Earthquake Research in China  2019, Vol. 33 Issue (4): 632-647     DOI: 10.19743/j.cnki.0891-4176.201904001
Study on Postseismic Impact of Wenchuan Earthquake on the Sichuan-Yunnan Region Based on Three-Dimensional Viscoelastic Finite Element Method
JIANG Fengyun1, ZHU Liangyu1, LI Yujiang2     
1. The Second Monitoring and Application Center, CEA, Xi'an 710054, China;
2. The Institute of Crustal Dynamics, CEA, Beijing 100085, China
Abstract: Based on the lateral segmentation and vertical stratification characteristics of the crustal medium in Sichuan-Yunnan region, and the asymmetry of the static dislocations on the coseismic fault plane of the Wenchuan MS8.0 earthquake, we built a three-dimensional viscoelastic finite element model of the crust in the Sichuan-Yunnan region. The postseismic impact of the Wenchuan MS8.0 earthquake on the Sichuan-Yunnan region was studied. The results show that:① The far-field horizontal deformation caused by the viscoelastic relaxation of the medium in the 10 years after the earthquake is about 0-20mm within the Sichuan-Yunnan diamond-shaped block, which has a greater influence on north side and smaller on south side. ② In the 10 years after the earthquake, the far-field vertical deformation caused by the viscoelastic relaxation effect of the medium is small, and it shows an increase of about 0-4mm in most areas of the Sichuan-Yunnan diamond-shaped block. ③ The Xianshuihe fault and the eastern segment of the East Kunlun fault, which are close to the seismogenic fault, show a high gradient on deformation fields after the earthquake. ④ In order to compare with the strong earthquake activity in the Sichuan-Yunnan region after the Wenchuan earthquake, the horizontal stress state and the Coulomb failure stress change of the active block boundary are also calculated. From the spatial distribution of the coseismic and postseismic displacement field, the fault activity characteristics reflected by the stress state and the stress loading of the fault layer reflected by the Coulomb failure stress change, there is a certain correlation with the spatial distribution of strong earthquake activity in this region.
Key words: Wenchuan MS8.0 earthquake     Finite element     Viscoelastic relaxation     Sichuan-Yunnan region    

INTRODUCTION

It is generally accepted that the short-term near field crustal deformation after a larger earthquake is mainly controlled by afterslip on the fault plane and its extension and the poroelastic rebound (Jouanne F. et al., 2011; Jónsson S. et al., 2003), and the long-term far-field deformation is mainly controlled by the viscoelastic relaxation driven by coseismic stress changes in the viscous lower crust and upper mantle below the brittle upper crust (Rice J. R. et al., 1983). Related studies have shown that the stress change (Coulomb failure stress change) caused by the viscoelastic relaxation is even more significant than the coseismic effect, which can lead to the instability of the surrounding fault and trigger the strong earthquakes. For example, Shen Zhengkang et al. (2003) simulated the stress evolution process caused by 5 MS≡7.0 strong earthquakes in the East Kunlun fault zone since 1937 using dislocation model in layered viscoelastic media, and calculated the Coulomb stress change for each subsequent earthquake on the fault plane. The resulting Coulomb failure stress changes of the first four earthquakes all increased the Coulomb failure stress of the 2001 MS8.1 Kunlun Kokoxili earthquake, and the viscoelastic relaxation of the middle and lower crust increased over time. For the first three earthquakes, the viscoelastic relaxation effects are more significant than the coseismic effects. Wan Yongge et al. (2007) used a dislocation model in a multi-layered viscoelastic media, used the long-term tectonic loading obtained from the MS≡7.0 earthquake and GPS data as the deformation source, and calculated the stress change generated by earthquakes. The evolution of Coulomb failure stress has been accumulated since the northeastern part of the Qinghai-Tibetan Plateau since 1920. The results show that 17 out of 20 major earthquakes occurred in this area where the Coulomb failure stress increased, showing triggering rate reached 85%.

