Earthquake Research in China  2019, Vol. 33 Issue (3): 489-502     DOI: 10.19743/j.cnki.0891-4176.201903003
The Influence of Thrust Fault Structure on Cross-fault Short-leveling Survey
YUE Chong1,2, QU Chunyan1, YAN Wei2, ZHAO Jing2, SU Qin3     
1. Key Laboratory of Earthquake Dynamics, Institute of Geology, China Earthquake Administration, Beijing 100029, China;
2. China Earthquake Networks Center, Beijing 100045, China;
3. Survey Engineering Institute, Sichuan Earthquake Agency, Ya'an 625000, Sichuan, China
Abstract: Aiming at different variation patterns of cross-fault short-leveling before earthquakes, the paper establishes the 2-D finite-element models with different crustal stratification and fault occurrence perpendicular to Longmenshan fault zone. By contact analysis and viscoelastic finite element method, the influence of fault structure on cross-fault short-leveling is obtained under the same constraint conditions, the results show that:with the increase of the horizontal projection distance of fault, the cumulative displacements of surface increase gradually in the models with fixed dip angles of the fault plane (model 1). However, when the horizontal projection distance exceeds 20km, the influence of fault's dip angle on the cumulative displacements of surface short-leveling will decrease significantly, and the cumulative displacements are maintained at about 1.5m. However, in the listric fault models (model 2), when the projection distance is less than 20km, the listric fault structure impedes the sliding of fault. The short-leveling variation rate is only half of model 1; as a result, the ability to reflect the regional stress enhancement by cross-fault short-leveling is further weakened. But when the horizontal projection distance exceeds 25km, the cumulative displacements significantly increase, with the maximum displacement reaching 1.75m. The results of equivalent stress show that the listric fault structure causes a sudden increasement in equivalent stress when the horizontal projection distance is 10km, higher equivalent stress values are accumulated between the projection distance of 5-20km, and then high-low stress difference zones are formed at the bottom of the fault plane and near the transition zone of low-high dip angle.
Key words: Cross-fault short-leveling     Finite element     Listric fault structure     Equivalent stress    

INTRODUCTION

The fault is a weak zone of crustal deformation. The preparation and generation of strong earthquakes are often accompanied by significant fault changes (Wang Yong'an et al., 2003). As effective means of fault deformation monitoring, the fixed-point cross-fault short-leveling/short-baseline surveys, which measures the surface vertical and horizontal differential movement between the two walls of fault, respectively, can reflect the movement changes of fault sections at the measuring points directly. However, it should be noted that the fault movement is not only controlled by the tectonic environment, but also by its geometrical distribution pattern, i.e. the structure of fault, which leads to significant differences in the sensitivity of different cross-fault leveling sites to regional crustal deformation or tectonic stress field changes. For example, before the Wenchuan earthquake, the movement rate of the entire Longmenshan fault zone was very low. There was no synchronous and significant precursory anomaly change appearing in the near-field cross-fault leveling sites (Zhang Licheng et al., 2009; Su Qin et al., 2010, 2014, Yue Chong et al., 2017), while the cross-fault leveling data at the Yongsheng and Xiaguan sites in Yunnan had a good anomalous response before the west Menglian MS7.3 and Lijiang MS7.0 earthquakes (Zhang Xinghua et al., 1996, 1997; Wang Yong'an et al., 2004). Are these different responses of cross-fault leveling related to the special structure of fault?

There are many previous studies on fault structure and surface rupture characteristics. For example, Aagaard et al. (2004) analyzed the influence of dip and rake of fault on surface displacement for the 1999 Chi-Chi earthquake; Zhang Zhuqi et al. (2010) used two-dimensional contact element model to analyze the influence of different fault dip angles on seismic activity and found that the movement of gentle-dip reverse fault at depth has an obvious promoting effect on the seismicity of high dip angle reverse fault in shallow areas. Using the existing seismo-geological data, Wei Lianping (2014) obtained the optimal two-dimensional simulated occurrence of the Beichuan-Yingxiu fault, and compared the rupture characteristics of different dip faults. However, there are few studies on the significant differences in cross-fault leveling between different sites before the earthquake and the impact of fault occurrence on the cross-fault short-baseline and short-leveling survey. Therefore, this paper takes the thrust faults in the Longmenshan area as an example to construct the two-dimensional finite element model with different crustal layers and different fault structures, and by contact analysis and viscoelastic finite element simulation, the influence of fault structure on the cross-fault short-leveling surveys under the same constraints is obtained. The results of the study help objectively understand the information about the variation of regional crustal deformation or tectonic stress field revealed by the cross-fault observation data.

