Earthquake Reaearch in China  2017, Vol. 31 Issue (1): 25-38
Research on Stress Drops and the Focal Mechanisms of the Xinyuan-Hejing ML6.8 Earthquake Sequences
Liu Jianming1, Wang Qiong1, Liu Jie2, Deng Fei3, Xiang Yuan1, Yang Wen2, Li Jin1
1 Earthquake Administration of Xinjiang Uygur Autonomous Region, Urumqi 830011, China;
2 China Earthquake Networks Center, Beijing 100045, China;
3 Earthquake Administration of Yunnan Province, Kunming 650224, China
Abstract: Based on the digital waveform data recorded by Xinjiang Digital Seismic Network for the Xinyuan-Hejing ML6.8 earthquake sequences of June 30, 2012, this paper analyzes the stress drops of earthquake sequences and the correlation coefficients of focal mechanisms significant for strong aftershocks. Firstly, the source parameters of the Xinyuan-Hejing ML6.8 earthquake sequences are obtained by applying the spectrum analysis and the Brune's source model. Then, the correlation coefficients of spectral amplitudes are calculated using the low-frequency spectral amplitude recorded by the same station for the different events. Finally, based on the results of the correlation coefficients of spectral amplitudes, the events with similar focal mechanisms are grouped using the clustering method. The results show that:(1) The stress drop values show a steady trend in the aftershock sequence calm period and the stress drop values show a rise-fall in strong aftershocks. (2) The moving average correlation coefficient of amplitude spectrum begins to spread after the main shock. It shows that the correlation decreases between the main shock and the aftershocks in mechanisms. (3) The results of focal mechanism groups show that the earthquake sequences are mainly strike slips. The stress distribution of the main pressure axis is nearly NS, which is the same as the structural stress field. (4) The magnitude and mechanism show that there is an agreement before the strong aftershock, which shows that the regional stress field is enhanced.
Key words: Xinyuan-Hejing ML 6.8 earthquake sequences     Stress drop     The correlation of the focal mechanism     Body-wave spectral amplitude     Clustering group

INTRODUCTION

An earthquake is a natural phenomenon of energy released by rapid rupture dips of the crust rocks when the stress of underground medium reaches its maximum intensity. Seismic waves recorded by seismic instruments carry abundant focal information such as seismic moments, stress drops and rupture sizes. Focal parameters can reflect the structural movements and stress-strains of a region. The study of the features of time-space changes of the various focal parameters can help understand earthquake preparations and stress background (Zhao Cuiping et al., 2011), and has real significance for the estimation of the earthquake tendency in the region, future strong earthquake prediction and earthquake risk assessment.

Earthquake stress drop is one of the focal parameters, and is the average difference between the average shear stress on the fault before and after the earthquake (Chen Zhangli et al., 2008). It has drawn wide attention from many scholars in the field of crustal stress field research and earthquake prediction (Chen Zhangli et al., 2008; Hua Wei et al., 2009; Liu Lifang et al., 2006; Annemarie et al., 2006). Chen Zhangli et al. (2008) found that the increase of stress drop of earthquake swarms with time is an important indicator of a foreshock sequence. Hua Wei et al. (2009) studied the time-space evolution of the stress drops of the Wenchuan MS 8.0 earthquake sequences. Liu Lifang et al. (2006) studied the time-space evolution of the stress drops of the Yao'an earthquake sequences and the Dayao the earthquake sequences. Annemarie et al. (2006) studied the corner frequencies, stress drops and radiation energy of four earthquake sequences in Japan. The research results show that during the preparation of large earthquakes and strong aftershocks, the stress drops of moderate and small earthquakes in the earthquake preparation zone has a process of enhancement and come to be stable after the earthquake. This paper thus studies the features of the time sequence of the stress drops of the Xinyuan-Hejing ML 6.8 earthquake sequences by calculating the stress drops of the sequences.