It has been more than 10 years since the Wenchuan MS8.0 earthquake occurred on May 12, 2008. There are few studies on the far-field postseismic deformation. Most of the studies (Tan Hongbo et al., 2009; Li Qiang et al., 2013) are limited to the use of elastic dislocation model, only considering the vertical stratification of the media without considering the complex horizontal heterogeneity of the study area. The Sichuan-Yunnan block generally has stronger rheological properties in middle and lower crust than the South China block (Ji Lingyun et al., 2015). Therefore, the viscoelastic relaxation effect in lower and middle crust after the Wenchuan earthquake caused by the coseismic stress changes makes the stress of the brittle crust layer in Sichuan-Yunnan area continues to concentrate after the earthquake, and consequently changes the deformation field after the earthquake. Compared with the dislocation model, the finite element method can take the heterogeneity of the earth?s medium into account. Luo G. et al., (2010) consider the background tectonic stress, vertical stratification and horizontal segmentation of the crust, using the three-dimensional viscoelastic-plastic finite element model to simulate the coseismic and postseismic Coulomb stress change after the Wenchuan earthquake. Several large earthquakes in the adjacent area were also simulated, and a good simulation result was obtained. However, the simulation focused on the triggering effects between earthquakes, and there is lack of comparison with the actual observations of the coseismic deformation field and the discussion about large-scale coseismic and post-seismic deformation fields. Therefore, with the help of finite element technique, this paper comprehensively considers multi-disciplinary data such as active block models, geophysics, geodesy, seismicity, etc., and constructs a three-dimensional viscoelastic finite element model considering vertical stratification and horizontal segmentation of crust. We use the coseismic rupture of Wenchuan earthquake provided by USGS (Ji C. et al., 2008) as a load, and the large-scale high-precision co-seismic GPS horizontal displacement field given by Wang Qi et al. (2011) as a constraint to study the spacial-temporal distribution relationship between the deformation field and the stress field caused by the viscoelastic relaxation of Wenchuan earthquake in the Sichuan-Yunnan region. In addition, after the Wenchuan earthquake, there were some significant changes in the moderate-strong earthquake activity in the Sichuan-Yunnan region. After the Wenchuan earthquake, the Xianshuihe fault (3 MS≡5.0 earthquakes) and the Daliangshan block (in addition to Lushan earthquake, 7 MS≡5.0 earthquakes occurred) show an active strong earthquake activity states. Therefore, in this paper, we use the finite element simulation to calculate the fault stress state and Coulomb stress variation of the main block boundaries for coseismic and postseismic Wenchuan earthquake time periods, and the correlation between the postseismic influence and the seismicity of the Wenchuan earthquake on the Sichuan-Yunnan region is further analyzed in combination with the temporal and spatial evolution of the deformation strain field after the earthquake.

1 THREE-DIMENSIONAL VISCOELASTIC FINITE ELEMENT MODEL OF THE SICHUAN-YUNNAN REGION

According to the Holocene activity faults in the Sichuan-Yunnan region and the three-dimensional velocity structure of the crust and upper mantle, considering the active faults and blocks that determine the geological tectonic movement and seismic activity, we established the three-dimensional geological structure model of the Sichuan-Yunnan region.

1.1 Media Partition and Physical Parameters

Active faults in Sichuan-Yunnan region control the occurrence and development of the main tectonic activities and become the boundary of the active blocks (Zhang Peizhen et al., 2003). According to the tectonic feature model of the Sichuan-Yunnan region, 10 blocks are defined as shown in Fig. 1.

