Earthquake Reaearch in China  2017, Vol. 31 Issue (2): 151-168
Comparative Study of Changes in Stress-drop of the Jinggu MS6.6 and Ludian MS6.5 Earthquake Sequences
Zhou Shaohui1, Jiang Haikun2, Qu Junhao1
1. Earthquake Administration of Shandong Province, Jinan 250102, China;
2. China Earthquake Networks Center, Beijing 100045, China
Abstract: The earthquake stress-drop values of two sequences were accurately calculated after taking away the effects due to regional earthquake anelastic attenuation and station site response, using waveform data and seismic phase data of sequences of the Jinggu MS6.6, and Ludian MS6.5 earthquakes in Yunnan. These results show that the stress drop with magnitude increases within the scope of this study of magnitude. After eliminating the influence of the magnitude, the average value of stress-drop in the Jinggu sequence is higher than that of the Ludian sequence at the same magnitude range. This may be related to the stress state in different regions. In terms of the changes of time and space of stress-drop, before MS5.8 strong aftershock, the stress-drop is "slowing down-turning up-keeping a high value" after the mainshock, meanwhile, almost all of the abnormally high stress drop value is distributed around the MS5.8 strong aftershock, showing that the stress environment in the region was increasing after the mainshock. And after the MS5.9 strong aftershock, stress-drop rapidly declines to a relatively stable state, meanwhile, the high value of stress-drop is distributed around the strong aftershock, showing that the regional tectonic stress gets more fully release, its stress environment begins to rapidly decrease. For the Ludian sequence without a strong aftershock occurring, the average value of stress drop is lower than that of the Jinggu earthquake sequence at the same magnitude range, while at the same time, the stress-drop of the aftershock sequence almost hasnt changed much. In the time after the mainshock, combined with the release characteristics of the main energy, the stress in the region is excessively released, the subsequent stress in the region gradually returns to normal. This may be the reason why the activity of Ludian aftershocks significantly was weaker and subsequently there were no strong aftershocks occurred.
Key words: Stress-drop     Aftershock sequence     Ludian earthquake     Jinggu earthquake

INTRODUCTION

With the continuous improvement of the digital observation technology of seismicity, attention is gradually paid to the study of aftershock prediction by calculating the source and medium parameters based on digital seismic data. This is an important future direction for development of the determination of post-seismic tendency (Jiang Haikun et al., 2015). Seismicity is a medium rupture in the source area or extension of the instability of the original fault under the action of the external load, whether it is rupture or extension of the instability of the original fault, and is the result of rock deformation to a certain extent under stress. In other words, the occurrence of earthquakes is related to the stress environment, where the rocks broke. In the case of aftershocks, the determination of the stress state of the source region has great significance to the judgment of post-seismic tendency and the prediction of strong aftershocks after an earthquake (Zhong Yuyun et al., 2004). Under the existing technical conditions, the stress state of the focal area can′t be directly measured due to earthquake occurrence in the deep underground. The strength, direction and mode of the local stress field are often studied using the focal mechanism, the stress-drop and the apparent stress (Chen Xuezhong, 2005). Among these, the stress drop indicates that the stress is changed on the dislocation surface when the earthquake occurs instantaneously. The change with time of the stress-drop of small earthquakes may reflect the change of the stress state (Hua Wei, 2007). Theoretically, if the stress-drop of small-moderate earthquakes in the aftershock sequence is gradually increased after a big earthquake, then the focal area is still in a high stress state, and there is a mechanical background condition for strong aftershocks to follow (Jiang Haikun et al., 2015). By calculating the source parameters of the aftershock sequence and analyzing the variation of the stress-drop with time and space, it is possible to understand the dynamic evolution of the stress state in the source region, which may have some significance for the prediction of a subsequent strong aftershock (Hua Wei et al., 2009).

