For earthquakes (ML≥2.0) that occurred from January 2006 to October 2018 around the MS5.7 Xingwen earthquake occurred on 16 December 2018 in Xingwen, Sichuan province, China, we statistically investigated the correlation between the phase of Earth's rotation and the occurrence of earthquakes via Schuster's test to determine the signals that triggered earthquakes before the MS5.7 Xingwen event. The results were evaluated based on the P-value where a smaller P-value corresponded to a higher correlation between the occurrence of an earthquake and Earth's rotation. We investigated the spatial distribution of P-values in the region around the epicenter of the MS5.7 Xingwen event, and obtained a result exhibiting a extremely low-P-value region. The MS5.7 event occurred inside near the northern boundary of this region. Furthermore, we analyzed the temporal evolution of P-values for earthquakes that occurred within the extremely low-P-value region and found that some extremely low P-values (less that 0.1%), i.e., significant correlation, were calculated for earthquakes that occurred before the MS5.7 Xingwen earthquake. Among sixty-one earthquakes with the lowest P-value, occurred from May 2014 to April 2018, a vast majority of them occurred during the acceleration of Earth's rotation. The lower P-value obtained in this study reveals that the Xingwen source body probably was extremely unstable prior to the occurrence of the MS5.7 Xingwen earthquake.
When the regions in the Earth’s crust reach a critical state for failure in strong earthquakes, tiny stress perturbations can trigger small earthquakes in and around the focal regions of them. It is known that a tiny change of stress in the crust can be caused by the variation in rate of Earth's rotation (Chen et al., 2018). When a strong earthquake is approaching, its source body could become extremely unstable where smaller earthquakes would be susceptible to the tiny change of stress, resulting in a strong correlation between the variations in rate of Earth's rotation and the occurrence of earthquakes. A significant correlation was found between Earth's rotation and small earthquakes occurring before the MS7.8 Tangshan mainshock (Wei et al., 2018).
In the present study, we focused on the MS5.7 Xingwen earthquake (date of occurrence: 16 December 2018), occurred in Xingwen, Sichuan province, China, with its epicenter located at 28.24°N, 104.955°E by China Seismic Network, to investigate the correlation between the variations in rate of Earth's rotation and the occurrence of earthquakes that occurred around its source region during pre-quake time interval.
2.
Data
Earthquakes used in this paper were obtained from the China Earthquake Networks Center, China Earthquake Administration. In the experiment we take earthquakes that occurred around the epicenter from January 2006 to October 2018, which epicenters were plotted in Figure 1. There isn’t any fault founded at the epicenter, the nearest fault, Huarongshan fault, is roughly fifty kilometers away to the northwest. Figure 2 shows the magnitude versus time for those earthquakes. The seismicty around the epicenter of the MS5.7 Xingwen event started to enhance violently in 2006, which remains to this day.
Figure
1.
The epicenters of earthquakes (ML≥ 2.0) that occurred from January 2006 to October 2018 and tectonic setting. Grey circles show the epicenters of earthquakes. Purple thick solid lines represent the Huarongshan fault. The red star represents the epicenter of the MS5.7 Xingwen earthquake. The focal mechanism solution shown in the figure was obtained by Guo Xiangyun (Result of emergency response on 16 December 2018)
The threshold magnitude determined by the G-R relation from 2006 to 2018 is less than ML1.0 in this region, the earthquakes with ML≥2.0 used for analysis should be recorded and determined wholly since 2006 (Figure 3).
Figure
3.
Accumulative number of earthquakes versus magnitude
The length of day concerning the Earth's rotation was also used in the analysis, and obtained from the Earth Orientation Center [http://hpiers.obspm.fr/eop-pc/]. Figure 4a shows the raw data of length of day with the standard length of day (24 hours) subtracted. Figure 4b indicates the seasonal changes in the length of day.
Figure
4.
The length of day concerning the Earth's rotation versus time. (a) The raw data downloaded from the Earth Orientation Center. (b) The seasonal changes in the length of day concerning the Earth's rotation
We statistically examined the correlation between the Earth's rotation and the occurrence of earthquakes. The method has been applied to analyze tidal triggering of earthquakes (Tanaka et al., 2002; Tanaka, 2010, 2012). From a time series of the seasonal change in rate of Earth's rotation, we calculated the phase angle of Earth's rotation at the occurrence time of each earthquake. We defined the phase angle as 0° at each maximum of rate of Earth's rotation, –180° at the first minimum on the left of the maximum, and 180° at the first minimum on the right one. The phase angle θ at the occurrence time of each earthquake was obtained by the following formula,
Where te denotes the occurrence time of an earthquake, and t0 the time at the maximum of length of day immediately before or after the earthquake occurrence. t–180 and t180 denote the times at the minimum of length of day immediately before and after the earthquake occurrence respectively (Figure 5). Based on the phase angles of all earthquakes, we statistically analyzed whether they had a significant correlation with Earth's rotation using Schuster’s test (Tsuruoka et al., 1995; Heaton, 1975). The experimental results were evaluated based on a P-value between 0 and 1. Generally, if P≤5%, the earthquakes could be considered non-random. The P-value of N earthquakes can be calculated according to the following formulas,
Figure
5.
