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Earthquake Reaearch in China  2017, Vol. 31 Issue (1): 90-106
Seismic Strain Energy Release of Active Faults in the Southeastern Margin of the Qinghai-Tibetan Plateau
Liu Jie1,2, Zhao Genmo2,4, Wu Zhonghai2,3, Li Jiacun1
1 National Administration of Surveying, Mapping and Geoinformation, Beijing 100830, China;
2 Institute of Geomechanics, Chinese Academy of Geological Sciences, Beijing 100081, China;
3 Key Laboratory of Neotectonic Movement & Geohazard, Ministry of Land and Resources, Beijing 100081, China;
4 Earthquake Administration of Tianjin Municipality, Tianjin 300201, China
Abstract: Using the methods of the Gutenberg magnitude energy empirical formula and the Benioff seismic strain energy release curve, we make a systematic study on seismic strain energy release of historical earthquakes in the southeastern margin of the Qinghai-Tibetan Plateau since 1500. This paper provides a periodic table of the earthquake strain energy release in the fault zones and the fault block areas. The study shows that seismic strain energy release is strong in the east and south, and weak in the west and north. The overall seismic strain energy release of the Yushu-Xianshuihe-Xiaojiang fault system is consistent with the quasi-periodic pattern. The seismic cycle of some fault zones and fault block areas shows synchronization to a certain extent. The risk cannot be ignored in the current large release period of seismic strain energy in the southeastern margin of the Qinghai-Tibetan plateau. Local seismic risk analysis shows that seismic risk is very high on the Anninghe-Zemuhe and Xiaojiang fault zones. These dangerous zones need follow-up research. In future, it is necessary to combine different research methods to improve the reliability of seismic risk assessment.
Key words: Southeastern margin of the Qinghai-Tibetan Plateau     Seismic strain energy     Seismic cycle     Seismic risk

INTRODUCTION

The southern segment of the North-South Seismic Belt of China is located in the southeastern Qinghai-Tibetan Plateau, which is the central main part of the "Qinghai, Tibet, Yunnan, Myanmar, Indonesia type structure", with the eastern Himalaya syntaxis and the nearly NS-trending Sagaing fault zone as its western boundary and the NW to near-NS trending, arc-shaped Yushu-Xianshuihe-Xiaojiang fault zone as its eastern boundary. It is the region experiencing the highest frequency and largest magnitude of strong earthquakes and the most serious geological and seismic hazards in China (Wu Zhonghai et al., 2015). Subject to extrusion from Himalaya arc and Myanmar arc on its west, and stopped by the Xinjiang and South China blocks on its north and east, the region has undergone significant crustal shortening and uplifting since the Cenozoic. In addition, rapid southeastward extrusion occurred in the region in the neotectonic period, and high-density active fault systems were developed. Since a large amount of strain energy was concentrated in the crust of this region and the stress mainly concentrated on the boundary faults of various scales, the strain process led to the repeated process of accumulation-release-re-accumulation-re-release of stress in the crust, making the region an area with the most frequent strong earthquake activity (Wu Zhonghai et al., 2014). However, through the analysis of earthquake data, it is found that there have been no M=7.0 or greater earthquakes happening in this region since the Lijiang M7.0 earthquake in 1996, and the region is in an abnormally quiet state. However, the leading edge of the rupture of the December 2004 M9.3 earthquake occurring in the southern Sumatra arc has arrived at the Myanmar arc. Also, the November 2001 M8.1 and May 2008 M8.0 earthquakes occurring successively in the northern part of Hoh Xil and Longmenshan fault produced large additional stress on the blocks in this region, which is conducive to inducing strong earthquakes. Meanwhile, after the May 12, 2008 MS8.0 Wenchuan earthquake, in Sichuan, multiple moderate earthquakes have occurred in the southwestern China region in Yushu, Yingjiang, Eryuan, Ya'an, Ludian, Jinggu and Kangding. Obviously, the prelude to another series of strong earthquakes in this region is opening (Zhao Genmo, et al., 2014; Wu Zhonghai et al., 2012; Liu Yanhui et al., 2014). Therefore, as a strong earthquake-prone area, the currently abnormally quiescent state in the southeastern margin of Qinghai-Tibetan Plateau may indicate the possibility of future large earthquake, and as the area has been seismically calm for 19 years since the 1996 Lijiang earthquake, this is worthy of attention.

1 METHOD AND DATA

Strain is a physical quantity closely related to tectonic stress and the earthquake process, and usually applied to dividing earthquake active periods (Ma Hongsheng et al., 2002). Strain energy E released by earthquake is calculated based on the Gutenberg-Richter magnitude-energy empirical relationship (Gutenberg et al., 1956), namely,

 $\lg E = 1.5{M_{\rm{S}}} + 4.8$ (1)

Benioff H. (1951) drew the strain energy release curve of the global M≥8.0 earthquakes in the period of 1904-1954, which characterizes well the decrease of global seismicity of large earthquakes in the early to mid 20th century. In the 1980s, Liu Zhengrong et al. (1983) and Luo Ronglian et al. (1983) applied the strain release curve to the study on the seismic activity characteristics of the Sichuan-Yunnan region, and pointed out that the Qianning-Kangding-Luding, Zhongdian-Dali, Mianning-Xichang regions would be seismogenic areas of future large earthquakes (Liu Zhengrong et al., 1983; Luo Ronglian, 1983). The 1996 Lijiang, Yunnan M7.0 earthquake occurred right in the Zhongdian-Dali section, which further confirmed the scientific validity of this method. Huang Zhongxian et al. (1964) also used this method to discuss the quiescence-active phenomenon of the main seismic zones in China and its relationship with tectonic movement. Ma Hongsheng et al. (2002) studied the seismicity of the active block areas in the Chinese mainland by calculating seismic strain energy accumulation and release, and discussed the trend of future seismic activity in each zone. Mogi et al. (1977) found that there is a phenomenon in which the interval between successive events reduced gradually in the sequence of large earthquakes in Kuril, Japan Trench during the period 1918-1973. He used a multi-spring-slider system to explain the corresponding mechanism, that is, the strength of the system consists of the strength of all the parallel springs, when one of the springs is damaged (an earthquake occurs), the strength is lost and the original structural forces would be borne by other springs. With the number of springs in the system (the number of earthquakes) increases, the intensity of the system is gradually weakened, and the time interval of adjacent earthquakes is also shortened in the form of exponential function. In the study of the rhythmic characteristics of the strong earthquakes in the Chinese mainland, Zhang Guomin (1987) divided the cycle of strong seismicity in the Chinese mainland into three stages, namely, the quiet episode, the transition episode and the strong seismicity episode. In this paper, the periods of seismic cycle are defined based on the Benioff seismic strain energy release curve to analyze the characteristics of seismic strain energy release of the study area and evaluate the current seismic activity.