On August 3 and October 7, 2014, the Ludian MS6.5 and Jingxiu MS6.6 earthquakes successively occurred in the Yunnan region, with similar magnitude and the same rupture pattern (both nearly NNW strike-slip faults). Both were respectively located in the east and southwest sides of the Sichuan-Yunnan rhomboidal block, and were related to the SN movement of the Sichuan-Yunnan rhomboidal block, but the two earthquakes did not occurred on the crustal boundary zone (Fig. 1(a)). The aftershock activity of the two earthquakes is quite different; as of January 7, 2015, the maximum magnitude aftershocks of the Ludian earthquake were the two MS4.7 earthquakes that occurred on August 4, and September 10, 2014. However, Jinggu successively saw two strong aftershocks with magnitude 5.8, 5.9 after two months. This provides an important earthquake example for the study and analysis of the aftershock sequence of stress-drop, and the study of a possible relationship between the changes of stress-drop and subsequent strong aftershocks.

 Fig. 1 Distribution of faults, stations and aftershocks in the study area (a)The distribution of the main active faults in the Sichuan-Yunnan region and the Ludian and Jinggu earthquakes; (b) is the magnification of the b-box in (a), the circle for the ML≥2.5 aftershocks of the Ludian MS6.5 earthquake sequence from August 3 to November 3, 2014; (C) is the magnification of the c-box in (a), and the circle is the ML≥2.5 aftershocks the Jinggu MS6.6 earthquake sequence from October 7 to January 7, 2014; the triangles of the figures (b) and (c) are the stations participates in the calculation, black triangles denote stations of the Yunnan Digital Seismic Network; green ones denotes mobile station; blue denotes the Qiaojia seismic array; red ones denote reservoir network stations

Based on the waveform and seismic phase data of the Ludian and Jinggu earthquake sequences, the stress-drop of ML2.5-5.0 earthquake events in the Ludian and Jinggu earthquake sequences is calculated respectively. In this paper, the comparative study of the general characteristics of stress-drop of the aftershocks in the same period after the mainshock, and the change of time and space of stress-drop, exploration of the potential differences of stress-drop in the early stage of subsequent strong aftershocks and follow-up without strong aftershocks, as well as the indication of the subsequent strong aftershocks by the change of time and space of stress-drop are carried out.

1 PRINCIPLE AND METHODS

The source parameters are calculated by inverting the source spectrum from the actual seismic waveform data, and then the seismic source spectrum is fitted with the theoretical source spectrum to obtain the corresponding source spectral parameters.

The seismic waveform data recorded by the seismic station contains information such as the source, seismic wave propagation path and site effects of stations (Liu Jie et al., 2003). The seismic displacement spectrum Uij(f) recorded by the station can be expressed as:

 ${{U}_{ij}}\left( f \right)=\left[ {{S}_{i}}\left( f \right){{P}_{ij}}\left( f \right)L_{f}^{'}\left( f \right)+{{N}_{j}}\left( f \right) \right]{{I}_{j}}\left( f \right)Su{{r}_{j}}$ (1)

Where f is the frequency; Si(f) is the seismic source spectrum of the earthquake i; Pij(f) is the propagation path effect between the earthquake i and the station j, describing the attenuation of the seismic wave during propagation, including geometric diffusion and inelastic attenuation; L'j(f) is the local site effects of stations j, which describes the amplification effect of the seismic wave from the media of near-surface stratum near station; Nj(f) is the ground noise near station j; Ij(f) is the instrumental response of the station j; Surj is the free surface effect near the station j, which describes the reflection characteristics of seismic waves incident on the free surface. Theoretically, the displacement of the reflected wave for the waves SH that produce reflections is equal to the displacement of the incident wave. The displacement of recorded wave SH is exactly twice the displacement of the incident wave, that is, Surj=2 in the station type (1) of the SH wave record of the terrestrial station, while the downhole record is Surj=1.

From the equation (1), in order to get the source spectrum Si(f), it is necessary to eliminate the noise term Nj(f), the instrumental response Ij(f), the propagation path effect Pij(f) (including geometric diffusion and inelastic attenuation) and the local site L′j(f) of station j from the seismic wave recording. At present, it is common practice to eliminate noise levels in the process of converting seismic signals from a time domain to a frequency domain using the delayed window spectrum technique (Chael, 1987; Huang Yulong et al., 2003), which can be calibrated by instrument calibration since the usually instrument response is the comprehensive effect of each part of the seismograph observation system (Liu Lifang et al., 2005; Hua Wei, 2007; Yang Jingqiong, 2010). The influence of the propagation path is eliminated by finding the medium quality factor Q, that is calculated using multiple multi-seismic joint inversion methods by using the three segment geometry attenuation model (Atkinson et al., 1992, 1995, Huang Yulong et al., 2003), and using multiple multi-seismic inversion methods to calculate the site effects of stations (Moya et al., 2000; Liu Jie et al., 2003).