Determination of the phase angle.“+” shows the occurrence time of an earthquake
where, θi denotes the phase angle of the i-th earthquake. N must be greater than 10. During the period from point A to point B (–180°≤θ≤0°) in Figure 5, the length of day increases, corresponding to the deceleration of Earth's rotation, and the length of day decreases from point B to point C (0°≤θ≤180°), corresponding to the acceleration of Earth's rotation.
4.
Results
The spatial distribution of the P-values for earthquakes (2.5≤ML ≤ 2.9) that occurred from November 2015 to October 2018 is shown in Figure 6. The time span of four years prior to the MS5.7 Xingwen earthquake was considered. Additionally, we used a spatial moving window of 0.2°×0.2° that was moved by 0.01° both along-latitude and along-longitude directions. When there are over 20 earthquakes in a window, P-value can be calculated. The spatial distribution of P<0.1% is shown in Figure 6b. A larger region with extremely low P-values was found from Figure 6b. The MS5.7 Xingwen earthquake was located inside near the northern boundary of the extremely low P-value region.
Figure
6.
Spatial distribution of the P-value for earthquakes (2.5≤ML ≤ 2.9) that occurred from November 2015 to October 2018. Grey star represents the epicenter of the Ms 5.7 Xingwen earthquake. A spatial window of 0.2° × 0.2° is moved by 0.01° in both the along-latitude and along-longitude directions. (a) P >0. (b) P <0.1%
For earthquakes (2.5≤ML≤2.9) that occurred in the extremely low P-value region, variation in P-value versus time can be obtained via taking a time window of 4 years moved by 6 months (Figure 7). The P-value of each time window is calculated according to formula (2), and the occurrence time of the last earthquake in each time window is taken to be the time of P-value.
Figure
7.
Calculation of variation in P-value versus time
Figure 8a shows a plot of variation in P-value versus time. Practically, the number of earthquakes in each time window is equal to or greater than 11 and therefore meets the requirement of greater than 10 for the analysis. Three extremely low P-values of less than 0.1% (above the 99.9% confidence level) were observed from October 2017 to October 2018, which revealed a unusually high correlation between the occurrence of an earthquake and Earth's rotation.
Figure
8.
(a) Variation in P-value versus time (the downward arrow '↓' shows the occurrence of the MS5.7 Xingwen earthquake). (b) Histogram showing the frequency of the phase angle of earthquakes that occurred from May 2014 to April 2018 when P-value was at the lowest
The P-value dropped rapidly to the lowest value (approximately 10–6 %) approximately from 4.8% in April 2018, i. e., several months before the MS5.7 earthquake occurrence. Such a lead time is of the same order of magnitude with that repeatedly reported for precursory seismic electric signals (SES) activities (Varotsos et al., 2013) which are believed to be emitted when the gradually increasing stress reaches in the future focal region a critical value (Varotsos et al., 1993), but slightly larger from the precursory time of around a few months corresponding to the appearance of the minimum of the order parameter fluctuations before major earthquakes in Japan (Sarlis et al., 2013).
For sixty-one earthquakes with the lowest P-value, occurring from May 2014 to April 2018, the distribution of phase angle is shown in Figure 8b. The histogram shows the frequency (in percentage) of the phase angle of those earthquakes. We found that among sixty-one earthquakes, about 67% of them occurred when the phase angle was greater than zero, which corresponded to the acceleration of Earth's rotation.
5.
Discussion and conclusions
We investigated the correlation between Earth's rotation and earthquakes that occurred before the MS5.7 Xingwen earthquake. A extremely low-P-value region was observed in the vicinity of the epicenter of the MS5.7 event. The MS5.7 event occurred inside near the northern boundary of this region.
In the extremely low-P-value region, three correlations between the earthquake occurrence and the Earth's rotation, with confidence level greater than 99.9%, were found in one year and more before the occurrence of the MS5.7 Xingwen event. Among the earthquakes that occurred when P-value reached to the lowest value, a bulk of those earthquakes occurred during the acceleration of Earth's rotation. When a strong earthquake is approaching, its source body could become extremely unstable where smaller earthquakes would be susceptible to the tiny change of stress. It is doubtless that a tiny change of stress in the crust can be caused by the variation in rate of Earth's rotation. Actually the significant correlation between the earthquake occurrence and the deceleration of Earth's rotation before the occurrence of the MS5.7 Xingwen event reveals the instability of its focal region. Therefore, our conclusions are that the lower P-value obtained in this study reveals that the Xingwen source body probably was extremely unstable prior to the occurrence of the MS5.7 Xingwen earthquake and a lower P-value obtained for a region could be considered as a precursor for the occurrence of a stronger earthquake.
Acknowledgments
The authors sincerely acknowledge the journal editors and anonymous reviewers for their help, support, checking and helpful comments to the manuscript. This research was supported by National Key R&D Program of China (No. 2018YFC1503405).
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Yong-gang Wei
Institute of Geophysics, China Earthquake Administration, Beijing 100081, China
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