1 DATA AND METHODS

This study focuses mainly on the influence of the structure of thrust faults on the cross-fault short-leveling. The Longmenshan fault zone is a good representative site for this study, where cross-fault short-leveling survey has been performed since the 1980s (Su Qin et al., 2010, 2014), and the data are relatively complete. During the observation period, two representative earthquakes, the MS8.0 Wenchuan and MS7.0 Lushan occurred. Therefore, the paper focuses on data from the three cross-fault short-leveling sites in Guanxian, Shuanghe and Qipangou (Qipangou's measurement was halted in 2013) in the Longmenshan fault zone before and after the two earthquakes. The distribution of the sites is shown in Fig. 1(a). The Qipangou site is located in the Houshan (Maoxian-Wenchuan) fault of the Longmenshan fault zone. The Guanxian and Shuanghe sites are located in the Qianshan (Anxian-guanxian) fault. The measurement period is monthly, with a total of 12 times per year. From the original curves, we can see that the short-leveling curves of the three sites did not show significant short-term precursory anomalies before the Wenchuan earthquake. The Wenchuan earthquake caused obvious displacement and deformation on the hanging wall and footwall of the three sites, and the variation range exceeds 8mm.

Fig. 1 The cross-fault short-leveling survey sites and the original curves

In order to further analyze the cross-fault leveling changes quantitatively, this paper calculates the change of intensity of fault activity at the cross-fault leveling sites before and after the Wenchuan earthquake, and then compares the average annual deformation rate of faults (Jiang Zaisen et al., 2009; Li Yuan et al., 2016; Yue Chong et al., 2017). The average annual deformation rate of fault is calculated as follows:

$ {v_t} = \frac{1}{n}\sum\limits_{{\rm{i}} = 1}^n {\left( {{h_i}^t - {h_i}^{t - 1}} \right)} \left( {i = 1,2 \cdots n} \right) $ (1)

where, n is the number of observation time in a year, and hit denotes the ith observation value of the tth year. When the calculated average annual deformation rate vt>0, it means uplift of the hanging wall of the fault, when vt < 0, it means descent of the hanging wall of the fault. Taking the origin time of the Wenchuan and Lushan earthquakes as the division point, the average annual deformation rate of cross-fault short-leveling before and after the two earthquakes is calculated, respectively, and the results are shown in Fig. 2. The average annual deformation rate of the Guanxian, Qipangou and Shuanghe sites before the 2008 Wenchuan earthquake is less than 1mm/a, and after the Wenchuan earthquake, obvious coseismic variations occurred in all three sites, the average annual deformation rate increased significantly. The maximum average annual deformation rate of the Qipangou site reached 10.01mm/a, the maximum deformation rate of the Guanxian site reached 7.36mm/a, and the maximum deformation rate of Shuanghe site reached 5.19mm/a. During the period from 2008 to 2013 after the Wenchuan earthquake, the three sites were in the post-earthquake adjustment phase, and the average annual deformation rate increased to some extent. Before and after the Lushan earthquake, there was no obvious increase in in Guanxian and Shuanghe sites. After 2014, the average annual deformation rates of the two sites were less than 0.5mm/a, and they were restored to the low-rate level like the rate before the Wenchuan earthquake.

Fig. 2 Average annual deformation rates of cross-fault short-leveling sites on the Longmenshan fault zone

Therefore, aiming at the low average annual deformation rate of the cross-fault short-leveling sites in the Longmenshan area, the finite element models with different crustal stratification and different fault structure are constructed for the area to simulate the impact of the fault structure on the displacement of ground surface level, so as to understand the regional crustal deformation or tectonic stress variation information reflected by cross-fault observation data more objectively.

2 MODEL'S GEOMETRY, PARAMETERS AND BOUNDARY CONDITIONS 2.1 Geometry

Combined with the seismic reflection profiles, surface rupture zone, surface geological data and precise location of aftershocks of the Longmenshan area, studies on the seismogenic structures and genesis of earthquakes have been conducted by researchers (Song Hongbiao et al., 1994; Chen Jiuhui et al., 2009; Xu Xiwei et al., 2008, 2013; Hubbard J. et al., 2009, 2010; Wang Fuyun et al., 2015; Chen Qifu et al., 2015). The results show that the faults within 10km from the surface are mostly high-angle faults, the angle is as high as 80° in the near surface and between 65°-80° on the whole (Xu Xiwei et al., 2008). The dip angle near the bottom is about 25° (Wang Qi et al., 2011). The distance of the fault plane projected on the horizontal plane is mostly between 10-20km.