After obtaining the source spectrum, the genetic algorithm is used to fit the seismic source spectrum and the theoretical source spectrum, and then the zero-frequency limit Ω0 and the corner frequency fc are obtained (Holland, 1975; Moya et al., 2000; Liu Jie et al., 2003). The following equations can be used to solve the seismic parameters such as stress drop Δσ, seismic moment M0 and source radius R, since this paper focuses on the small-moderate earthquakes that satisfy the Brune disc model (Brune, 1970, 1971):

 $\Delta \sigma = \frac{7}{{16}} \cdot \frac{{{M_0}}}{{{R^3}}}$ (2)
 ${M_0} = \frac{{4\pi \rho v_{\rm{S}}^{\rm{3}}{\mathit{\Omega} _0}}}{{{R_{\theta \varphi }}}}$ (3)
 $R = \frac{{2.34{v_{\rm{S}}}}}{{2\pi {f_{\rm{c}}}}}$ (4)

Among these, ρ is the regional medium density of the study area, vS is the propagation velocity of S-wave, and ρ=2.7g/cm3, vS=3.5km/s in the Sichuan-Yunnan region (Ruan Xiang, 2007; Yang Jingqiong et al., 2010). Rθφ is the radiation pattern coefficient of the SH wave, averaging 0.41 (Stork et al., 2004).

2 THE DATA

This paper focuses on the stress-drop characteristics of aftershock activity at the early stage after the earthquake (within 3 months after the earthquake). According to the CENC earthquake catalog, as of November 3, 2014, the Ludian earthquake sequence had recorded a total of 236 ML≥2.5 aftershocks, among which there were 150 ML2.5-2.9 aftershocks, 79 ML3.0-3.9 aftershocks and 7 ML4.0-4.9 aftershocks. The largest magnitude aftershocks were two ML4.7 earthquakes that occurred on August 4, 2014 and September 10, 2014. At the same time, as of January 7, 2015, the Jinggu earthquake sequence had 289 aftershocks of ML≥2.5, among which 156 were ML2.5-2.9, 115 were ML3.0-3.9, 18 were ML4.0-4.9 and 2 were ML≥5.0 with magnitude ML 5.8, 5.9 that occurred successively on December 6, 2014.

In this study using the waveform data of the Ludian earthquake sequence recorded by four stations in the Yunnan Digital Seismic Network (two fixed stations and two mobile stations) and three stations in the Qiaojia seismic array were used. The waveform data of the Jinggu earthquake sequence recorded by four stations of Yunnan Digital Seismic Network (three fixed station and one mobile station) and the four reservoir stations (Fig. 1), that followed each earthquake was recorded by at least three stations, and there are at least three seismic records for each station (Liu Jie et al., 2003; Hua Wei et al., 2009). Seismic records with better waveforms and capable of 1.5 times SNR are used for this study.

3 CALCULATING RESULTS AND ANALYSIS 3.1 Seismic Wave Attenuation and the Site Response of Station

To calculate the seismic wave attenuation and the station site response, the fixed stations of the Yunnan Digital Seismic Network and the mobile station set up after the earthquake (Fig. 1) were selected in the vicinity of the earthquake sequence. For the Ludian area, 22 data items were recorded for the seven stations are selected, the calculation of the Q-value is Q(f)=189.8f0.4614; For the Jinggu area, 24 seismic data items recorded by 8 stations are selected, and the calculation of the Q value is Q(f)=223.8f0.3531. A relatively small Q0 and a high η value can be seen in the Ludian area, which reflects the regional difference of the Q-value in northeastern Yunnan and southwestern Yunnan, which may have some relationship with the geological structure. Western Yunnan (Mainly Baoshan block) on the upper crust is relatively low-speed area, but the lower crust is not found in the low-speed layer; however, the upper crust of the eastern part in Yunnan is a relatively high-speed area, the middle and lower crust have generally developed a low-speed layer, the same as the basic understanding of the low Q (attenuation fast) at low speed and the high-speed with high-Q (slow attenuation) (Su Youjin et al., 2006).