Fig. 1 Major active faults and blocks in the Sichuan-Yunnan regions F1: East Kunlun fault; F2: Tazang-Wenxian fault; F3: Ganzê-Yushu fault; F4: Xianshuihe fault; F5: Longmenshan fault; F6: Mabian fault; F7: Anninghe-Zemuhe fault F8: Ludian-Zhaotong fault; F9: Xiaojiang fault; F10: Red River fault; F11: Jinshajiang fault; F12: Deqên-Zhongdian fault; F13: Baiyu fault; F14: Nujiang fault; F15: Nantinghe fault; F16: Longling-Lancang fault Ⅰ: South China block; Ⅱ: Bayan Har block; Ⅲ: Northwest Sichuan block; Ⅳ: Central Yunnan block; Ⅴ: Daliangshan block; Ⅵ: Eastern Tibet block; Ⅶ: Eastern Lhasa block; Ⅷ: Myanmar block; Ⅸ: Baoshan block; Ⅹ: Jinggu block

When constructing the finite element geometric model, the horizontal division of the block model is mainly set based on the 10 blocks defined above(Fig. 2). The vertical stratification of the model and the media parameters of each block are mainly based on the crust and upper mantle structure revealed by the P- and S-wave velocity in the Sichuan-Yunnan region (Wang Chunyong et al., 2015; Wu Jianping et al., 2006, 2009), specifically set as follows: ① Wu Jianping et al.(2006, 2009) shows that there are generally low-velocity layers in the middle and lower crust of Sichuan-Yunnan region, while it is not obvious for the South China block. Therefore, when setting medium parameters, the existence of low velocity layer and the horizontal heteronegeity of the middle and lower crust are considered. We set the viscosity of middle and lower crust for the Bayan Har block, the Northwest Sichuan block, the Central Yunnan block, the Daliangshan block, the Baoshan block and Jinggu block to be 1.0×1018Pa·s, set the viscosity in the stable South China block to be 1.0×1021Pa·s and set viscosity in other regions to be 1.0×1020Pa·s. ② Existing research (Wang Chunyong et al., 2015; Wu Jianping et al., 2006, 2009) shows that the upper crust of the nouth-south seismic zone is unified into a medium with higher strength, and there is a significant correlation between lateral crustal properties and tectonics. Therefore, the upper crust is uniformly set to a strong brittle layer with a high viscosity, but the elastic modulus setting reflects the relatively hard characteristics of the South China block compared to other regions. ③ Upper mantle in the whole area has the same medium parameters and is calculated according to the seismic wave velocity (Wang Hui et al., 2007). The viscosity is ~1.0×1020 Pa·s. ④ Because the coseismic displacement of Wenchuan earthquake needs to be loaded on Longmenshan fault and the coseismic slip can be considered as instantaneous slip without friction, the Longmenshan seismogenic fault is designed as a contact surface with no friction. The setting of fault depth, dip angle and slip distribution is based on the finite fault solution given by Ji C. et al., (2008). ⑤ In order to simplify the model, dip angle of other faults in the study area are set to be 90 degrees. Referring to Wang Hui's method (Wang Hui et al., 2007), the setting of faults is replaced by a weak body with a smaller viscosity (1.0×1020 Pa·s). The specific block division and stratification parameters are shown in Table 1. In order to minimize the influence of boundary effect on calculation results, we extend the study area to be 200km larger. On the basis of the above geological model, a three-dimensional viscoelastic finite element model of the Sichuan-Yunnan region is established by means of ANSYS finite element software (Fig. 4). The model ranges from 94~ to 110~E, 21~ to 34~N, and the vertical area is 100km deep from the surface to the top of the upper mantle. The model is divided by SOLID185 and SOLID186. The whole finite element model is divided into 555, 330 elements and 737, 989 nodes.

Fig. 2 Three dimensional viscoelastic finite element model in the Sichuan-Yunnan region

Table 1 Parameters of the model in the Sichuan-Yunnan region

Fig. 4 The observed coseismic horizontal displacement vector of the Wenchuan earthquake (Wang Qi et al., 2011) (a) and the simulated coseismic horizontal displacement vector of Wenchuan earthquake (b) and the residual error between the simulated and the observed coseismic horizontal displacement vector of Wenchuan earthquake (c)
1.2 Coseismic Fault Model of the Wenchuan Earthquake