Quite an amount of research (Diao Guiling et al., 2005, 2011; Xie Zhaodi et al., 2010; Xu Xiwei et al., 2014) shows that stress state influences seismic activities. Focal mechanism solution directly reflects the current crust situation and the motion features of fault structures, and is significant for the understanding and prediction of earthquake formations. Cheng Yong (1978) proposed to use the consistency parameter of the focal mechanism solution for the description of seismic activities. Diao Guiling et al. (1992, 1994) suggested the method of systematic clustering analysis. Their studies with their systematic clustering analysis of the times before and after the Kaoki M 6.6 earthquake on November 16, 1983 in Hawaii, USA found that there is a drop of the consistency parameters between the focal mechanism and the tectonic zone stress field before a large earthquake. Wang Yongge (2000, 2008) used the space rotation of a double-couple source focal mechanism to calculate the focal mechanism stress directions of the small earthquakes before the two MW > 7.0 earthquakes in southern California and found that the focal mechanisms of the epicenter and its adjacent areas a half year before the earthquake is more likely to be similar to that of the main shock. Many seismologists captured seismic precursor information of strong earthquakes based on the consistency of the focal mechanisms of small earthquakes, and determined the risks of large earthquakes or the possibilities of a strong aftershock after a large earthquake (Gao Guoying et al., 2010; Zeren Zhima et al., 2009; Fan Junxi et al., 2003; Cheng Wanzheng et al., 2006).

At present, many focal mechanism solutions such as P-wave first motion (Liu Jie et al., 2004), moment tensor inversion (Huang Jianping et al., 2009) and the CAP method (Lv Jian et al., 2008; Zheng Yonog et al., 2009) can meet the needs of MS ≥4.0 earthquakes with clear wave forms and good station surroundings, but cannot calculate for a large amount of focal mechanism solutions of small earthquakes. Lund et al. (2002) proposed to use the relativity of the body wave spectral amplitude to study the focal mechanism changes of moderate and small earthquakes in an earthquake sequence. The advantage of this method is not for the solution of each moderate and small earthquake focal mechanism, but for the description of the focal mechanism consistency of an earthquake group. Zhu Hang et al. (2006) and Cui Zijian et al. (2012) used this method to obtain temporal sequence coefficients of the body-wave spectral amplitudes and apply them to the determination of the strong earthquake and small earthquake sequence. However, this method can only describe the relativity of the whole focal mechanism solution in a certain time period. To obtain the relationship between multiple earthquakes, Deng Fei et al. (2014) used the correlation coefficient of body-wave spectral amplitudes in group clustering, in order to more comprehensively reflect the changes of the focal mechanism solutions of an earthquake sequence.

The ML 6.8 earthquake occurred on June 30, 2012 in Xinyuan-Hejing of the middle section of Tianshan. The earthquake sequence is a typical main-after shock type with a large number of aftershocks. The consistency of the stress drops and the focal mechanism solutions of the moderate and small earthquakes can be used to study the temporal-spatial changes of the aftershocks. Thus, this paper first uses the method of wave-spectrum analysis and Brune's focal model to calculate the focal parameters of the Xinyuan-Hejing ML 6.8 earthquake sequences. Then we calculate the body-wave zero source spectrums of the different events of the earthquake sequences at the same stations. Finally, we calculate the correlation coefficients of the spectral amplitudes of the earthquakes, and conduct the clustering grouping of the earthquake sequence focal mechanism solutions.

1 RESEARCH METHOD 1.1 Focal Spectrums and Seismic Stress Drops

The seismic wave seismic instruments record is comprehensive information including seismic focal effects, seismic wave travel path effects, station (site) responses and instrumental responses. To determine the focal parameters, the first step is to deduct propagation path effects, station site responses and instrumental responses from the seismic records, that is, to obtain focal spectrums.

The Fourier amplitude of any surface seismic movement observed by a station can be represented as

 ${U_{ij}}\left(f \right) = {\mathit{\Omega }_i}\left(f \right)\cdot{P_{ij}}\left(r \right)\cdot{F_{ij}}\left({f, r} \right)\cdot{S_j}\left(f \right)\cdot{I_j}\left(f \right)$ (1)

Where f is frequency, Ω(f) is the ith focal spectrum, Pij (r) is geometric attenuation function, r is the distance between the earthquake and the station, Sj (f) is the site response of the jth station, Ij (f) is the instrumental response of the jth station, and Fij (f, r) is the inelastic attenuation parameters.