Figs. 2 and 3 are use of Moya et al. (2000) of the multiple multi-seismic source joint inversion method to obtain the site response of stations of the Ludian, Jinggu area. From Fig. 2 and Fig. 3, 15 stations have a site response value of 1 to 2. Among these, the site response of B04, L5301 stations in Ludian is relatively stable, there is no obvious frequency amplification, and it can be better recorded in the ground motion band. The site response of C05, ZAT, QIJ have a significant change in the frequency range of 1-20Hz, and the high frequency side is obviously reduced; at the same time, the site response of A03 and L5303 is increased from low frequency to high frequency and then rapidly decreases (Fig. 2).

 Fig. 2 The site response of stations in the Ludian source area The blue line is the result of a single earthquake; the red line is the result of the whole fitting

 Fig. 3 The site response of stations in the Jinggu source area The blue line is the result of a single earthquake; the red line is the result of the whole fitting

The site response of SIC, JIG, LIC stations in the Jinggu area is are relatively low, and the site response of LIC, BAD is relatively stable. The site responses of XIC, JIG, L5309, LUL, SIM, HEP have a significant C change in the 1-20Hz frequency range, and the high frequency side significantly decreases (Fig. 3). Site response is mainly affected by the topography and geomorphology of the location of stations, the platform conditions of the stations and the local geological structure (Zhang Hongcai et al., 2015). Soft sedimentation sites have a greater effect on ground motion magnification, hard bedrocks are smaller andthe site response of the bedrock station is relatively flat in most frequency bands (Shearer, 1999). In addition, the local medium characteristics of the receiving sites have little difference in the absorption of the low frequency part of the source spectrum, but have a relatively strong absorption capacity for the high frequency part of the seismic wave, and thus it has a significant effect on the high frequency band of the seismic spectrum (Ye Jianqing, 1998). In the vicinity of the epicenter of the Ludian earthquake, the lithology of platform of QIJ station is conglomerate, ZAT station is basalt, and L5301 and L5303 stations are bedrock. The platform lithology of the other stations is not known. In the these rocks, the lowest hardness is the conglomerate, followed by the basalt, and the highest hardness is the bedrock, which is clearly visible from Fig. 2. The maximum amplification is more than 2 for the low-band in QIJ station, while the for other stations it is smaller. In the Jinggu area, the lithology of the platform of the SIM, JIG and LIC stations is known as sandstone, and the other lithology of the other stations is unknown. Therefore, the site response can not be simply compared by the lithology of the station platform. In addition, for the change of the site response in the high-frequency of each station, the combination of topography and geomorphology of the stations, local geological structure and other factors is needed for further analysis.

3.2 The Stress-drop of Aftershocks of the Ludian and Jinggu Earthquake Sequences

Based on the calculation of the Q of the area near the Ludian and Jinggu earthquake epicenter and the site response of the stations, the stress-drop of the two earthquake sequences within 90 days after the earthquake are respectively calculated as ML2.5-5.0 and the other calculation conditions are satisfied, among which there are 99 earthquakes in the Ludian earthquake sequence, with 173 earthquakes in the Jinggu earthquake sequence, respectively accounting for 42% and 60% of their earthquake sequences at the same time for the simultaneous earthquakes (Figs. 4, 5). From Fig. 4 and Fig. 5, we see that the earthquakes from which we can calculate stress-drop mainly cover the more prominent earthquake events in each time period, whether it is the Ludian earthquake sequence or the Jinggu earthquake sequence.

 Fig. 4 The M-t diagram of the ML≥2.5 earthquakes, and in which can be used to calculate the stress-drop of the Ludian earthquake sequence (Red is earthquake events which can be used to calculate the stress-drop; black is the earthquake events which cannot be used to calculate the stress-drop)

 Fig. 5 The M-t diagram of the ML≥2.5 earthquakes which can be used to calculate the stress-drop of the Jinggu earthquake sequence (Red is the earthquake events which can be used to calculate the stress-drop; black is the earthquake events which cant be used to calculate the stress-drop)

Fig. 6 shows the distribution statistics of stress-drop of the Ludian and Jinggu earthquake sequences. It can be seen from Fig. 6 that the distribution of stress-drop of the Ludian earthquake sequence is more concentrated (less than 9MPa), and the earthquakes with stress-drop less than 6MPa account for about 94%, less than 4MPa. The numerical distribution of stress-drop in the Jinggu earthquake sequence is relatively discrete (mostly less than 12MPa). Compared with the Ludian earthquake, the earthquakes with stress-drop less than 9MPa account for about 83%, less than 6MPa and 4MPa respectively account for about 68% and 49%. The stress-drop system of aftershocks of the Jinggu earthquake sequence is higher than that of the Ludian earthquake sequence.