When studying the accumulation and release of strain in some region, the completeness of the seismic data in the area must be taken into account: First, the relative completeness in time, i.e. whether the selected seismic data contains a complete seismic activity cycle; second, relative completeness in space, that is, the seismic data used should conform spatially to the seismogenic block structure (sometimes called the earthquake zone). In the analysis of characteristics of the seismic time series, seismicity is characterized by alternating between relatively quiescent and significantly active periods in time. Therefore, this feature should be taken into account when examining the completeness of seismic data (Ma Hongsheng et al., 2002).

The study area is 95°-105°E, 21.5°-35°N. The data is selected from the catalogue of historical M>6.0 earthquakes in China Earthquake Information Network, 2015, with reference to the published earthquake catalogs (Seismological Bureau of Yunnan Province, 1988; Department of Earthquake Disaster Prevention, China Earthquake Administration, 1995). In the southeastern margin of the Qinghai-Tibetan Plateau, most of the earthquakes are shallow ones, and the corresponding fault width is calculated as twice the depth of the source (Huang Fuming, 2004, 1987), so the width of seismic zone is set 25km on both sides of the fault, and the epicenter in the earthquake catalog is taken for reference. The distribution of seismic source of this area has an obvious regional and zonal feature from the macroscopic point of view. The zonal feature is due to the control of the Yushu-Xianshuihe-Xiaojiang fault system and the Litang-Dali-Nantinghe tectonic belt, and the regional feature caused by the breaking of interior blocks during the clockwise rotation extrusion process in this area. According to this characteristic, in order to analyze the characteristics of strain energy release, this paper divides the study region into the Yushu-Xianshuihe-Xiaojiang fault system (including the Yushu-Garzê fault zone, Xianshuihe fault zone, Anninghe-Zemuhe fault zone, Xiaojiang fault zone and the Tonghai fault zone), the Litang-Dali-Nantinghe tectonic belt (including the Litang fault zone, the northwestern Yunnan fault zone and the Nantinghe-Wanding fault zone), and six fault block areas (including the Changdu fault block area, Batang-Zhongdian fault block area, Mabian-Zhaotong fault block area, Panzhihua-Chuxiong fault block area, Tengchong-Baoshan fault block area and Simao fault block area).

 Fig. 1 Zoning map of the rotational tectonic systems in the Sichuan-Yunnan region F1: Yushu-Xianshuihe-Xiaojiang fault system (including: F1-1: Yushu-Garzê fault zone, F1-2: Xianshuihe fault zone, F1-3: Anninghe-Zemuhe fault zone, F1-4: Xiaojiang fault zone, and F1-5: Tonghai fault zone); F2: The Litang-Dali-Nantinghe tectonic belt (including F2-1: The Litang fault zone, F2-2: The northwestern Yunnan fault zone, and F2-3: the Nantinghe-Wanding fault zone). The major fault block areas (including Ⅰ. The Changdu fault block area, Ⅱ. Batang-Zhongdian fault block area, Ⅲ. Panzhihua-Chuxiong fault bolock area, Ⅳ. Mabian-Zhaotong fault block area, Ⅴ. Tengchong-Baoshan fault block area, and Ⅵ. Simao fault block area)
2 SEISMIC RAIN ENERGY RELEASE IN THE SOUTHEAERN MARGIN OF THE QINGHAI-TIBETAN PLATEAU

In Fig. 2, the red dashed line indicates the process of earthquake activity, that is, a seismic activity cycle includes roughly three periods of quiescence, acceleration and large release.

 Fig. 2 Accumulative strain energy release curve (left) and M-t diagram (right) of the M≥7.0 earthquakes in the southeastern margin of the Qinghai-Tibetan plateau since 1500

The southeastern margin of the Qinghai-Tibetan Plateau is the region with the highest frequency and intensity of strong earthquakes, as well as the most serious seismic and geological disasters in China, where 37 earthquakes with magnitude greater than 7.0 have occurred since 1500, including 11 with magnitude greater than 7.5 and one with magnitude 8.0. It is found from Fig. 2 that there is a seismic cycle in the southeastern margin of the Qinghai-Tibetan Plateau since 1500. The quiescence period is 1536-1733, and though there were M=7.0 earthquakes occurring occasionally in this stage, the energy release was relatively slow. The acceleration period is 1733-1925, the duration of this period is almost equivalent to the quiescence period, but the strain release rate was significantly increased. There was an M=8.0 earthquake, and the number of M≥7.0 earthquakes was significantly increased. Meanwhile, there is a relatively active stage and relatively quiet stage, about which we will not go into details in this paper. The large release period is from 1941 to the present, lasting for 73 years. This stage begins with the two magnitude 7.0 earthquakes of Gengma and Lancang in 1941, then is followed by the intensive large earthquakes. The rate of strain release at this stage is much greater than the period of quiescence and acceleration, being at a record high stage. During the last 20 years since the M7.0 earthquake in Lijiang in 1996, the rate of seismic strain energy release has declined. However, since the beginning of the new century, in the context of the global seismicity entering a new active period, seismicity of moderate-strong earthquakes in the study region has increased in recent years, the large release period may not have ended, so the seismie activity may still be strong in the southeastern margin of the Qinghai-Tibetan Plateau.