The instrumental response of a certain type of seismic instrument is given.

If the geometric attenuation function, quality factor and site response are all given, then the solution of the focal spectrum is

 ${\mathit{\Omega }_i}\left( t \right) = {{{\mathit{\Omega }_0}} \over {1 + {{\left( {{f \over {{f_0}}}} \right)}^2}}}$ (2)

where the three-section geometric attenuation model proposed by Atkinson et al. (1992) is used for the seismic wave geometric attenuation, and the multi-station joint inversion proposed by Moya et al. (2000) and Liu Jie et al. (2003) is used for site response.

According to Brune's model (Brune et al., 1970), stress drops can be represented as

 $\Delta \sigma = {{14{\rm{ \mathsf{ π} }}\rho {\mathit{\Omega }_0}} \over {{{2.34}^3}{R_i}\left( {\theta , \varphi } \right)}}$ (3)

where Ω0 is the zero frequency limit value of amplitude spectrum, ρ is the density with the value of 2.9g/cm3, Ri (θ, φ) is the emission factor of the seismic waves, θ and φ stand for the azimuth and the off-source angle from the earthquake to the station with the value of $\sqrt {2/5}$.

1.2 Correlation Coefficient of Body-wave Spectral Amplitudes

When two earthquake focuses are close enough to each other, i.e. the distance is shorter than that of the epicenters, then the geometric diffusions, inelastic attenuations, site responses and instrumental responses of the two earthquakes recorded by the same station will be the same. Then the observed spectrum value ratio of the same station in the same frequency is represented as

 ${{{U_{1j}}\left( f \right)} \over {{U_{2j}}\left( f \right)}} = {{{R_{1j}}\left( {\theta , \varphi } \right)} \over {{\rm{ }}{R_{2j}}\left( {\theta , \varphi } \right)}}\cdot{{{M_{01}}} \over {{M_{02}}}}\cdot{{1 + {{(f/{f_0}\left( 2 \right))}^2}} \over {1 + {{(f/{f_0}\left( 1 \right))}^2}}}$ (4)

When f$\ll$f0 (1) and f0 (2), the above equation can be expressed as

 $\frac{{{U}_{1j}}~({{f}_{0}}~)}{{{U}_{2j}}~({{f}_{0}}~)}\text{ }=\frac{{{R}_{1j}}~\left( \theta , \varphi \right)}{{{R}_{2j}}~\left( \theta , \varphi \right)}\text{ }\cdot \frac{{{M}_{01}}}{{{M}_{02}}~}$ (5)

where U1j (f0) and U2j (f0) represent the zero frequency observed spectrum values and $\frac{{{M}_{01}}}{{{M}_{02}}~}$ is a constant.

Equation (5) shows that the zero frequency observed spectrum ratio of the two earthquakes in the same focal zone has a linear relationship with the radiation pattern factors, and the latter is determined by the trends, dips and shipping angles of the geometric features of the earthquake focal mechanism solutions. It is thus concluded that when earthquakes occur within a small range, their propaganda paths and site responses are exactly the same. Then the difference between the zero frequency observed spectrum values recorded by different stations basically comes from the difference of the earthquake focal mechanisms. The research of Cui Zijian et al. (2012) reveals that there is an obvious difference between the focal mechanism changes of a foreshock sequence and a non-foreshock sequence. There is more obvious similarity between the focal mechanism solutions of foreshock sequences and the correlation coefficient of spectral amplitudes is close to 1.0. The similarity of the focal mechanism solutions of non-foreshock sequences is weak, and the correlation coefficient of spectral amplitudes goes farther away from 1.0. This feature is of important precursory significance. Therefore, the comparison of the zero frequency observed spectrum values of different earthquakes at the same station can be used to speculate the difference between the focal mechanisms between earthquakes.