 Fig. 6 The distribution statistics of stress-drop of Ludian and Jinggu earthquake sequences

Fig. 7 shows the relationship between the stress-drop and the magnitude of the two seismic sequences, and the confidence interval and the prediction interval under 90% confidence and the results of linear fitting are given. The 90% confidence interval represents a stress-drop for a given magnitude earthquake, where the average has a probability of 90% in this interval, and 90% of the predicted interval represents a stress-drop for a given magnitude earthquake. The stress-drop of a single earthquake has a probability of 90% in this interval. There is a trend of a stress-drop increase with intensifing magnitude, and the increase of the stress-drop of the Ludian earthquake sequence is obviously larger than that of the Jinggu earthquake sequence.

 Fig. 7 The relationship between stress-drop and magnitude (a)Ludian earthquake sequence; (b)Jinggu earthquake sequence

Although the trend of stress-drop increasing with intensifing magnitude is clear, but as can be also seen from Fig. 7, the distribution of stress-drop with the magnitude of two earthquake sequences is very discrete, indicating that the relationship between stress-drop and magnitude is very complex. Fig. 8 shows the distribution of the mean stress-drop and its error. As seen from Fig. 8, the average stress-drop increases with increasing magnitude. It can be also seen from Fig. 8 that the results of the exponential fitting are better than those of linear fitting from the relationship between the mean stress-drop and the magnitude, but it is not clear whether this phenomenon has a clear physical meaning. From the error distribution relative to the average, the results show that the stress-drop of the Jinggu earthquake is more discrete than that of the Ludian earthquake. In fact, the stress drop of a small-moderate earthquake being positively correlated with magnitude seems to be a common phenomenon (Mayeda et al., 1996; Mori et al., 2003; Tusa et al., 2008; Zhao Cuiping et al., 2011; Hua Wei et al., 2011).

 Fig. 8 The average stress-drop of the aftershocks of different magnitudes varies with the magnitude (a)Ludian earthquake sequence; (b)Jinggu earthquake sequence The red dots are the mean values of the stress-drop of different magnitudes, and the error bars indicate the degree of dispersion about the measured data of the stress-drop of the aftershocks with this magnitude relative to the mean stress-drop; blue stars are the number of aftershocks with this magnitude. It can be seen that there are few earthquakes with high magnitude that cant give the size of the error bar; black lines are nonlinear exponential fitting results of the mean stress-drop with magnitude, the Ludian sequence is △σ=0.13495ML2.70275, the Jinggu sequence is △σ=0.61556ML1.91324
3.3 Comparative Analysis of Stress-drop in Aftershocks of Different Seismic Sections in the Ludian and Jinggu Earthquake Sequences

In order to deduct the influence of the magnitude, and to keep as much as possible enough earthquake samples to analyze, this paper respectively selects two magnitude scopes within ML2.5-2.9, ML3.0-3.4 for the comparison of the stress-drop of the earthquake from the seismic sequences change over time. Table 1 and Table 2 show the average and MAD of seismic stress-drop in ML2.5-2.9, ML3.0-3.4 of two sequences in 60 days after earthquake. From Table 1 and Table 2, the average stress-drop of the aftershocks of the Jinggu earthquake sequence is significantly higher than that of the Ludian earthquake sequence at the same magnitude. The stress-drop of the aftershocks indicates the level of stress in the source area after the mainshock (Jiang Haikun et al., 2015), which means that although the magnitudes of the main earthquakes of Ludian and Jinggu are similar, the stress level of the epicenter and the nearby area of the Jinggu earthquake is higher than that of the Ludian earthquake after the mainshock, which may be the root cause of Jinggu having a strong aftershock activity Ludian having weak aftershock activity after the mainshock. MAD is the deviation of the statistical data from the mean values. Column 6 of Table 1 and Table 2 shows that for earthquakes in the same magnitude range, the discrete degree of stress-drop of the Jinggu earthquake sequence is significantly higher than that of the Ludian earthquake. The greater the discrete degree within, the larger the magnitude.