The release of seismic energy in the southeastern margin of the Qinghai-Tibetan Plateau indicates that the seismic activity has been increasing for nearly 500 years since 1500. However, each fault will have its own characteristic, that is, the strain energy release characteristic, and this characteristic is closely related to the fault location and property as well as the regional stress field environment. The characteristics of each fault are not static, but vary with the change of large-area regional tectonic stress. Based on the study of the characteristics of these faults and fault blocks, the past status of the fault (block) is analyzed to determine the current stage and future trend of seismic activity to assess the seismic hazard of this area.

3 MAJOR ACTIVE FAULT ZONES

There are two major active fault zones in the study region, namely, the Yushu-Xianshuihe-Xiaojiang active fault zone and Litang-Dali-Nantinghe active fault zone. In this section, we will discuss the global and local features of these two fault zones, respectively.

3.1 The Yushu-Xianshuihe-Xiaojiang Fault System

The two black lines in Fig. 3 are parallel to each other, indicating the average rate of seismic strain energy release in a certain period of time. The upper black line indicates that the magnitude is predictable. The black line below indicates that the time is predictable. The absence of a black straight line indicates that the release rate cannot be determined from the strain energy release curve during the study period. This is the same for other strain energy release curves in this paper.

 Fig. 3 Accumulative strain energy release curve (left) and M-t diagram (right) of the M≥6.0 earthquakes in the Yushu-Xianshuihe-Xiaojiang fault system since 1500

Statistics on the seismic activity in this fault system since 1500 (Fig. 3) show that three seismic cycles appeared on the fault system. The quiet period of the first cycle is from 1606 to 1713, and there were no earthquakes of magnitude 6.0 or above in 107 years of this period. The acceleration period of energy release is 1713-1725, the large release period is 1725-1733, and there were two earthquakes of M≥7.0 in the 8 years of this period. The quiet period of the second cycle is from 1733 to 1786, the release accelerating period is 1786-1816, and the large release period is 1816-1850, and in the 34 years of this period, there were 2 M7.5 and one M8.0 earthquakes. The quiet period of the third cycle is from 1850 to 1887, the release accelerating period is 1887-1955, and the large release period is 1955-1973, in the 18 years of this period there were three M7.5 and above earthquakes. Presently, it is in the transition stage from the quiet period of the fourth cycle to the energy release accelerating period, so strong earthquake activity will increase significantly. In view of the average rate of earthquake strain release of the second and third cycles, the Yushu-Xianshuihe-Xiaojiang fault system has now produced the seismic energy equivalent of an M7.5 earthquake.

(1) The historical earthquake record of Yushu-Garzê fault began from 1738, the seismic strain release rate is small in the nearly 300-year period, and there were only 2 M≥7.0 earthquakes on the fault, which are the 1896, M7.0 Luoxu, Shiqu County, Sichuan Province earthquake and the 2010 M7.3 Yushu, Qinghai earthquake. In this period the seismic activity of the fault zone was relatively low. It can be seen from Fig. 4(a) that there was no strong earthquake cluster on the whole fault zone, and the release acceleration stage of the two seismic cycles is not very obvious. The energy released in the large release stage is not great. Currently, the seismic activity of the Garzê-Yushu fault zone is weak (Table 1).

 Fig. 4 Accumulative strain energy release curve (left) and M-t diagram (right) of M≥6.0 earthquakes on the faults of the Yushu-Xianshuihe-Xiaojiang fault system since 1500 (a) Yushu-Garzê fault zone, (b) Xianshuihe fault zone, (c) Anninghe-Zemuhe fault zone, (d) Xiaojiang fault zone, (e) Tonghai fault zone

Table 1 Periodic table of seismic strain energy release of the faults and blocks in the Yushu-Xianshuihe-Xiaojiang fault system

(2) The Xianshuihe fault zone has the highest seismic strain energy release in the Yushu-Xianshuihe-Xiaojiang fault system, where the accumulation and release rate of the seismic strain energy is very large. There have been 8 earthquakes with M≥7.0 in the nearly 300 years since 1700, indicating that the seismic activity of the Xianshuihe fault zone is very high. From Fig. 4(b) we can see that on the whole there were two seismic cycles on the Xianshuihe fault, 1725-1816 and 1816-1891. The starting time of the quiescent period of the first cycle is unknown, the acceleration period is up to 1786, the large release period is 1786-1816, the quiescent period of the second cycle is 1816-1893, the acceleration period is 1893-1955, and the large release period is from 1955 to 1981. Considering the M6.3 Kangding, Sichuan earthquake occurring in 2014, this fault zone may now be in the transition stage from the quiescent period of the third cycles to the acceleration period. Currently, the earthquake activity of the fault is moderate (as shown in Table 1).

(3) There is a phenomenon of "few small earthquakes, but large earthquakes being very big" on the Anninghe-Zemuhe fault zone, and the seismic strain energy release rate in the whole fault zone is moderate. Moderate-strong earthquakes are few in the 314 years from the 1536 M7.5 north of Xichang, Sichuan earthquake to the 1850 M7.5 Xichang-Puge, Sichuan earthquake. From Fig. 4(c), there are two seismic cycles on the Anninghe-Zemuhe belt, which are 1536-1850 and 1850 to the present, respectively. The seismically quiet period of the first cycle is from 1536 to 1732, the acceleration period is 1732-1850, the large release period is 1850-1850; the quiet period of the second cycle is from 1850 to 1913, and the acceleration period is from 1913 to the present. Now it is in the acceleration period of the second cycle, the earthquake activity is strong (Table 1).