There have been many published studies on the coseismic slip model of the Wenchuan earthquake. Ji C. et al., (2008) only consider the mid- to far-field seismic wave and using a single plane in their model, which is relatively simple. Chen Yuntai et al. (2008) also have only one fault plane in their model, but they add near-field seismic wave data as constraints. Subsequent earthquake rupture models consider many observations such as geodesy, seismic waves, and InSAR (Shen Zhengkang et al., 2009; Wang Qi et al., 2011; Fielding E. J. et al., 2013; Wan Yongge et al., 2017). They consider several fault segments and the dip angle variation along dip, resulting a relatively complicated model and more accurate result. Tan Hongbo et al. (2009) compared the models from Chen Yuntai et al. (2008) and Ji C. et al., (2008) and found that the differences between the coseismic and post-earthquake effects of different models are mainly concentrated near faults, whereas the difference at medium to far fields is small. Considering the large spatial scale of the model, and the focus of examining the far-field coseismic and postseismic deformation in our study, a simple model from Ji C. et al., (2008) is used (Fig. 3) so as to facilitate the processing of the coseismic fault plane during the establishment of the finite element model. This simple model has some differences between the simulation and the actual results, but for the analysis of the far-field, the difference can be ignored. The arrow in Fig. 3 shows the direction of movement of the footwall relative to the hanging wall. The optimal selection of the seismogenic fault parameters are: strike 229~, dip 33~, and divided into 21 and 8 fault patches along strike and dip, respectively. For each subfault, the dimension is 15km/5km, and the rake and total slip of each subfault are given.

Fig. 3 Cross section of the fault with slip distribution (form Ji C., 2008)
1.3 Model Boundary Constraints and Coseismic Loading Methods

In order to obtain the true postseismic deformation field of the Wenchuan earthquake in the Sichuan-Yunnan region, it is necessary to obtain a coseismic displacement field close to the actual observation. Wan Yongge et al. (2011) provided us with a reliable, high-density, large-scale Wenchuan earthquake horizontal displacement field (Fig. 4(a)). The results show that: ① The coseismic horizontal deformation field of Wenchuan earthquake is obviously asymmetric, where deformation on the hanging wall (on the Qinghai-Tibetan Plateau side) is significantly larger than that of the foot wall (on the South China block side). This can also be seen in the near-field coseismic deformation of the InSAR results (Shen Zhengkang et al., 2009). ② The co-seismic impact of the Wenchuan earthquake from south to the north of eastern boundary of the Sichuan-Yunnan diamond-shaped block has a clockwise rotation characteristic, which close to the horizontal movement of the background tectonics. In Northwestern Yunnan block it shows a near-north-south movement. The middle block shows a clear south-westward overall movement, and there are still nearly 10mm coseismic variables in the northwestern and the central part of the Yunnan block.

Related researches (Wang Hua et al., 2007; Funning G. J. et al., 2007; Shao Zhigang et al., 2008; Li Ning et al., 2017; Ji Lingyun et al., 2017) show that the asymmetry of the coseismic deformation field is mainly caused by the following: ① there is a significant difference in the properties at two sides of the seismogenic fault; ② the effective viscosity caused by the viscoelastic relaxation after the earthquake changes laterally; ③ there are multiple nearly parallel shear bands in the fault; ④ the fault dip, that is, the fault is not an upright fault and there is a dip angle. For the seismogenic fault of Wenchuan earthquake, Longmenshan fault, both the obvious differences in media properties on both sides of the fault and fault dip can cause the asymmetry of the coseismic deformation field. In the second case, the impact is negligible in short term compared to the co-seismic rupture. Since the Longmenshan fault is relatively concentrated, the third case can also be ignored. For this reason, we considered the 33~ northwest dipping of the seismogenic fault when building the finite element model, and also considered the difference in the properties of the two sides of the seismogenic fault. We use the approximate zero-displacement boundary condition on the boundary condition setting, where the bottom of the model is fixed in vertical direction and the horizontal direction is free, the side boundaries of the model is fixed in horizontal and the vertical is free, and the top surface of the model is a free surface. The loading of the coseismic static displacement of the fault plane is referenced from Li Yujiang et al. (2013), which uses the symmetric loading of the hanging wall and footwall of the fault plane, that is, each plane undertakes half of the total coseismic slip. In such coseismic loading mode, the coseismic deformation field obtained by our simulation have a large difference in medium to far-field deformation compared to actural coseismic observation.