Lund et al. (2002) proposed a calculation method of the correlation of body-wave spectral amplitudes that the correlation coefficient is calculated via the inversion of the zero frequency spectral amplitudes of the direct body waves of the earthquakes in the same focal zone and is used to describe the difference between the focal mechanisms. For S-wave three-component wave records, three zero frequency spectrum values can be obtained at each station: vertical, radial and tangential (SZ, SR, ST). The correlation coefficient calculation helps to obtain the similarity between the seismic events. The correlation coefficient rxy of the body-wave spectral amplitudes is defined as

 ${{r}_{xy}}~=\frac{{{\sum }_{i, j}}~({{x}_{ij}}~-\bar{x})({{y}_{ij}}~-\bar{y})}{\sqrt{{{\sum }_{i, j}}~{{({{x}_{ij}}~-\bar{x})}^{2}}{{({{y}_{ij}}~-\bar{y})}^{2}}}}$ (6)

where xij and yij stand for the log of the jth spectrum value components of the two different seismic events at the ith station. x and y is the average of xij.

1.3 Clustering Group

The correlation coefficient of the body-wave spectral amplitude can only describe the correlation degree of the total focal mechanism in a certain time period, and Deng Fei et al. (2014) therefore proposed using clustering grouping in the correlation analysis of focal mechanisms to further describe the evaluation of focal mechanism. The basic idea of clustering grouping is to group the data into different types or clusters. The data in the same cluster have strong similarity while those in different clusters have great difference.

On the basis of the obtain of the correlation coefficients of the spectral amplitudes of the earthquake events in a sequence, this paper uses the cluster averaging method to group the correlation coefficients of the earthquake events according to their values and get binary tree clustering graphs. The group-average method takes the average distance of the two clusters as the distance between the clusters (Zhou Haiyan et al., 2010), that is

 ${{D}_{G}}~\left( p, q \right)=\frac{1}{LK}\sum\limits_{i\in {{G}_{p}}}{\sum\limits_{i\in Gq}{{}}}~{{d}_{ij}}~$ (7)

where Gp and Gq are different clusters: L and K are the sample numbers of Gp and Gq respectively. This paper defines the distance as the difference between 1 and the correlation coefficient of the spectral amplitude, meaning that the shorter the distance between the points, the higher the similarity between them.

2 MATERIAL SELECTION

This paper collects the waveform data of ML ≥2.5 earthquakes in the Xinyuan-Hejing ML 6.8 earthquake sequences recorded in the Xinjiang Regional Digital Seismic Network and inverts for 103 focal parameters and calculates the correlation coefficients of focal mechanism solutions of 85 earthquakes and clusters them on this basis. Considering that the stations with different locations are used and the distances between the stations to the focal zones are larger than those between earthquakes, this paper selects five stations in different locations, i.e. Xinyuan station △=118km (XNY), Shitizi station △=157km (STZ), Jinghe station △=194km (JHE), Korla station △=215km (KOL) and Karamay station △=245km (KMY), to calculate the correlation coefficients of the spectral amplitudes (Fig. 1). The multi-station joint inversion (Atkinson et al., 1992) is used to obtain the Q value of inelastic attenuation in the middle section of Tianshan Q (f)=465.2f0.53 (Liu Jianming et al., 2014). The inversion method of Moya et al. (2000) is used to obtain the station site responses (Tang Lanlan et al., 2011; Liu Jianming et al., 2014).

 Fig. 1 Focal distributions of the Xinyuan-Hejing ML 6.8 earthquake sequences and participating stations
3 CALCULATION RESULT AND ANALYSIS 3.1 Focal Parameters of the Earthquake Sequences

We use the Brune's disc model to calculate the stress drops of ML ≥2.5 earthquakes in the Xinyuan-Hejing ML 6.8 aftershock sequences (Fig. 2). The result shows that the stress drops of the 102 aftershocks in the aftershock sequences are 0-8MPa. There is not clear dependent relationship between the stress drops of ML ≤3.5 aftershocks and the earthquake scales. The stress drops of some ML > 3.5 aftershocks (red dots in Fig. 2) show positive correlation with the earthquake scales. Therefore, this paper excludes the stress drops which have obvious correlations with the earthquake scales when discussing average stress drops.

