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Mann-Kendall Mutation Analysis of Temporal Variation of Apparent Stress in Qinba Mountains and Its Adjacent Areas

In this abstract, we use the Mann-Kendall Mutation analysis to determine the source parameters of 125 earthquakes in the Qinba Mountains and its neighboring areas between 1997 and 2013. Seismic moments, apparent stress, and seismic radiant energy of the earthquakes were calculated. The Mann-Kendall mutation test was used to analyze the temporal data of the apparent stress. The results indicate that there occurred three downward mutation points in apparent stress in June 1998, October 1998 and March 1999, and then only one earthquake, Wudu 4.5earthquake with magnitude greater than 4 occurred in this area till September 2001. The average apparent stress decreases from 0.16 MPa from July 1997 to March 1999 to 0.15 MPa from April 1999 to September 2001. After the rising mutation point in apparent stress in October 2001, the average apparent stress increases from 0.15 MPa from April 1999 to September 2001 to 0.18 MPa from October 2001 to December 2013. A series of moderate to strong earthquakes with ML4.9, ML6.0, ML5.9, and ML5.2 then occurred in April 2003, May 2008, July 2008 and September 2009. The results demonstrate that the Mann-Kendall mutation analysis can fairly reflect the trend of apparent seismic stress, which is helpful for seismic activity prediction.


Introduction
Seismic radiant energy and seismic moment are two basic parameters describing the source of an earthquake. The ratio of these two parameters is related to apparent stress. The above three parameters describe the characteristics of the seismic source from different aspects [1,5,10]. Seismic apparent stress was proposed in the 1960s and has been studied in various aspects in recent years [4,18]. One of the aspects is the research of earthquake prediction, which has been taken mainly in mainland China for nearly 20 years [3,9,[19][20]. The increase in apparent stress, especially sudden changes in apparent stress, may indicate an increase in the risk of earthquakes. However, how to accurately and reasonably detect the mutation point of apparent stress is still a challenge. The Mann-Kendall method is a rank-based nonparametric test that can be used to detect monotonic trends in a time series. Whether the time series trend is linear or the data follow a normal distribution, the Mann-Kendall method can be used to determine the trend of incomplete data, and can effectively reduce the impact of data uncertainty [7,14]. Therefore, compared with the parametric testing methods requiring data normality and sensitivity to data bias, such as linearity and other regression, the Mann-Kendall method has more advantages in determining the mutation points and change trends of the data [6,8].
Qinba Mountains and its adjacent areas are the tectonic boundaries between eastern and western China. They are also the adjustment zones for the differential movement of tectonic blocks such as the north and south part of China. The seismicity of this area is weak in history, but it has increased in recent years. Series of strong earthquakes such as Ningqiang6.0 earthquake on May 27, 2008, the Ningqiang 5.9earthquake on July 24, 2008, and several earthquakes with magnitude greater than 5 occurred in this area. Some preliminary researches have been done for the source parameters of earthquakes in this area, but the seismic radiant energy is basically estimated from the relationship between magnitude and energy, so the parameters such as radiated seismic energy and apparent stress are not determined directly [11,[16][17]. In this paper, by using the digital seismic data recorded in Shaanxi Digital Seismic Network from 1997 to 2013, seismic moments, radiant energies, and apparent stress of 125 earthquakes with magnitudes from 1.2 to 6.0 in the Qinba Mountains and its adjacent areas were determined separately. The Mann-Kendall mutation then analyzed the temporal series of the apparent stress.

Data
One hundred twenty-five earthquakes records were selected through the regional earthquakes recorded by the Shaanxi digital seismic network from July 1997 to December 2013, with clear waveforms, low background noise, and high ratios of signal-to-noise. More than 4 stations record each earthquake. After zero drift, line drift correction, instrument response correction, and propagation path attenuation correction to the seismic waveforms, the low-frequency amplitude, corner frequency, and highfrequency attenuation rate of the seismic source spectrum were measured. According to the Brunedisk dislocation model, the seismic moment, stress drop, source scale, and corner frequency were obtained, and seismic radiant energy is determined through spectral integration of seismic waveform [18]. Then apparent stress is determined by the formula given by Wyss and Burne. The stations and the epicenters of the selected earthquakes are shown in Figure 1.