Table 1 The average stress-drop of ML2.5-2.9 aftershocks in 60 days after the Ludian MS6.5 earthquake and Jinggu MS6.6 earthquake

Table 2 The average stress-drop of ML3.0-3.4 aftershocks in 60 days after the Ludian MS6.5 earthquake and Jinggu MS6.6 earthquake
3.4 Variation of Stress-drop of Aftershocks of Ludian and Jinggu Earthquake Sequences with Time

The stress-drop represents the stress change on the dislocation plane when the earthquake staggered instantly, the change of the stress-drop with time may reflect the change of the stress state (Hua Wei, 2007). We can indirectly understand the variation in local tectonic stress during the process of the earthquake sequence activity by analyzing the change of the earthquake stress-drop with time.

Fig. 9(a) and Fig. 9(b) show the variation of seismic stress-drop of the ML2.5-2.9, ML3.0-3.4 aftershocks in the Ludian MS6.5 earthquake with time in the 80 days after mainshock. Linear fitting results and confidence intervals and prediction intervals show under 90% confidence probability. It can be seen from Fig. 9, although the variation of the stress-drop of the ML2.5-2.9, ML3.0-3.4 aftershocks respectively showed a gradual recovery and continued decline trend after the Ludian MS6.5 earthquake, but not statistically significant. The results of linear fitting about the variation of seismic stress-drop with time show that the slope is very small, close to 0 (0.00768±0.00433, -0.01496±0.00437, respectively). This means that the stress-drop of aftershocks is almost constant with time from a statistical point of view. The energy released by the mainshock of the Ludian MS6.5 earthquake is unusually large relative to the energy released by the same magnitude earthquake (Zhao Zhonghe, 2014), so that the stress released in the source area is more abundant during the main rupture process. The stress change in the focal area after the earthquake is a process of weak adjustment and gradual recovery, which is also a possible reason for the weak aftershocks of the Ludian earthquake.

 Fig. 9 The variation of seismic stress-drop of the aftershocks in the Ludian MS6.5 earthquake and Jinggu MS6.6 earthquake with time The vertical dots in (c) and (d) indicate the occurrence time of the M5.8 and M5.9 strong aftershocks

2 The Consultation Report PPT of the Underground Fluid Group in the CENC on December 4, 2014.

After 16 hours of the M5.8 strong aftershock on December 6, the M5.9 strong aftershock occurred in the aftershock area of the Jinggu earthquake. It can be seen from Fig. 9(c) and 9(d) that the stress-drop of the aftershocks decreased rapidly after the M5.9 strong aftershock, and the declining trend of the stress-drop in the ML2.5-2.9 earthquake section lasted about 5 to 6 days. The declining trend of the stress-drop in the ML3.0-3.4 earthquake section lasted about 15 days, and then was maintained at a relatively low level. In fact, the aftershock activity of the Jinggu earthquake sequence tended to end after the M5.9 strong aftershocks, the frequency of the aftershocks rapidly decreased, and no ML≥2.5 earthquake occurred.

3.5 Spatial Difference of Stress-drop in Aftershocks of Ludian and Jinggu Earthquake Sequence

Fig. 10 shows the spatial distribution of the stress-drop of ML≥2.5 aftershocks on the 80th day after the earthquake of the Ludian MS6.5 earthquake. Fig. 10 shows that the distribution of the aftershocks of the Ludian earthquake sequence were characterized by the conjugate distribution of NNW and NEE directions (Wang Weilai et al., 2014; Cheng et al., 2015). Most of the aftershocks with high stress-drop were around the mainshock distribution. Compared with the NNW direction, NEE not only had less frequent of aftershocks, but the stress-drop of the aftershocks was also generally lower than that of the NNW. The reason may be that the rupture of the Ludian earthquake started along the NEE, and its fracture activity triggered faulting of the NNW. The rapid expansion of the NNW slowed down the further development of the NEE to rupture, eventually forming in conjugate rupture as a focus on the NNW to rupture (Zhang Yong et al., 2015; Xu Lisheng et al., 2014; Cheng Jia et al., 2016). From stress drop of the Ludian seismic sequence changes with time (Fig. 9(a), 9(b)), the stress-drop of the Ludian earthquake sequence was a process of gradual recovery with time, and the stress-drop of the aftershocks distributed along the NNW fault was generally higher than that of the NEE.