 Fig. 2 Relationship between the stress drops of the Xinyuan-Hejing ML 6.8 aftershock sequences and the scales (Red dots are the earthquakes excluded)

Fig. 3 is the evolution in time of the stress drops in the Xinyuan-Hejing ML 6.8 aftershock sequences. After the exclusion of the stress drops obviously correlating with the scale, the average of the stress drops in the aftershock sequences is 2.47MPa (dot lines in Fig. 3). Fig. 3 shows that in several days after the mainshock, the stress drops of the aftershocks fall basically in the range of 4-8MPa, with six aftershocks of the scales above 4.0. After that, the stress drops gradually return to the average stress level, showing that the focal zone stress after the shock is in the process of adjustment. During this period, the stress drops of July 6-8 rose gradually. From July 9 on, the stress drop values were lower than the average stress level. Five days later, the ML 4.1 aftershock occurred on July 13. On August 7-14, the stress drops of the aftershocks rose clearly again with a larger amplitude and longer time than the ML 4.1 aftershock. The largest aftershock in the sequence, the ML 4.9 aftershock, occurred nine days later, on September 1. Generally speaking, in the quiet period of the aftershock sequence, the stress drop values are stable, and the stress drops before the strong aftershocks has a rise-fall change. The earthquake tendency judgment can take into account the change of the stress drops of the earthquake sequences with time in the assessment of the risk of strong aftershocks.

 Fig. 3 Stress drop changes in the Xinyuan-Hejing ML 6.8 aftershock sequences with time (Dot lines are the average lines of the stress drops)
3.2 Correlations of Sliding Average Spectral Amplitudes

For further understanding of the changes of correlation coefficients of spectral amplitudes before and after the mainshock, Cui Zijian et al. (2012) improved the body-wave spectral amplitude correlation analysis of micro earthquakes originally proposed by Lund et al. (2002), and applied the method to the judgment of small earthquake swarm sequence. The specific principle is to arrange the earthquakes in a time sequence with the earthquake m and the previous one m -1 in a group, and calculate the rxy of the two earthquakes in each group and get their correlation coefficient rxy with N=m (m-1) /2. Then calculate the average of rxy, and the result stands for the correlation degree of the spectral amplitudes within the group at the m moment of the earthquake. This paper uses this method and moves with a step of one earthquake and calculate the average of the correlation coefficients of the zero frequency spectral amplitudes in each group. We obtain the correlation coefficients of the spectral amplitudes of the Xinyuan-Hejing ML 6.8 earthquake sequences with time changes (Fig. 4). The result shows that the correlation coefficients of the average moving spectral amplitudes of the aftershocks are 0.54-0.62, denoting that the focal mechanism solutions after the mainshock are dispersive, and the correlation of the mechanism solutions with the mainshock lowers, showing the small possibility of a subsequent greater earthquake. Our research result is consistent with that of Cui Zijian et al. (2012), i.e. in small earthquake sequences, the focal mechanism solution is dispersive, and the correlation coefficient of the moving average spectral amplitude varies in low value along the time curve.

 Fig. 4 Correlation coefficient curve of the moving average spectral amplitude of the Xinyuan-Hejing ML 6.8 earthquake sequences
3.3 Clustering Analysis of the Correlations of Sequence Focal Mechanism Solutions

The correlation coefficient of the moving average spectral amplitude describes the correlation degree of the whole focal mechanism solution in a certain time section. We conduct the clustering grouping of the focal mechanisms of the Xinyuan-Hejing ML 6.8 earthquake sequences for correlation coefficients of more body-wave spectral amplitudes. Fig. 5 shows the relationship between the swarm groups of the Xinyuan-Hejing ML 6.8 earthquake. The earthquake focal mechanism solutions belongs to Group 4. Except Group 4 where there is no correlation between the earthquakes, Groups 1 to 3 have a correlation coefficient of 0.52 -0.53 between each group and the correlation coefficient within the group is higher.