(4) The total amount of earthquake strain energy release in the Xiaojiang fault is relatively large, next to the seismic energy release of the Xianshuihe fault. An M8.0 earthquake occurred in Songming, Yunnan in 1833, which is the largest earthquake occurring on Yushu-Xianshuihe-Xiaojiang fault system since 1500. From 1500 to the present, the overall seismic activity of the fault has been relatively strong. From Fig. 4 (d), there are three seismic cycles on the Xiaojiang fault zone. The quiet period of the first cycle is from 1500 to 1713, the acceleration period is from 1713-1733, and the large release period is in 1733. The quiet period of the second cycle is from 1733 to 1789, the acceleration period is from 1789 to 1833, and the large release period is in 1833. The quiet period of the third cycle is from 1833 to 1909, the acceleration period is from 1909 to present. It is currently in the acceleration period of the third cycle, the earthquake activity is strong (Table 1).

(5) The total earthquake strain energy release on the Tonghai fault zone is high, and the earthquake strain energy release rate is high. The 1970 M7.8 Tonghai, Yunnan earthquake is the largest magnitude earthquake since the historical records on the fault zone. It can be seen from Fig. 4(e) that there are two seismic cycles on the fault zone, the quiet period of the first cycle is from 1606 to 1755, the acceleration period is from 1755 to 1799, and the large release period is in 1799. The quiet period of the second cycle is from 1799-1887, the acceleration period is 1887-1970, and the large release period is in 1970. It is now in the seismic quiescence period of the third cycle, and the earthquake activity is weak today (see Table 1).

3.2 Litang-Dali-Nantinghe Tectonic Belt

The seismic strain energy release rate is higher in the Litang-Dali-Nantinghe tectonic belt, and there were 7 earthquakes of magnitude 7.0 and above occurring since 1500, and the maximum magnitude earthquake is the 1515, M7 3/4 Yongsheng, Yunnan. From the Fig. 5, it can be found that there has been one seismic activity cycle in the tectonic belt since 1500. The quiet period of the seismic cycle is from 1515 to 1623, the acceleration period is from 1623 to 1925, these periods are characterized by moderate-strong seismicity with magnitude less than 7.0. The large release period is from 1925 to the present. In the period of 71 years from the Dali, Yunnan M7.0 earthquake in 1925 to the 1996 M7.0 Lijiang, Yunnan earthquake, 5 earthquakes with M≥7.0 occurred. In this stage, seismic strain energy was released intensively. Now, the tectonic belt is at the end of large release period and the possibility of the occurrence of large earthquakes cannot be ruled out.

 Fig. 5 Accumulative strain energy release curve (left) and M-t diagram (right) of M≥6.0 earthquakes in the Litang-Dali-Nantinghe tectonic belt since 1500

(1) Due to the absence of historical earthquake records of the Litang fault zone, there is only earthquake data for the recent 100 years. According to these earthquake records, earthquakes in the fault zone are mostly of magnitude less than 6.0 (not shown in the figure), except for the 1948 Litang, Sichuan M7.3 earthquake, and the rate of energy release is very slow. Considering the short time and small number of earthquakes, the analysis result is not very reliable using the Benioff curve. Therefore, the seismic hazard of this zone cannot be ruled out, and in-depth study on other aspects is needed (Table 2).

Table 2 Periodical table of seismic energy release of the faults in the Litang-Dali-Nantinghe tectonic belt

(2) The northwest Yunnan rift zone is the central part of the whole Litang-Dali-Nantinghe tectonic belt, and it is also a lever to adjust the stress distribution in eastern and western Yunnan. From 1500 to present, an M7 3/4 earthquake and 3 earthquakes with M7.0 occurred, between which moderate earthquakes occurred constantly and often, and seismic activity was strong. As can be seen from Fig. 6(b), there is a seismic cycle on the zone. The quiet period is from 1515 to 1652, the energy release acceleration period is 1652-1925, the large release period is from 1925 to present. The division between the acceleration period and large release period of this zone is not so obvious. This may be because there are many faults on this zone and they are intertwined in energy releasing. Now the rift zone is in the large release stage. According to the release rate of the large release period, the current seismic activity is moderate (Table 2).

 Fig. 6 Accumulative strain energy release curve (left) and M-t diagram (right) of M≥6.0 earthquakes on each fault in the Litang-Dali-Nantinghe tectonic belt (a) Litang fault zone; (b) Northwest Yunnan rift zone; (c) Nantinghe-Wanding fault zone

(3) The historical seismic records of the Nantinghe-Wanding fault zone are few, but the seismicity is characterized by few small earthquakes but very great large earthquakes, owing to the complexity of the fault and its own characteristics. However, this feature has brought greater difficulty to seismic research. From 1931 to the present, the 1941, Gengma, Yunnan M7.0 earthquake and the 1976 Longling, Yunnan M7.3 earthquake occurred. The time interval between the two earthquakes is 35 years, and now 38 years have been passed since the Longling earthquake. Considering the interval of the two earthquakes, the earthquake risk of the fault is still high. Some scholars hold that the recent risk of large earthquakes of the fault is high, but more research is needed to demonstrate the reliability of this view (Table 2).

4 MAJOR ACTIVE FAULT-BLOCK AREAS

Large earthquakes in the southeastern margin of the Qinghai-Tibetan Plateau are basically distributed in two main fault zones, although the other parts were mostly hit by moderate earthquakes, large earthquakes did occur occasionally. The geological structure of the southeastern margin of the Qinghai-Tibetan Plateau is complex with intensive tectonic activities. Blocks between the large fault zones are fragmented, and within the blocks, moderate earthquakes are distributed irregularly. The remaining blocks are divided into six major block areas, namely: the Changdu fault block area, Batang-Zhongdian fault block area, Panzhihua-Chuxiong fault block area, Mabian-Zhaotong fault block area, Tengchong-Baoshan fault block area, and Simao fault block area, which are discussed respectively below.