Based on settings stated above, the boundary conditions follow the practice of Li Yujiang et al. (2013) constraining the perimeter and bottom of the model, and making other directions that can move freely. So far, most of the loading methods for coseismic static dislocation fault plane are symmetric loading of the hanging wall and footwall (Li Yujiang et al., 2013), that is, each plane undertakes half of the total coseismic slip. Through calculation, we found that this loading method has a better fitting on the near field, but has poor performance in the middle and far field that incapable of fully reflecting the asymmetry deformation fields. Through analysis, we believe that in addition to the above four cases, the asymmetry of coseismic deformation may be related to the state of motion at the two plates of the fault, namely the active plane and the passive plane. The Qinghai-Tibetan Plateau was pushed northeastward by the Indian Plate. Under the constraints of the external tectonic environment, the west of Longmenshan is characterized by east-west motion perpendicular to the Longmenshan fault, while the South China block, especially the stable Sichuan Basin, is relatively stationary relative to the Qinghai-Tibetan Plateau. This indicates that Qinghai-Tibetan Plateau side of the Longmenshan fault is the active plane, while the South China block side is a relatively stable passive plane. In other words, the constraints of the tectonic boundary between the South China block and the Qinghai-Tibetan Plateau are inconsistent. This inconsistency may result in a larger co-seismic slip of the hanging wall than that of the footwall, which makes the coseismic deformation show a more significant feature of the hanging wall than that of the footwall in a larger range. Therefore, we intend to achieve the best match between the simulated horizontal displacement (mainly the mid-far field) and the actual observation by adjusting the static slip ratio of the hanging wall and foot wall of the fault. When the actual proportion is given, we should ensure that slip in the hanging wall is always larger than that of the foot wall, so as to conform to the physical mechanism. The results of trial calculation show that the horizontal displacement field (Fig. 4(b)) obtained when the ratio of co-seismic slip between the upper and lower plates is 7.5 ̄2.5 is close to the actual observation result (Fig. 4(a)).

It should be emphasized that because of the simplifications of the boundary conditions of the finite element model, crustal media, seismogenic fault dip and simulated slip distribution, the simulation results and the observation results have significant differences. The value vector difference can be seen more clearly in Fig. 4(c). The differences are mainly as follows: ① The simulated value near the fault is smaller than the actual observation value. This may be due to the coseismic rupture model used is the far-field seismic waveforms. Inversion is obtained without the constraints of near-field. ② The entire Sichuan-Yunnan region and the Sichuan Basin are far away from the seismogenic zone, and the simulated velocity field is larger than the observed velocity field, and there is systematic deviation. The reason may be that the boundary condition in the finite element simulation is only constraint to the normal direction, however the actual situation may be different. On the other hand, it may be the adjustment of the coseismic static slip ratio of the footwall and hanging wall. Only one ratio is used, which may be too simple. ③ In the whole area except the vicinity of the seismogenic zone, the velocity field in most areas have a residual of less than 10mm between the observation and simulation.

Although the simulation results have obvious differences compared with the observations, the overall patterns of the entire coseismic deformation field, especially the mid-field have good match with the actual observations (Fig. 4(a)). Therefore, it is reasonable to study the coseismic and postseismic deformation fields of the Wenchuan earthquake using the above-mentioned co-seismic loading ratio and boundary constraint method.

2 THE POSTSEISMIC IMPACT OF WENCHUAN EARTHQUAKE IN THE SICHUAN-YUNNAN REGION AND ITS IMPLICATION

Based on the above boundary conditions and static coseismic rupture loading of fault plane, we calculated the coseismic displacement and postseismic displacement field 1, 5 and 10 years after the Wenchuan earthquake caused by viscoelastic relaxation. The horizontal principal stress state and Coulomb stress change are also calculated. Combined with the characteristics of strong earthquake activity in the Sichuan-Yunnan region in recent years, the temporal and spatial evolution of these physical quantities are analyzed and verified.