Methods
Using the Brune dislocation model, the source spectrum is obtained after instrument response correction, geometric diffusion correction, and medium attenuation correction, and the zero-frequency limitΩ 0 and corner frequency 0 are measured. Then earthquake moment 0 , stress drop Δ and focal rupture radius a are obtained according to the following formula [18]:  Where d is the distance between seismic focus and receiver, R is the radiation factor, is the velocity with value of 3.5 km/s, is density with the value of 2.7 × 10 3 / 3 .Radiated seismic energy is given by [12] = 4 ∫ 2 ( ) Where ( )is the corrected seismic spectrum, is seismic velocity. Seismic apparent stress is given by Where μ is the rigidity with the value of 3.3 × 10 4 and E is the radiated seismic energy. The Mann-Kendall method is a rank-based nonparametric test. It determines the existence of a trend regardless of whether the trend is linear or whether the data follows a normal distribution. A time series (x1, x2, ..., xn) is provided, and a rank series is constructed to represent the cumulative number of samples xi＞xj(1≤j≤i). Then is given by: Mean value and variance of which is calculated by: The test statistic is defined as: If the computed statistic value is greater than the critical value ∝/2 of the standard normal distribution at the significance level, it indicates that there is a statistically significant positive or negative trend in the data series. The time series is arranged in reverse order, and then statistic is defined as for formula (9) and calculated according to formula (6): The predefined significance levelα is taken as 0.05, then the critical value ∝/2 is ±1.96then the curvesof , and the straight line of the critical value can be drawn. If is positive, it indicates an increasing trend. While a negative value indicates a decreasing trend. When the value exceeds the critical value, it indicates that the increasing or decreasing trend is significant. If there exist intersecting points of the two curves of and , and the value of the intersecting points is between the critical values, the moment corresponding to the intersection may be the moment when the mutation starts [2,15].

Results and Discussion
In this study, seismic moments, radiant energies, and apparent stress of 122 earthquakes with magnitude from 1.2 to 6.0 in studied areas are determined from July 1997 to December 2013, and the apparent stress was analyzed by Mann-Kendall mutation test. The temporal curve of apparent stress is shown in Figure 2.
The average apparent stress during the study period in this region is 0.16 MPa, and the variance is 0.50 MPa. If the changing of the apparent stress from the mean value is more than twice the variance, these points are seen as abnormal points. Combined with the M-T diagram of the region, there are no abnormal points of the apparent stress before Shiquan 4.9 earthquake on April 24, 2003, Ningqiang 6.0 earthquake on May 27, 2008, Ningqiang 5.9 earthquake on July 24, 2008, and Ningqiang 5.5 earthquake on September 19, 2009. If the value of apparent stress is seen as abnormal when it exceeds the average value, there are too many abnormal points in the curve, and shows no corresponding relationship between earthquake activity and their abnormal points.   The Mann-Kendall mutation test was then used to analyze the change of the apparent stress from July 1997 to December 2013 in the studied areas. The results are shown in figure4.The M-Ktest shows five mutation points during this period. These five mutation points are divided into three swarms, and the middle three points are divided into the same group because they are very close together. The first swarm included one mutation point in November 1997, and the second swarm contains three mutation points, which are in June 1998, October 1998 and March 1999. Finally, the last swarm involved one mutation point in September 2001. The first swarm is not used for analyzing because the previous data is too little. The second swarm shows a decreasing trend, and the third swarm shows a clear increasing trend. Shortly after the three mutation points in the second swarm, Wudu 4.5 earthquake occurred on April 15, 1999, and

Conclusions
This study aimed to identify the trends in seismic activity in the Qinba Mountains area and its adjacent areas, Shaanxi, China, from 1997 to 2013. Seismic moments and seismic radiant energy of the earthquake were calculated, and the temporal curve of apparent seismic stress in the studied area was obtained. The Mann-Kendall mutation test was used to analyze the temporal data of the apparent stress in the area. After the mutation points of apparent stress indicating a decreasing trend in June 1998, October 1998 and March 1999, only one earthquake with a magnitude greater than 4 occurred in this area before September 2001. Therefore, the average apparent stress decreases after the mutation point. After the mutation point of apparent stress indicating an increasing trend in September 2001, a series of moderate to strong earthquakes occurred in this area. And the average apparent stress in the region roses. The results show that the Mann-Kendall mutation test method can fairly predict the trend of apparent seismic stress, which is helpful for seismic activity prediction.