coefficient results, in which the window length is 9 days and step length is 1 day. Fig. 1 shows the curves before and after filtering. It can be seen that the correlation coefficient dropped more significantly after filtering.
(4) Spatial analytical method: background value (average value over the course of no earthquakes and abnormalities), abnormal value (correlation coefficient during the period of abnormalities), difference value (results obtained by subtracting the background value from abnormal value) and normalized value (the difference is normalized) of correlation coefficient of geomagnetic vertical component diurnal variation between geomagnetic station and reference station in the study area are calculated, and the above spatial data are normalized by using Kriging interpolation method (Li Min, 2011) to get contour data of correlation coefficient required in this study.
1.2 Data SelectionThe Southwest China region (22.6°-31.3°N, 97.2°-109.8°E) covers parts of provinces and autonomous regions such as Tibet, Yunnan, Sichuan, Chongqing, Guizhou and Guangxi. In this paper, spatial correlation coefficients of geomagnetic vertical component diurnal variation are calculated between stations including Zayu, Tonghai, Chuxiong, Yongsheng, Nanshan, Muli, Shimenkan, Xichang, Weicheng, Chengdu, Dawu, Enshi, Fengjie, Fuling, Xiannvshan, Guiyang, Hechi, Shizhu, Wushan, Wanzhou and Yongning in the study area (Fig. 2) and the reference stations, Xinyi station in Jiangsu and Hongshan station in Hebei.
Due to poor stability and continuity of correlation coefficient curves between the 5 geomagnetic stations, e.g. Chuxiong, Yongsheng, Shimenkan, Xichang and Weicheng stations and the references stations, of which curves of Chuxiong, Yongsheng and Shimenkan stations shown in Fig. 3 are not adopted in the analysis of abnormal features before earthquakes.
(1) Background and threshold values should be determined before analyzing anomaly characteristics of time series curves of the spatial correlation coefficient of geomagnetic vertical component diurnal variation. In this study, the mean value of correlation coefficient R- is taken as the background value in the period when there is no abnormality and no earthquakes in the study area, and is taken as the threshold value after deducting the double mean-square deviation. The main calculation results are shown in Table 1.
(2) Fig. 4 and Fig. 5 show the spatial correlation coefficient curves of geomagnetic vertical component diurnal variation in Southwest China from January 1, 2013 to February 28, 2015. From April 1 to March 20, 2014, the correlation coefficient curves between Tonghai, Nanshan, Muli, Guiyang, Hechi and Yongning geomagnetic stations in Southwest China and Xinyi and Hongshan reference stations present quasi-synchronous downward changes. During the period of abnormal changes, there are two complete stages of changes of "declining-transition-picking up", of which the first stage is from April 1 to 22 with its turning point on April 15, and the second stage from April 23 to May 20, with its turning point on May 1. Specific anomaly parameters are listed in Table 1. The Yingjiang M_{S}6.1 earthquake and Ludian M_{S}6.5 earthquake occurred successively in the study area within 3 months after the end of the above abnormal changes.
(3) Diurnal variation of the geomagnetic vertical component is relatively weak from every November to February (Fig. 4 and Fig. 5), the signal-to-noise ratio is low in mid and low latitude regions, the spatial correlation is poor, and the fluctuations of the correlation coefficient curves often overwhelm abnormal changes, therefore, when the spatial correlation method of geomagnetic diurnal variation is adopted, this time period is classed as an invalid time period from every November to February (the gray part in the figures), without analysis.
(4) From June 20 to July 20, 2013, correlation coefficients of geomagnetic vertical components between Tonghai, Nanshan, Muli, Guiyang, Hechi and Yongning stations and Xinyi and Hongshan reference stations are all subject to quasi-synchronous decrease changes, and within one month after the abnormal changes, the Minxian-Zhangxian M_{S}6.6 earthquake occurred in Gansu on July 22, 2013. From September 1 to October 10, 2014, correlation coefficients of geomagnetic vertical components between Tonghai, Nanshan, Muli, Guiyang, Hechi and Yongning stations and Xinyi and Hongshan reference stations are all subject to quasi-synchronous decrease changes, and within three months after the abnormal changes, the Jinggu M_{S}6.6 earthquake and the Kangding M_{S}6.3 earthquake occurred in Yunnan and Sichuan on October 7, 2014 and November 22, 2014 respectively.
(5) From July 28 to August 13, 2014, the correlation coefficients between Muli, Hechi and Yongning stations and Xinyi station present quasi-synchronous anomalies, while their correlation coefficients with Hongshan station show no obvious abnormal changes (Figs. 4 and 5), and a similar phenomenon occurred from October 15 to 25, 2014. These two groups of changes are caused by the reference station, which has relatively low precursory anomaly reliability, therefore, they are not considered as anomalies before the Ludian M_{S}6.5 earthquake. Thus it can be seen that there are many causes for the appearance of correlative anomalies, which may be caused by calculated stations, or reference stations, therefore, it is necessary to introduce a number of reference stations for calculations in future analysis.