It can be seen from the simulated coseismic horizontal displacement contour map (Fig. 5(a)) that, similar to the actual observation results, the coseismic impact of the Wenchuan earthquake mainly extends along both sides perpendicular to the seismogenic fault, and the deformation strength and range of the hanging wall are obviously greater than footwall, there are obvious asymmetry between the upper and lower plates. At the same time, there is also a certain displacement component parallel to the fault. It shows that the coseismic deformation is mainly characterized by thrust fault with right-lateral strike-slip component. It should be noted that the simulated Wenchuan earthquake has a greater impact on the coseismic impacts in the eastern part of the Sichuan-Yunnan border than the actual observations.

Fig. 5 The calculated horizontal deformation contour map of coseismic (a) and postseismic 1 year (b), 5 years (c) and 10 years (d) (exclude coseismic deformation) after the Wenchuan earthquake

From the horizontal deformation field after the Wenchuan earthquake, the deformation in the first year after the earthquake (Fig. 5(b)) is mainly concentrated near the seismogenic zone, and the deformation strength of the hanging wall is significantly larger than that of the footwall. However, in terms of impact range, influence of the footwall is larger than that of the hanging wall. The range of deformation field 5 years and 10 years after the earthquake (Fig. 5(c), (d)) extends over time follows the coseismic deformation. Among them, the extension from the eastern part of the Sichuan-Yunnan border to the southwest Yunnan and northwest Yunnan is more obvious. This is consistent with the distribution of the NE-trending strata in the Sichuan-Yunnan region after the Wenchuan earthquake. In addition, in the process of the range expansion of the deformation, along the boundary of the north and south sides of the Bayan Har block, a high deformation gradient zone is identified, which gradually enhanced with time. In this process, the 2010 Dawu MS5.4, the 2011 Luhuo MS5.7, and the 2014 Kangding MS6.3 strong earthquake occurred on the southern boundary of the Xianshuihe fault, and recently the 2017 Jiuzhaigou earthquake occurred in the northeast corner of its northern border, which may be related to the postseismic impact of the Wenchuan earthquake in the region. In addition, the postseismic deformation of the Daliangshan block increased significantly with time, and the horizontal deformation amount reached 20mm in 10 years after the Wenchuan earthquake. This area is also the active area of strong earthquakes after the Wenchuan earthquake.

From the vertical deformation characteristics (Fig. 6), similar to the coseismic horizontal deformation, the coseismic vertical deformation mainly extends along the vertical fault direction of the east and west sides of the Longmenshan fault, and the footwall near the fault appears as subsidence, and the hanging wall appears as uplift. Within a certain range of the fault (about 300km on the hanging wall and about 150km on the footwall), the deformation shows uplift, extends to both sides and then appears as a subsidence zone. As the distance from the fault increases, the coseismic vertical deformation decays faster. The southwestern part of the fault showed a significant uplift, while the northeastern part of the fault showed alternating uplift-subsidence characteristics. One year after the earthquake, the postseismic vertical deformation is mainly concentrated in the smaller area near fault. The vicinity of hanging wall near fault shows continuous uplift consistent with the coseismic deformation, and the footwall still appears to be subsidence. The far-field apprears to be a subsidence zone opposite to the coseismic deformation. The vertical deformation after the earthquake continues to expand outward with time, similar to the horizontal deformation. In addition to expanding at directions perpendicular to the fault plane, the expanding direction also has the characteristics of extending from the eastern Sichuan-Yunnan border to the northwestern and southwestern Yunnan.