As seen from Fig. 7, basically the number of earthquakes with magnitude greater than 6.0 was small in all of the fault block areas before 1900. This is because that the magnitude of earthquakes inside the fault block area is generally small on the one hand, and these areas are sparsely populated on the other hand. The two factors together result in the lack and seriously missing of historical earthquake data in the fault block areas. In this study, the author tried to reduce the magnitude of earthquake to magnitude 5.0 for the calculation, but the result is not obviously improved, and the trends of the current graphics are basically consistent. Fortunately, the seismic data after 1900 is relatively complete and reliable. Therefore, the analysis of this section focuses on the seismic data from 1900 to the present to analyze the current seismic activity of the fault block areas.

 Fig. 7 Accumulative strain energy release curve (left) and M-t diagram (right) of M≥6.0 earthquakes in fault-block areas (a) Changdu fault block area, (b) Batang-Zhongdian fault block area, (c) Panzhihua-Chuxiong fault block area, (d) Mabian-Zhaotong fault block area, (e) Tengchong-Baoshan fault block area, (f) Simao fault block area

(1) There were one M=7.0 and 4 M≥6.5 earthquakes occurred in the Changdu fault block area since 1600. It can be seen from Fig. 7(a), that there is a seismic cycle in this area. The quiet period is from 1642 to 1791, the acceleration period is from 1791 to 1938, and the large release period is from 1938 to 1979. After that, the area entered the quiet period of the next cycle. The 2013 Zogang, Tibet M6.1 earthquake indicates the beginning of the transition from the quiescence to the acceleration period (Table 3).

Table 3 Periodic table of seismic strain energy release of each fault block area

(2) A total of one M7 1/4 and two M≥6.5 earthquakes occurred in the Batang-Zhongdian fault block area since 1800. As can be seen from Fig. 7(b), there were two seismic cycles in this area. The quiet period of the first cycle is from 1722 to 1870, the acceleration period is ignored, and the large release period is in 1870. The quiet period of the second cycle is from 1870 to 1920, the acceleration period is from 1920 to 1989, and the large release period is in 1989. It is now in the quiet period of the next cycle (Table 3).

(3) There were 7 earthquakes with M6.5-6.9 occurring in the Panzhihua-Chuxiong fault block area ever since the historical records, but no M=7.0 or greater earthquake occurred. As can be seen from Fig. 7(c), there is one seismic cycle in this area. The quiet period of the cycle is from 1755 to 1955, the acceleration period is ignored, and the large release period is from 1955 to present. Now, the area is still in the large release period. Due to tectonic and seismogeological conditions, the faults inside the block fault areas are small in scale, activity is weak, and there were no earthquakes of magnitude 7.0 or greater occurring in history. Thus, this area is prone to frequent moderate earthquakes, and the probability of a large earthquake is small, the seismic activity is moderate (as shown in Table 3).

(4) According to the historical earthquake records, there were a total of one magnitude 7.0 or greater earthquake and 3 earthquakes with M≥6.5 occurring in the Mabian-Zhaotong fault block area so far. Fig. 7(d) shows that there is a seismic cycle in this area. The start of the quiet period is unknown and its end was in 1917, the acceleration period was from 1917 to 1935, and large release period was from 1935 to the present. It may now be in the end of the large release period, or in the transition to the quiet period of the next cycle, the seismic activity is moderate (Table 3).

(5) So far, there have been a total of 6 earthquakes with M≥6.5 occurring in the Tengchong-Baoshan fault block area according to the historical earthquake records. Fig. 7(e) shows that there is a seismic cycle in this area. The quiet period of the cycle was 1577-1876, the acceleration period was 1876-1929, the large release period was 1929-1976. Now it is in the transition phase of the quiet period to the acceleration period of the next cycle, the seismic activity is moderate (Table 3).

(6) According to the historical earthquake records, there were a total of 5 M≥7.0 earthquakes and 11 M≥6.5 in the Simao fault block area. Fig. 7(f) shows that there is a seismic cycle in this area. The quiet period is 1884-1923, the acceleration period was from 1923 to 1988, and the large release period was from 1988 to the present. Currently, the area is in the end of the large release period or the transition to the quiet period of the next cycle, the seismic activity is moderate (see Table 3).

The time of the earthquake catalog records in the six fault blocks is relatively short, and because of the small number of large earthquakes, it is doubtful whether the periods and the large release period divided in Fig. 7 are accurate. However, taking into account the particularity of fault block areas and the low probability of large earthquakes inside the block areas, most of the M≥6.0 earthquakes occur in clusters, which can be considered as a large release period of strain energy. In Fig. 2, the most recent large release period in the southeastern margin of the Qinghai-Tibetan Plateau is from 1941 to present, and the decay trend has been visible. In Fig. 3, the most recent large release period in the Yushu-Xianshuihe-Xiaojiang fault system was from 1955 to 1973, and in Fig. 5, and the most recent large release period of the Litang-Dali-Nantinghe tectonic belt was from 1925 to the present. In summary, the end time of the large release period in the block areas be reliable. It should be pointed out that the large release period on the Panzhihua-Chuxiong fault zone seems to be inconsistent with the rest of the fault block areas, which has been in the large release period all the time and does not show any trend of slowing down, so it is worth noting that it may be related to the preparation of large earthquakes on the Anninghe-Zemuhe fault and Xiaojiang fault. On the west of the fault block area, the Lijiang M7.0 earthquake occurred in the northwest Yunnan rift zone in 1996, and on its south, the M7.8 Tonghai earthquake occurred in 1970. The energy release of Xianshuihe fault on the north is huge. Only the two fault zones on the east have not been hit by M≥7.0 earthquakes in the more than 150 years and are now in the release acceleration period, which may signify a high risk of large earthquakes on the Anninghe-Zemuhe fault and Xiaojiang fault.