 Fig. 10 The spatial distribution of the stress-drop of ML≥2.5 aftershocks on the 80th day after the earthquake of the Ludian MS6.5 earthquake The red star denotes the mainshock; black denote the earthquakes which haven't calculate the stress-drop

Fig. 11 shows the spatial distribution of aftershock stress-drop at different time periods of the Jinggu M6.6 earthquake sequence. Fig. 11(a) shows that the aftershock distribution had certain segmentation characteristics before the M5.8 strong aftershocks on December 6, and can be divided into three segments, namely, northwest, middle and southwest. The high stress-drop seismicity is mainly distributed in the southeast of the mainshock, that is, the middle and southwest segments of the distribution of the aftershock sequence. From another point of view, the vast majority of earthquakes with high stress-drop occured around M5.8 strong aftershocks, and the stress-drop of aftershocks in the northwest edge of the mainshock were relatively low. This indicates that the stress level of the southeastern side of the mainshock was relatively high after the M6.6 earthquake, which may also be a reason for the continuous occurrence of M5.8 and M5.9 strong aftershocks in this area. It can be seen from Fig. 11(b) that the aftershocks are mainly distributed near the strong aftershocks in the southeast of the mainshock, and there are further signs of extending southward. The high stress-drop is mainly distributed near the strong aftershocks and its southeast.

 Fig. 11 The spatial distribution of the stress-drop of ML≥2.5 aftershocks of the Jinggu M6.6 earthquake (a) From mainshock to the MS5.8 strong aftershock occurring on 02:43 a.m. December 6; (b) 20 days after the MS5.9 strong aftershock occurring on 18:20 p.m. December 6 Red star denotes the mainshock; blue star denotes the MS5.8 strong aftershock, green star denotes the MS5.9 strong aftershock; black circle denote earthquakes which haven't calculate the stress-drop
4 DISCUSSION AND CONCLUSIONS

(1) At present, the relationship between stress-drop and magnitude is controversial. Some researchers believe that the large earthquake sequence usually has strong stress-drop changes, but the stress-drop of the whole seismic sequence is rarely dependent on the seismic moment, that is, the stress-drop is similar to the constant; it is constant with the change of the seismic moment (Shearer et al., 2006; Hardebeck et al., 2009; Allmann et al., 2007, 2009; Annemarie et al., 2011). Other researchers suggest that the stress is dropping with magnitude increasement (Mayeda et al., 1996; Mori et al., 2003; Tusa et al., 2008; Zhao Cuiping et al., 2011; Hua Wei et al., 2012). At the same time, Chen Yuntai et al. (2000) have pointed out that "large" earthquakes have different situation from "small" earthquakes, i.e., for "large" earthquakes with different seismic moments, the stress-drop is close to the constant, and the magnitude of the earthquakes is distinguished from the rupture area and the dislocation; for "small" earthquakes with different seismic moments, the stress-drop increases with increasing magnitude (or seismic moment). The stress-drop in the magnitude range of this study shows a tendency to increase with increasing magnitude. Therefore, the impact of magnitude needs to be eliminated in the application of the stress-drop method.

(2) Although the magnitude of the Ludian mainshock is equal to that of the Jinggu mainshock, the average stress-drop of the Jinggu earthquake sequence is higher than that of the Ludian earthquake sequence in the same magnitude range, which reflects that the stress level of the Jinggu source and the surrounding area is significantly higher than that of the Ludian after the mainshock. This may be the fundamental reason for the Jinggu sequence showing strong aftershocks after the mainshock and the activity of Ludian aftershock being significantly weaker. At the same time, the degree of dispersion of the aftershock stress-drop of the Jinggu earthquake sequence is also higher than that of Ludian earthquake sequence in the same magnitude range. The greater magnitude, the more obvious of the difference is. There is more evidence that the stress-drop is higher in the Jinggu earthquake area; the M6.6 mainschock on October 7 and the M5.8 and M5.9 earthquakes on December 6 occurred on the "Hope" day of solid tide modulation and have obvious tidal modulation characteristics, indicating that the Jinggu earthquake area has a high stress background 3.