Fig. 6 The calculated vertical deformation contour map of coseismic (a) and postseismic 1 year (b), 5 years (c) and 10 years (d) (exclude coseismic deformation)

From the coseismic and postseismic principle stress change at main block boundaries, we can see that (Fig. 7): ① Its impact on southern section of Garzê-Yushu fault, Luhuo-Dawu-Qianning section of Xianshuihe fault and northern section of Jinshajiang fault is mainly the tensile stress perpendicular to the fault strike, which gradually increases with time postseismically. Especially for the Xianshuihe fault, the cumulative tensile stress change the 10 years after the Wenchuan earthquake has exceeded the coseismic variation. The 2010 Dawu MS 5.4, the 2011 Luhuo MS5.7 and the 2014 Kangding MS6.3 strong earthquake occurred successively along the Xianshuihe fault. The magnitude, of earthquake is increased over time, and it has a significant correlation with the stress field after the Wenchuan earthquake. ② The Anning-Zemuhe-Xiaojiang fault, Mabian fault, Red River fault, and the southern Jinshajiang fault are characterized by variations of compressive stress at an angle to the strike of the fault. The principal compressive stress direction (NNE) of the Anninghe-Zemuhe-Xiaojiang fault is opposite to that of the background tectonic stress (NNW), which makes the fault appear to be dextral and has negative influence. The strong earthquake activity after Wenchuan earthquake is suppressed. The characteristics of strike-slip activity of the Red River fault are consistent with the background tectonics showing dextral strike-slip, but the magnitude is relatively small. In the middle and southern part of the Jinshajiang fault, it is characterized by compressive stress perpendicular to the fault. ③ The coseismic and postseismic deformation of Wenchuan earthquake have the greatest impact on Xianshuihe fault, followed by the northern Jinshajiang fault, Anning-Zemuhe fault, Mabian fault, Ludian-Zhaotong fault, the middle and southern part of the Jinshajiang fault, Red River fault and Lijiang-Xiaojinhe fault, and have the smallest impact on Xiaojiang fault. Considering the characteristics and extent of the impact, the main area of strong earthquake activity in Sichuan-Yunnan region after Wenchuan earthquake has good consistency.

Fig. 7 The calculated horizontal principal stress of the block boundary of coseismic (a) and postseismic 1 year (b), 5 years (c) and 10 years (d) after the Wenchuan earthquake (exclude coseismic deformation)

In order to further analyze the influence of the Wenchuan earthquake on faults of main block boundaries in the Sichuan-Yunnan region, the stress changes caused by the Wenchuan earthquake are projected to the slip direction of the fault plane.The Coulomb failure stress changes are used to indicate its impact on the surrounding faults. The specific calculation formula refers to Jaeger J. C. et al., (1969). The effective friction coefficient in the calculation is 0.4 according to the practices of Stein R. S. et al., (1992) and King G. C. P. et al., (1994). The geometries of the receiving fault are given by Deng Qidong et al. (2003). Since the seismic source depth of the study area is mostly in the range of 0 to 25km, we study the Coulomb failure stress change generated by the Wenchuan earthquake at a depth of 10km. We also calculated the Coulomb failure stress changes at other depths. However, the generally pattern and magnitude did not change much.