5 DISCUSSION 5.1 Characteristics of Seismic Strain Energy Release

By studying the seismic strain energy curves in the southeastern margin of Qinghai-Tibetan Plateau, we obtain the following characteristics:

(1) From the view of the amount of seismic strain energy release, the seismic strain energy release in Yushu-Xianshuihe-Xiaojiang fault system accounts for 50.67% of the total seismic strain energy release in the southeastern margin of the Qinghai-Tibetan Plateau, so this fault system, with the seismic energy release amounting to more than half of the total release, becomes an important boundary zone and energy absorption and release zone of the southeastern margin of Qinghai-Tibetan Plateau, among which, the Xianshuihe fault zone has the largest release, accounting for 35.9% of the total energy release of the Yushu-Xianshuihe-Xiaojiang fault system. The seismic strain energy release in the Litang-Dali-Nantinghe arc-shaped tectonic belt accounts for 13.73% of the total seismic strain energy release in the southeastern margin of the Qinghai-Tibetan Plateau, and the release in the northwest Yunnan rift zone accounts for 66.9% of the total energy release of the arc-shaped tectonic belt. The seismic energy release in the fault block areas accounts for 35.60% of the total energy release, in which the release in the Simao fault-block area accounts for 52.7% of the total energy release of all fault block areas. The amount of seismic energy release reflects the intensity of seismicity and crustal movement.

(2) From the view of seismic cycles of the fault, the seismicity on most faults shows cyclic pattern, i.e. seismic cycle, which consists of a seismic quiescence period, release acceleration period and large release period. This feature is also known as the quasi-periodic recurrence earthquake model. This characteristic is very obvious in the faults, such as the Xianshuihe fault zone F1-2, Tonghai fault zone F1-5, Northwest Yunnan fault zone F2-2, Batang-Zhongdian fault block area Ⅱ, Simao fault block area Ⅴ, etc., where the Xianshuihe fault zone F1-2 and most fault block areas meet the quasi-periodic cluster recurrence pattern. The duration of the cycles and the amount of energy released on the same fault are not fixed, which are related to the rupture process, rupture mechanism and rupture condition of the fault in each cycle. It is possible that a seismic cycle has completely released the accumulated strain energy, then the subsequent quiescence period will be longer; and maybe, a cycle releases only part of the strain energy, and when entering into the next quiet period, the accumulation of strain energy will continue, so the quiet period is shorter. In addition, the impact of the surrounding rupture system will accelerate or slow down the accumulation and release of strain energy. Also, the inter-plate large earthquakes can often have an impact on the wide range of crustal stress fields.

(3) It is found in the study that, as shown in Fig. 4, the first seismic cycle in the Xianshuihe fault zone F1-2 coincides with the second seismic cycle in the Xiaojiang fault zone F1-4; The second seismic cycle in the fault zone F1-2 almost coincides with the second seismic cycle in the Tonghai fault zone F1-5. Such a phenomenon can also be found in the periodic table of seismic strain energy release of each fault and fault block in Table 1. This synchronization means that the duration of seismic cycle and the periods in the cycle are similar in multiple faults. This may be because when the strain energy of multiple faults accumulates to the corresponding critical state, a sudden release of strain energy of a fault may trigger the release of strain energy of other faults. As a result, the seismic cycles of these faults will exhibit synchronization to some degree.

In the study, it is also found that there are some general problems existing in this study method:

(1) The fault zone is a complex chaotic self-organizing system. Due to the limitations of current understanding, the subjectivity of segmentation and partitioning of the fault system applied to the study will also affect the scientific nature and the correctness of assessment in earthquake research.

(2) The Benioff strain energy release curve method uses the relationship of the square of seismic energy with time. In this way, the strain energy of a magnitude 8.0 earthquake is about 5.6 times that of a magnitude 7.0 earthquake. In the traditional calculation, the energy difference between two adjacent magnitudes is about 30 times, and the small earthquakes are negligible, but in the Benioff strain release curve method, the effect of the small earthquake is amplified. In this way, the absence of ancient small earthquakes in the earthquake catalog will significantly affect the reliability of this method. One good side, the data about magnitude 6.0 or greater earthquakes from 1900 to present are relatively complete and reliable.

(3) The strain energy release of earthquakes in the intra-plate active faults in China differs from that of the plate-margin earthquakes on the time scale. The recurrence period of earthquakes is very different in the two cases. For intra-continental earthquakes, the recurrence period is as long as several thousand years. The whole seismic activity period of a fault zone is several tens to several hundred years. The length of the historical data has great impact on reliability.

5.2 Analysis of Future Seismic Risk

Tables 1, 2 and 3 summarize the detailed situation of seismic strain energy release in each fault zone and fault block area in the study area. The available data since 1500 shows that there are 5 fault (block) zones that have two complete seismic cycles each, 6 zones that have one complete seismic cycle each, and there is no complete seismic cycle in the remaining three zones.

Currently, there are four fault (or block) zones that are in the quiescence period, they are Yushu-Garzê fault zone F1-1, Tonghai fault zone F1-5, Changdu fault block area Ⅰ, and Batang-Zhongdian fault block area Ⅱ, two in the acceleration period, namely: Anninghe-Zemuhe fault zone F1-3 and Xiaojiang fault zone F1-4, and two in the large release period, namely, northwest Yunnan fault zone F2-2 and Panzhihua-Chuxiong fault block area Ⅲ. Four fault zones or blocks are in the transition period, which are Xianshuihe fault zone F1-2, Mabian-Zhaotong fault block area Ⅳ and Tengchong-Baoshan fault block area Ⅴ that are in the transition from the quiet period to the acceleration period, and Simao fault block area Ⅵ that is transitioning from the large release period to the quiescence period. For the remaining two areas, their status can't be determined due to the limitations of seismic data, which are the Litang fault zone F2-1 and Nantinghe-Wanding fault zone F2-3.