2.2 Spatial Distribution FeaturesSpatial scanning of the Southwest China region has been done, and vertical component data from 16 geomagnetic stations are used, including Chengdu, Zayu, Dawu, Enshi, Fengjie, Fuling, Guiyang, Hechi, Muli, Nanshan, Shizhu, Wushan, Wanzhou, Xiannvshan, Yongning and Tonghai stations. The key spatial scanning results are shown in Fig. 6 and Fig. 7.
(1) From May 1 to June 20, 2013, the spatial correlation coefficient curves of geomagnetic vertical components between calculated stations in Southwest China and reference stations show no abnormal changes, and no prominent earthquakes occurred during this period. The mean value contour map of the correlation coefficients during this period shows the background characteristics of spatial distribution of spatial correlation of geomagnetic vertical components in Southwest China (Figs. 6(a) and 7(a)). When there is no abnormal change, the distribution of the contour line of the spatial correlation coefficient is generally dependent on the position of the reference station. The further away from the reference station, the smaller the correlation coefficient is, and there is no high gradient zone.
(2) Figs. 6(b) and 7(b) show contour lines of spatial correlation coefficients of the geomagnetic vertical component diurnal variation in Southwest China on April 14, 2014, which is near the turning point of abnormal changes. Nearly EW-trending contour lines which differ from the background distribution appear in the Southwest China region, and a high gradient is also present. Figs. 6(c) and 7(c) show the contour maps of spatial correlation coefficients after removing the background value, where high gradient anomalies are more prominent. Figs. 6(d) and 7(d) show the contour maps of spatial correlation coefficients after normalization and removing background value. The results show that there are high gradient zones with a normalized range between 0.4-0.7 in the study area, and high gradients of correlation coefficients corresponding to different reference stations are consistent in trend. The epicenters of Yingjiang M_{S}6.1 earthquake and Ludian M_{S}6.5 earthquake are located in the gradient zone and its adjacent area.
(4) Results of former studies show that the variation of geomagnetic anomalies is inversely proportional to epicentral distance, that is, the spatial distribution after removing the background value should present a feature where outward radiation gradually decreases with the epicenter as the center (Lin Mei et al., 1982). However, the results of this study show that there is a high value area on one side of the epicenter and a low value area on the other side, and no significant negative correlation has been found between anomalies and epicenter distance. The mechanism for the distribution characteristics of spatial correlation coefficient contour lines during the period of abnormal changes obtained in this study will be analyzed in the discussion section of this paper.
3 CONCLUSION AND DISCUSSION(1) Before the Yingjiang M_{S}6.1 earthquake and the Ludian M_{S}6.5 earthquake in 2014, among the 16 geomagnetic stations that participated in the analysis, correlation coefficients between 6 geomagnetic stations including Tonghai, Nanshan, Muli, Guiyang, Hechi and Yongning and Xinyi and Hongshan reference stations all show good morphological consistency and a decrease of threshold value. Spatial scanning of the Southwest China region during the period of abnormal changes shows that high gradient zones which differ from background distribution appear in the correlation coefficient contour maps after removing the background value and normalization (with a normalized range between 0.4-0.7), and the epicenters of the Yingjiang M_{S}6.1 earthquake and Ludian M_{S}6.5 earthquake are located in the gradient zone and its adjacent area respectively.
(2) Spatial scanning results show that high gradient zones that differ from the background distribution only appear during the period of abnormal changes, and the epicenters of the Yingjiang M_{S}6.1 earthquake and Ludian M_{S}6.5 earthquake are located in the gradient zone and its adjacent area respectively. It is considered that the mechanism of high gradient anomaly of spatial correlation is similar to that of a geomagnetic low-point displacement (Feng Zhisheng et al., 2009; Chen Huaran et al., 2009), which may be due to the formation of short-term, nearly EW-trending high-conductivity channels in the Southwest China region during the period of abnormal changes. Local varying magnetic fields caused by electric currents in channels is superimposed on diurnal variation, which leads to big morphological differences in diurnal variation on two sides of the channels, thus a high gradient zone of correlation coefficient is formed. The high-conductivity channels are also usually low-velocity and high-heat regions in upper mantle and crust, and are prone to strong earthquakes (Ding Jianhai et al., 2011). Of course, this is only a hypothesis. As research continues in the future, this spatial distribution feature will be explained more reasonably and scientifically.