From the results of Coulomb failure stress change (Fig. 8): ① Coulomb failure stress generated by coseismic slip increases mainly at faults including the southern and northern ends of the Longmenshan fault, Garzê-Yushu fault, Xianshuihe fault, Baiyu fault, and eastern end of East Kunlun fault. The Coulomb failure stress increase of these parts exceeds 0.01MPa, reaching the threshold of strong earthquake triggering (King G. C. P. et al., 1994. Most of these Coulomb failure stress change increased on the basis of coseismic changes with time after the earthquake, but the increase was not significant. After the Wenchuan earthquake, MS>5.0 earthquake subsequently occurred on these faults, including 2010 MS7.1 Yushu earthquake on Garzê-Yushu fault, the 2013 MS7.0 Lushan earthquake on the southern section of Longmenshan fault and the 2014 MS6.3 Kangding earthquake on Xianshuihe fault. ② Faults with increased coseismic Coulomb stress, even not significant, include the Mabian fault on the eastern boundary of the Daliangshan block, the Ludian-Zhaotong fault on the southern boundary of the Daliangshan block, the Jinshajiang fault, and the Xiaojin River in Lijiang. In the southern section of the fault and the Nanting River fault, the Coulomb stress increase is less than 0.01MPa. The Coulomb failure stress of the Ludian-Zhaotong fault gradually increased with time after the earthquake. It reached 0.01MPa in 10 years after the earthquake. Several earthquakes with MS≡5.0 occurred in the vicinity of the fault, including the Ludian MS6.5 earthquake on August 3, 2014. The Coulomb failure stress of the Lijiang-Xiaojinhe fault increased with time after the earthquake. The 10-year Coulomb stress of the southern section was close to 0.01MPa, and the 2012 Ninglang MS5.7 earthquake occurred nearby. The Coulomb failure stress increased with time after the Jinshajiang fault, and the Coulomb stress increased with time after the earthquake in Nanting River, but it was not significant. ③ Faults with decreased coseismic Coulomb failure stress include the seismogenic fault in the middle part of Longmenshan fault, the Aninghe-Zemuhe-Xiaojiang fault, the northern part of Lijiang-Xiaojinhe fault, the Red River fault and the eastern part of East Kunlun fault. Except for the northern segment of Xiaojinhe fault in Lijiang, where the Coulomb failure stress changes from coseismic unloading to postseismic loading, the postseismic effects on other faults are consistent with the coseismic effect, all of which have the characteristics of different degrees of unloading enhancement. In short, there is a certain correlation between the loading and unloading situation reflected by coulomb failure stress change and the spatial distribution of strong earthquake activity affected by the coseismic and postseismic impact of Wenchuan earthquake. It should be said that due to the differences in the models and methods used in this paper, the coseismic Coulomb failure stress changes obtained in this paper and the results obtained by Wan Yongge et al. (2009) using dislocation methods are significantly different.

Fig. 8 Coulomb failure stress change projected on the fault plane and in the slip direction of the active faults in the Sichuan-Yunnan region generated by the coseismic (a) and postseismic 1 year (b), 5 years (c), 10 years (d) after the Wenchuan earthquake
3 DISCUSSION AND CONCLUSIONS

Based on the three-dimensional viscoelastic finite element method, using the large-scale Wenchuan earthquake coseismic horizontal displacement field given by Wang Qi et al. (2011) as a constraint, we simulate the temporal and spatial evolution of the coseismic and postseimsic deformation field and stress change caused by the Wenchuan earthquake. In the simulation process, not only the horizontal and vertical heterogeneity of the earth media in the Sichuan-Yunnan region are considered, but also the static coseismic slip ratio of the footwall and hanging wall is adjusted, so that our simulation results are as far as possible to be consistent with observations in the middle and far field.

The strong earthquake activities have good correlation with the spatial distribution of the simulation of the coseismic and postseismic deformation fields in the Sichuan-Yunnan region, the fault activity characteristics reflected by the stress state, and the stress loading on fault plane reflected by the Coulomb failure stress change, which has certain significance for understanding and explaining observational anomalies in the Sichuan-Yunnan region after the Wenchuan earthquake. However, there are still many inconsistencies in the simulation results compared with the actual observations. There are still problems to be discussed and solved in the simulation process. It mainly includes the following aspects: ① The finite element boundary constraints have an important impact on the results. Different boundary conditions may yield different results. This paper adopts the practice of most scholars where the normal of the model boundary is constrained and the tangential of the boundary is set to be free, which may be different from the real situation. It could also be the main reason why the far-field coseismic deformation in our simulation is relatively large compared with the observation results. Therefore, exploring boundary condition constraints that are more effective, reasonable, and close to the actual situation is a problem that needs to be further solved in the simulation process, such as Luo et al. (2010). ② This paper simply uses the ratio of coseismic static slip of the hanging wall and footwall to simulate the coseismic deformation field. It is too simple to use only one ratio, and it may be one of the reasons for the difference in data fitting. ③ The model does not consider the effect of gravity and background tectonic stress field. Gravity and background tectonic stress also have certain influence on coseismic and postseismic deformation. In addition, the complexity of the crustal medium itself (topography, discontinuity of the fault, etc) will have an impact on the simulation results. Further exploration and research are needed in the subsequent numerical simulation work.

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