The structural characteristics, the activity behavior and the historical earthquake records of the fault zones and block areas are different and the conditions are complicated. It is also complicated to study the current earthquake risk based on the division of seismic cycle, as one cannot make sweeping generalizations. Therefore, it is necessary to discuss it based on specific regions concerned in combination with the knowledge and methods of structural geology and seismogeology for different research areas. Based on the division of the seismic cycles, this paper combines the specificity of the corresponding regions to make the primary seismic hazard assessment.

Based on the analysis of the periods and current stages of the seismic strain energy release in each fault and fault zone, it is found that the faults and fault blocks in the acceleration and large release periods of strain energy release are currently under high seismic activity, those in the transition stage are under moderate seismic activity, and those in the quiet period are under low seismic activity. On this basis, the following assessment is made: The currently high seismic activity areas are: the Anninghe-Zemuhe fault zone F1-3, Xiaojiang fault zone F1-4; the currently moderate seismic activity areas are: Xianshuihe fault zone F1-2, northwest Yunnan fault zone F2-2, Panzhihua-Chuxiong fault block Ⅲ, Mabian-Zhaotong fault zone Ⅳ, Tengchong-Baoshan fault block Ⅴ, and Simao fault block area Ⅵ; the currently low earthquake activity areas are: Yushu-Garzê fault zone F1-1, Tonghai fault zone F1-5, Changdu fault block area Ⅰ, and Batang-Zhongdian fault block area Ⅱ.

6 CONCLUSION

According to the study of the characteristics of strain energy release of historical earthquakes, the strain energy release in the study region is characterized in three aspects as follows:

(1) The seismic strain energy release since 1500 is very different between faults and fault block areas. Most of the energy is released in the Yushu-Xianshuihe-Xiaojiang fault system and Litang-Dali-Nantinghe tectonic belt, as well as the Simao fault block area in the south. The energy release in the rest of the block areas is small. Generally, the release intensity is strong in the east and south, and weak in the west and north.

(2) Seismic cycle coincides with quasi-periodic or quasi-periodic cluster recurrence pattern. Most of the seismic cycles contain three periods of quiescence, release accelerating and large release which appear alternately. This further proves the correctness of the pattern proposed by the predecessors of the rhythm of the continental earthquakes (Zhang Guomin et al., 1987).

(3) The seismic cycles in some faults exhibit synchronization to some degree.

The southeastern margin of the Qinghai-Tibetan Plateau today is still in the later stage of a large release period of seismic strain energy release as a whole, and it cannot be determined how much energy will be released. From the local point of view, the Anninghe-Zemuhe fault zone and the Xiaojiang fault zone are in the acceleration period of the seismic strain energy release, the current seismic activity is high in these two fault zones.

This method is very effective in studying the seismicity and assessing the earthquake risk and can reflect the characteristics of the historical earthquake activity of the study region to a certain extent, which is of reference significance to the assessment of an earthquake hazard zone. However, due to the hugeness and complexity of the seismic system, the single method has limitations. Therefore, it is necessary to carry out comprehensive research in combination with other research methods to further improve the objectivity and reliability of seismic activity assessment.

REFERENCES
 Benioff H. Global strain accumulation and release as revealed by great earthquakes[J]. Geological Society of America Bulletin, 1951, 62(4): 331–338. DOI:10.1130/0016-7606(1951)62[331:GSAARA]2.0.CO;2. China Seismic Information. The Earthquakes with MS ≥ 5.0 in China (since 780 B. C. ), 2015. http://www.csi.ac.cn/publish/main/813/4/index.html. Deng Qidong, Ran Yongkang, Yang Xiaoping, et al. Activity Structure Map of China (1:40 00000)[M]. Beijing: Seismological Press, 2007 Department of Earthquake Disaster Prevention.China Seismological Bureau. The Historical Earthquake Catalog of China[M]. Beijing Seismological Press, 1995 Gutenberg B., Richter C.F. Magnitude and energy of earthquake[J]. Annals of Geophysics, 1956, 9(1): 1–15. Huang Fuming, Yang Zhixian. Stress accumulation and release in the Xianshuihe Fault Zone[J]. Acta Seismologica Sinica, 1987, 9(2): 128–142. Huang Zhongxian, Chen Hong. Variation of seismicity in Chinese continent and its relation to tectonic movement[J]. Earthquake Research in China, 1996, 12(4): 403–410. Liu Yanhui. Application of GIS to Seismichazard Analysis around South-eastern Qinghai-Xizang Plateau [D]. Master thesis. Beijing: China University of Geosciences, 2014 (in Chinese with English abstract). Liu Zhengrong, Luo Ronglian, Chen Yuru. The patterns and periods earthquakes in Sichuan and Yunnan Provinces[J]. Journal of Seismological Research, 1983(1): 97–108. Luo Ronglian, Chen Yuru, Liu Zhengrong. Seismicity characters in Sichuan and Yunnan Provinces-Strain release and strong earthquakes[J]. Journal of Seismological Research, 1983(2): 133–139. Ma Hongsheng, Liu Jie, Zhang Guomin, et al. The seismicity research in the subregions of Chinese mainland using strain accumulating and releasing model[J]. Acta Seismologica Sinica, 2002, 24(6): 569–578. Mogi K. Seismic activity and earthquake prediction[C]. In: Proceedings of the Symposium on Earthquake Prediction Research, 1977, 203-314. Seismological Bureau of Yunnan Province. Compilation of Seismic Data in Yunnan Province[M]. Beijing: Seismological Press, 1988 Wu Zhonghai, Long Changxing, Fan Taoyuan, et al. The arc rotational-shear active tectonic system on the southeastern margin of Tibetan Plateau and its dynamic characteristics and mechanism[J]. Geological Bulletin of China, 2015, 34(1): 1–31. Wu Zhonghai, Zhao Genmo, Long Changxing, et al. The seismic hazard assessment around south-east area of Qinghai-Xizang Plateau:A preliminary results from active tectonics system analysis[J]. Acta Geologica Sinica, 2014, 88(8): 1401–1416. Wu Zhonghai, Zhao Xitao, Fan Taoyuan, et al. Active faults and seismologic characteristics along the Dali-Ruili railway in western Yunnan Province[J]. Geological Bulletin of China, 2012, 31(2-3): 191–217. Zhang Guomin. Rhythmic characteristics of high seismic activity in China mainland[J]. Seismology and Geology, 1987, 9(2): 27–37. Zhao Genmo, Wu Zhonghai, Liu Yanhui. The active faults interaction, stress triggering and differential responses on the southeastern margin of the Tibetan plateau[J]. Geological Bulletin of China, 2014, 33(4): 470–484.