(3) Some problems in the calculation of spatial correlation of geomagnetic diurnal variation are discussed as below:
1) The selection of reference station is particularly important for spatial correlation analysis of diurnal variation, which determines the reliability of the research results. In actual cases, the following selecting principles are followed: ① Geomagnetic data of good quality (the results of quality evaluation of geomagnetic observations on the Geomagnetic Network of China can be used as a good reference). ② Usually two or more stations are selected as reference stations. ③ There should be some distance between reference stations.
2) Difference in latitude and longitude at different geomagnetic stations will cause phase diversity of geomagnetic diurnal variation, and time delay processing should be performed during calculation to eliminate the effect of longitude.
3) The results of geomagnetic spatial correlation are of great noise, which is not conductive to the extraction and identification of anomalies; therefore, filtering should be performed to filter out high-frequency noise.
4) By analyzing observational data of the Jiangsu region, Feng Zhisheng et al. (2005) found that from every November to next February, diurnal variation of the geomagnetic Z component in mid and high latitude regions was weak, with low signal-to-noise ratio and low correlation (Feng Zhisheng et al., 2005). In this study, data of geomagnetic vertical component and total field (only in northern areas) from most geomagnetic stations in China since 2008 are calculated with the spatial correlation method, and the results are consistent with the conclusions obtained by Feng Zhisheng et al. (2005). The method is unable to extract geomagnetic anomalies from every November to the end of February.
5) Through the study of earthquake cases such as the Yingjiang M_{S}6.1 earthquake and the Ludian M_{S}6.5 earthquake, it is found that an important point for the identification of spatial correlation anomalies of geomagnetic diurnal variation is the recognition of anomaly form. Many abnormal changes with higher reliability don't have the prominent amplitude of anomalies, but have the characteristics of gradual "declining-transitional change-picking up" with good consistency. Therefore, it is suggested that the identification of anomalies should not be limited to whether the threshold value is exceeded.
6) The results of spatial correlation of geomagnetic diurnal variation have poor stability compared with those obtained by methods such as the load-unload response ratio method and the daily variation ratio, which makes the method prone to false alarms. It is therefore necessary to combine the original data, and log of calculated stations and reference stations, and change reference stations for analysis and elimination, so as to reduce the fault rate.
7) Whether strong magnetic disturbances such as magnetic storms need to be considered when the spatial correlation method is used for analysis has been debated by scholars. The author thinks that correlation coefficient is a ruler to measure the morphologic consistency of diurnal variation between stations. When magnetic disturbance occurs, geomagnetic diurnal variation patterns between different stations tend to be more consistent, and the magnetic disturbances increase the correlation coefficient. From this point of view, the effect of magnetic disturbances cannot necessarily be considered in practical analysis.
8) The methods of geomagnetic low-point displacement (Ding Jianhai et al., 2009), load-unload response ratio (Feng Zhisheng et al., 2000), daily variation ratio (Feng Zhisheng et al., 2001; Dai Yong et al., 2015) and spatial correlation of geomagnetic diurnal variation are used to extract diurnal variation distortion, among which geomagnetic low-point displacement mainly extracts phase distortions, load-unload response ratios and the daily variation ratio mainly extracts amplitude distortions, and spatial correlation of geomagnetic diurnal variations extract the overall diurnal variation distortion including amplitude and phase. Therefore, the mechanism of abnormal characteristics with the above four methods should be similar. However, due to the different distortion features of diurnal variation extracted by various methods, the results vary, and the occurrence time of anomalies is not necessarily the same. For example, the geomagnetic low-point displacement method is sensitive to phase, thus the results tend to show anomalies when phase distortion is prominent, while the load-unload response ratio is sensitive to amplitude distortion, and the results tend to be abnormal only when amplitude distortion is prominent.
(4) In this study, when analyzing the correlation anomaly characteristics before the Yingjiang M_{S}6.1 earthquake and the Ludian M_{S}6.5 earthquake, not only was time sequence features analyzed, spatial analysis is also introduced.However, due to relatively sparse and irregular distribution of geomagnetic stations involved in spatial analysis in the study area, the reliability of spatial distribution results of correlation is reduced. Therefore, it is suggested that mobile geomagnetic observations are followed to arrange fixed geomagnetic stations in key defense areas from the perspective of station spacing, network layout and instrument consistency. This will increase effective geomagnetic data output, and will promote the development of space-time information mining technology for geomagnetic data, and will also improve the utility ratio of geomagnetic data.
ACKNOWLEDGEMENTGrateful acknowledgement to research professor Gao Lixin and assistant research professor Li Hongyu for their selfless help in the implementation of this study and the preparation of manuscript.
This paper has been published in Chinese in the journal of Earthquake, Volume 37, Number 3, 2017.
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2. 江苏省地震局，江苏 南京 210014