 Fig. 5 Clustering groups of the Xinyuan-Hejing ML 6.8 earthquake sequence

Table 1 shows the focal mechanism solutions of the MS ≥4.0 earthquakes in the Xinyuan-Hejing ML 6.8 earthquake sequences obtained by Li Zhihai et al. (2014). The result shows that the earthquake focal mechanism solutions are all a strike-slip type and the difference lies in the amount of thrust components. The P-axis azimuth has an obviously advantageous distribution with the major direction of NS (Fig. 6), consistent with the tectonic stress field in the NS direction in the mid-eastern section of north Tianshan (Long Haiying et al., 2008; Zhang Hongyan et al., 2014). This shows that the middle section of Tianshan had a clear horizontal compressive stress in the NS direction.

Table 1 Focal mechanism solutions of the ML ≥4.0 earthquakes in the Xinyuan-Hejing ML 6.8 sequences

 Fig. 6 The Xinyuan-Hejing earthquake sequence and azimuth distribution of P-axis

The result of the comparison of the focal mechanism solutions of the MS ≥4.0 earthquakes and the clustering groups can be easily seen. (1) The focal mechanism solution of the main shock (serial No. as 1) is Group 2, where the characteristic of the focal mechanism solution is a strike-slip earthquake with a larger thrust component (Li Zhihai et al., 2014) and the P-axis azimuth is in the near NS direction. (2) The focal mechanism solution of the group with the serial No.2 is Group 3, which is a strike-slip earthquake with the thrust component smaller than Group 2 and the P-axis azimuth in the near NS direction. (3) The focal mechanism solution of the group with the serial No.2 is Group 3, which is a strike-slip earthquake with the thrust component smaller than Group 3 and the P-axis azimuth in the near NNW direction. In short, the focal mechanism solutions of the Xinyuan-Hejing ML 6.8 earthquake sequences are consistent with the strike-slip earthquakes as the major type. As time goes on, the thrust components of the focal mechanism solutions of the aftershock sequence get smaller. The azimuths of Group 2 and Group 3 are both near NS with the azimuth of Group 2 of 358° representing that of the two groups. The P-axis azimuth turns from near NS to NNW (Fig. 8), showing that the focal mechanisms of the earthquake sequence tend to be dispersive, the control of the tectonic stress field tends to get weaker and the major earthquakes are moderate and small earthquakes that may occur depressively.

 Fig. 7 The dip angle T-axis varied with time

 Fig. 8 Azimuth of P-axis varied with time

The grouping of the scales and focal mechanism solutions of the Xinyuan-Hejing ML 6.8 earthquake sequences shows that during the period between the mainshock and July 2 (seismic event 50), there were six ML ≥4.0 aftershocks, and because there are too many groups of focal mechanism solutions, there is no good consistency between the focal mechanism solutions. The focal mechanism solutions of the August 7 to 23 aftershocks (seismic events 76 -80) have good consistency and there is also consistency between the stress directions and the tectonic stress field of the focal mechanism solutions. A strong aftershock of ML 4.9 (seismic event 81) occurred later on September 1. This phenomenon shows that the focal mechanisms before a strong aftershock have a good consistency, showing the enhancement of the control of the regional stress fields which helps the occurrence of the subsequent strong aftershock.

 Fig. 9 Group evolution of the scales and focal mechanism solutions of the Xinyuan-Hejing ML 6.8 earthquake sequences
4 DISCUSSION AND CONCLUSION

We reach the preliminary conclusion after the calculation of the stress drops and the spectral amplitude correlation coefficient of the 2012 Xinyuan-Hejing ML 6.8 earthquake sequences as well as the clustering of the focal mechanisms of the earthquake sequences and the results are as follows:

(1) The stress drops of the ML ≤3.5 aftershocks of the Xinyuan-Hejing ML 6.8 earthquake sequences have no obvious dependent relationship with the scale. The stress drops of the ML > 3.5 aftershocks have a positive correlation with the scale. The stress drop of the main shock is 53.375MPa with a complete release of energy. The stress drops of aftershocks change with time, which shows that in the quiet stage of the aftershock sequence, stress drop changes tend to be stable. The stress drops before the strong aftershock have a rise-fall change.