3 Rescue Surveillance Report of CENC on December 7, 2014([2014] Pro 40).

(3) In the case of the variation of stress-drop with time, the stress-drop of aftershocks is almost unchanged for the Ludian earthquake sequence with no strong aftershocks after the mainshock. Combined with the analysis of the characteristics of the mainshock energy release, this may be due to the huge release of the mainshock energy, as the stress release is relatively adequate and the change of the source stress after the mainshock is only weakly adjusted and gradually restored. This may also be the reason for the weak aftershocks of the Ludian earthquake.

Before the occurrence of the M5.8 strong aftershocks in the Jinggu earthquake sequence, there was a transformation process of the stress-drop in the "slowing down-turning up-maintaining a high value" sequence after the mainshock, which showed the local stress at the source recurrence of extrusion enhancement after a period of time after the mainshock, then the stress-drop of aftershock increased and was maintained at a relatively high value until the M5.8 strong aftershock occurred. At the same time, the stress-drop decreased rapidly and remained relatively stable after the occurrence of the M5.9 strong aftershock, indicating that the stress of the focal area may have been fully released after the M5.9 strong aftershock. Thus, the change of post-earthquake stress drop with time may have some indication of subsequent strong aftershocks.

From view of fracture mechanics, more and more micro-cracks in the rock produced many tensile fractures under the action of differential stress before cracking, resulting in the expansion of rock volume. As long as there is differential stress, this phenomenon will still appear even under high confining pressure conditions (Brace et al., 1966). According to the expansion-diffusion model (Nur, 1972; Scholz et al., 1973), the expansion of the original rock mass before the strong earthquakes reduces the original pore saturation pressure, and the shear capacity of the rock mass increases with decreasing pore pressure, resulting in the phenomenon of expansion and hardening of the rock, which increases frictional resistance, and thus the fault is temporarily stabilized (the time of the aftershock is also significantly reduced at that time). At the same time, the water in the surrounding rock mass gradually penetrates the unsaturated zone, and the frictional resistance increases as time passes, the shear capacity of the rock mass decreases and the earthquake occurs. Therefore, the fluid plays an important role in the expansion-diffusion model. The underground fluid in the Jinggu area may be enriched, and the upper crust of the Jinggu earthquake area is composed of cretaceous sandstone and mudstone (Cai Linsun et al., 2002), allowing the presence of a large amount of aqueous fluid during its formation. On the other hand, the epicenter of the Jinggu mainshock is only about 30km from the suture zone of the Lancangjiang river, and it is possible for the upper crust to trap a large amount of aqueous fluid in the formation of the suture zone of the Lancangjiang river (Li Yonghua et al., 2014).

In the spatial variation of the stress-drop, most aftershocks with high stress-drop value in the Ludian earthquake sequence are around the mainshock distribution. In the Jinggu earthquake sequence, before the M5.8 earthquake occurred, most of the high stress-drop aftershocks occurred around the strong aftershock of M5.8 which indicated that the stress level of this area was relatively high after the occurrence of the M6.0 mainshock, and this may be the reason for continuous occurrence of the M5.8, M5.9 strong aftershocks in this region after the mainshock. However, the high stress-drop values of the aftershocks are around the strong aftershocks after the M5.9 aftershocks. This further shows that most of the abnormal high-value stress drop is not around the occurrence of strong earthquake distribution, but tends to be distributed in a certain region if a strong earthquake occurs, so the stress level in this region is relatively high, and there is then a possibility of strong earthquake occurrence in this area.

The change of stress-drop with time is related to the occurrence of strong earthquakes in the earthquake sequence. Its variation in space also seems to have some correlation with the location of strong earthquakes, and tracking the temporal and spatial variation of the aftershock stress-drop may provide a certain reference for the judgment of strong aftershocks.However, proof from more earthquake cases is needed because the information in this article is limited.

ACKNOWLEDGMENTS: Thanks to the guidance of research professor Hua Wei, and to Liu Lifang and He Jiabin for their help in the process of collecting waveform data. Thanks to Song Jin, Yang Wen and Deng Fei for their useful help and discussion in this study.

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1. 山东省地震局，济南市历城区港西路2066号，济南 250102;
2. 中国地震台网中心，北京 100045