1 国家测绘地理信息局, 北京莲花池西路28号 100830;
2 中国地质科学院地质力学研究所, 北京市海淀区民族大学南路11号 100081;
3 国土资源部新构造运动与地质灾害重点实验室, 北京 100081;
4 天津市地震局, 天津 300201


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## Modelling – mixed effects – concepts

In the previous post, we ran through an extended example of a mixed-effects modelling analysis of the ML lexical decision data. We ended the post by getting p-values for the effects of the predictors included in our model. That was the model apparently justified by a likelihood ratio test comparison of maximum likelihood (REML=F) models varying in fixed effects but constant in possessing random effects of subjects and items on intercepts.

You will recall that I said in that post that:

In following posts, we shall 1. perform some checks on whether the fixed effects appear justified with respect to data hygiene 2. examine what random effects seem justified, looking at random effects on intercepts and random effects on slopes.

— that will happen but I want to consider some of the words I am using.

Creative commons – flickr – Florida Memory: Fisherman with his son, Naples, Florida, 1949

I am reading the great introductory text on multilevel modeling by Snijders & Boskers (2004). There, they begin their book with a clear, simple, explanation of the normal data collection situation for many of us.

You will know that statistical models, for example, ordinary least squares (OLS) regression assume that observations should be sampled independently. In regression, the distribution of errors – the differences between model prediction and data observation for any observation – should consist of errors with a normal distribution, with any one error independent of any other. If we think about the normal situation in which we find ourselves, that independence assumption will be invalid. Most of the time, we are asking participants to read some set of words, and everyone will be asked to read all the words. If you plot the participants’ data or the responses to each item, you will see that, as you might expect, some people are slow and some fast for most responses to most words, while some words are easy and some hard for most people.

You can consider this illustration of some reading data, as an illustration of that point.

Notice:

— The lattice of plots shows:

1. The average RT for each person – and for each word – varied. You might guess what the average over all people or all words would be. Now consider how each person’s average RT varies from the average RT over all people, or how each word’s average RT varies from the average RT over all words. The average outcome is called the intercept, a term you will have encountered before in regression. Estimating the deviation of a person or a word from the overall average is a matter of estimating random effects on person or word on intercepts, or, random intercepts. In the mixed effects modeling code in R, we designate this as:

$(1|subject) + (1|item)$

2. The slope of the effect of, here, frequency on reading RT also appears to vary between people. There might be an average effect of frequency on RT overall. You could call the frequency effect the fixed effect here. We can see that, most of the time, more frequent words are associated with shorter RTs. However, the slope of that effect is more or less steep for some people. That variation in slope can be estimated as random effects of person on slopes, or random slopes. However, the variation in the frequency effect might also be considered to be of theoretical interest and, critically, it might be captured by, for example, an interaction between the effect of frequency and the effect of some participant attribute that conditions or modulates the frequency effect by a systematic (rather than a random) person effect.

Let’s return to Snijders & Boskers (2004). They note that one can often, for reasons of efficiency (consider how much easier it is to give everybody the same sample of words than different samples) or other pragmatic considerations, that data collection often proceeds through multistage sampling. One might test in a set of schools, a sample of schools, and in those schools test samples of children. It is a mistake to consider that the children are sampled independently (an assumption you would be making if you applied OLS regression to such data). That is because the children are clearly grouped by school (and thus not independent samples). Similarly, it would be clearly a mistake to consider that the observations for each person or each word are somehow independent. They are dependent because the data can be considered to cluster or group by person or by word. The consequence of ignoring this structure will be inflated Type I error rate, or finding things that are not really there.

Snijders & Boskers (2009) next point out, however, that if data are collected in multistage sampling we might, for theoretical or practical reasons, want to make inferences about effects occurring at each stage. (This is also noted by Baayen, Davidson & Bates (2008) in comments that led me to consider how the effects of item attributes might vary between readers systematically rather than merely at random.) We might want to know how school environment or policy affects teacher practice or how both school policy and teacher attitudes affect student performance. We might want to know how the kind of reader you are affects reading performance but also how the kind of word you read affects performance. We might, further, be interested in how effects that operate at one level or over one kind of cluster interact with effects operating at other levels or over other kinds of cluster.

The more that observations within a cluster are similar to each other (compared to other clusters) the more we might be concerned about the characteristics of the cluster, the higher level units.

We must not forget longitudinal observations, and shall return to the situation where data are clustered because people are tested repeatedly over time.

Snijders, T.A.B., & Bosker, R.J. (2004). Multilevel analysis: An introduction to basic and advanced multilevel modeling. London: Sage Publications Ltd.

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