The previous studies of stress drop changes with time have a result consistent with that of the current study. Hua Wei et al. (2009) studied the sectional focal parameters of the 2008 Wenchuan MS 8.0 earthquake sequences. The stress drops between Beichuan and Qingchuan before May 17 were continuously at high value levels and after that day the major activity zone of the ML ≥5.0 aftershocks moved to this section and the Qingchuan MS 6.4 strongest aftershock took place. Hardebeck et al. (2009) studied the correlation between the high stress drop distribution on a fault and shear stress and blocking region, and found that the high stress drop concentrated region is a potential focal core region of moderately strong earthquakes. Thus, the aftershock sequence stress drop change with time has a definite referential value for the tendency judgment after an earthquake.

(2) The correlation coefficient of the moving average spectral amplitudes shows that the correlation coefficients of the moving average spectral amplitudes of the aftershocks fall between 0.54-0.62, which means that the correlation between the focal mechanism solutions after the main shock is low, and the change denotes a low possibility of the reoccurrence of a large earthquake. That is consistent with the reality. Therefore, we believe that the spectral amplitude correlation coefficient can be used as an indicator for a small earthquake sequence and a strong earthquake sequence. Our result shows a consistency with that of Cui Zijian et al. (2012) who studied three ordinary small earthquake swarms and two strong and small earthquake swarms in northwestern Yunnan.

(3) The clustering grouping of the Xinyuan-Hejing ML 6.8 sequences, combined with the known MS ≥4.0 earthquake focal mechanism solutions, shows that the focal mechanism solutions can be divided into 4 groups. Except for Group 4, which shows no correlation between the earthquakes, all earthquake focal mechanism solutions are of a strike-slip type with the main stress axis distributed mainly in the near NS direction. The direction is consistent with the NS tectonic stress field in the mid-eastern section of the north Tianshan. This shows that there is an obvious function of the horizontal compressive stress in the near NS direction in the middle section of Tianshan before the earthquake. The result is consistent with that of research by Wang Qiong et al. (2015) on earthquake sequence focal mechanisms via P-wave wave first motions.

Also, there is some randomness in the small earthquake focal mechanisms, but large sampling shows there is a consistency between the advantageous stress field distribution and tectonic stress field. This proves that with a certain size of sampling, the advantageous tendency of the small focal mechanism solutions also reflects the regional stress field direction.

(4) The clustering evolution of the scales and focal mechanism solutions shows that the aftershock focal mechanism solutions before the strong aftershock reflect the consistency of stress fields and tectonic stress fields. There is also a good consistency between the focal mechanism solutions and this proves the enhancement of the regional stress field control which has a prediction significance for the subsequent strong aftershocks. On the other way round, the increase of the focal mechanism solution types and the dispersion of the main stress directions show the weakening of the regional stress field control and the principal subsequent aftershocks will be moderate and small earthquakes.

(5) The methods of spectral amplitude correlation coefficients and clustering grouping help to understand as many focal mechanism solutions of small earthquakes as possible and clearly study the whole changing process of the focal mechanism solutions of moderate and small earthquakes in an earthquake sequence. Based on this joint time features of the stress drops in an earthquake sequence, the study of the stress levels of the regional stress field has a physical and quantitative significance in the determination of the risks of future earthquakes in the focal zone. In reality, the application of correlation coefficients of stress drops and spectral amplitudes to foreshock sequences or small shock sequences has an important role in the fast judgment of the earthquake after the occurrence of the earthquake.

ACKNOWLEDGEMENTS

The authors owe their greatest gratitude to the anonymous peer previewers for their constructive opinions and advice.

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1 新疆维吾尔自治区地震局, 乌鲁木市新市区科学二街338号 830011;
2 中国地震台网中心, 北京 100045;
3 云南省地震局, 昆明 10000