Therefore, this paper combines the research results of the above scholars and designs two types of fault models. Model 1 is a straight flat fault plane (with fixed dip angle) model, and model 2 is a "listric" fault model, the dip of fault plane is unfixed, with the dip angle of 20° at the bottom and 80° at the near-surface, and the whole fault plane is a spline curve. The distance of the two models' fault planes projected to the horizontal plane are designed to be 5km, 10km, 15km, 20km, 25km, 30km (the null point of the horizontal projection distance is located at the location of the surface outcrop of the Longmenshan fault). Therefore, the model 1 and model 2 each get six model results. The schematic diagram of the models is shown in Fig. 3.

Fig. 3 The schematic diagram of the models
2.2 Parameters

The longitudinally layered viscoelastic finite element model is built based on the stratification characteristics of the crustal medium in the Sichuan-Yunnan region (Hubbard J. et al., 2009, 2010; Zhu Shoubiao, 2009), in which the upper crust is considered as an isotropic elastic model, the lower crust and the upper mantle are of viscoelastic Maxwell material, and the viscosity coefficient is set according to the research results of Shi Yaolin et al. (2008) and Zhu Shoubiao (2010). The lower crust viscous coefficient of the Qinghai-Tibetan Plateau is smaller than that of the Sichuan Basin. The length of the whole model is designed to be 600km and the depth is 60km. The depth of the eastern margin of the Qinghai-Tibetan Plateau is designed to be 20km for the upper crust and 40km for the lower crust. The depth of the Sichuan Basin is 20km for the upper crust, 20km for the lower crust and 20km for the upper mantle. The depth of the fault is uniformly set to be 20km, the physical parameters of the crust mainly refer to recent research results (see Table 1, Wu Jianping et al., 2006; Wang Chunyong et al., 2008; Zhu Shoubiao et al., 2010; Zhu Aiyu et al., 2015, 2016a). Contact elements are adopted to simulate the discontinuous deformation characteristics of the fault. The surface-surface contact type is adopted. The hanging wall of fault plane is set as the master surface, while the footwall of fault plane is set as the slave surface. Taking the fault model with a projection distance of 30km in the model 2 as an example, 150 pairs of contact elements are generated. Combining with the parameters of the study area in the relevant papers of the previous research in the study area (Byerlee J.O., 1978; Li Yujiang et al., 2014; Zhu Shoubiao et al., 2010; Zhu Aiyu et al., 2015, 2016b), the initial friction coefficient μ of the fault plane is determined to be 0.6. The cross-fault leveling line is laid on both hanging wall and footwall of the fault, with a length of 2km (including 1km on the hanging wall and 1km on the footwall of the fault). The specific layout position is indicated by the green line in Fig. 4. The results of the accumulative leveling displacement are calculated based on the nodes on the hanging wall and footwall of the fault.

Table 1 Physical parameters of the model

Fig. 4 Schematic diagram of mesh generation and boundary conditions of the model
2.3 Boundary Conditions

There is a large uncertainty in the determination of quantitative parameters of long-term slip characteristics of fault (Xu Xiwei et al., 2017; Chen Qifu et al., 2018), so the in situ recurrence period of the Wenchuan earthquake varies greatly. Using geological data or GPS slip rate results, the recurrence period of strong earthquakes is estimated to be between 1, 000-10, 000 years (Zhu Shouqi et al., 2009; Zhang Peizhen et al., 2008; Burchfiel B. C. et al., 2008); Paleoearthquake studies (Ran Yongkang et al., 2009, 2014) show that the average recurrence period is around 3, 000 years. The results of the viscoelastic finite element model (Liu Chang et al., 2017) show a recurrence period between 4, 200 and 6, 500 years for strong earthquakes similar to the Wenchuan earthquake. In order to study the long-term influence of thrust fault occurrence on the surface fault leveling, we take a time length of 6, 000 years, which include most of the recurrence research results, as the time step for simulation. According to the GPS calculation resutls, the crustal shortening in the range of 500km west of Longmenshan (along the direction of the two-dimensional model) is 3-5mm/a (Jiang Zaisen et al., 2009), and the paper takes a relative velocity load of 5mm/a applied to the west side of the model. In this paper, the finite element software ABAQUS is used to carry out the simulation calculation of the model, in which the model uses four-node plane strain element for mesh generation, and densified mesh is generated near the fault plane. The minimum interval of mesh generation is 0.5km (as shown in Fig. 3). Taking the 30km horizontal projection model in Model 2 as an example, a total of 9, 900 meshes and 10, 522 nodes are generated.

The boundary conditions of the model are set as follows: the left side of the model is under the action of displacement load; the right side of the model simulates the blockage of the Yangtze block, the horizontal direction is fixed and the vertical direction is free; the bottom boundary of the model is vertically fixed and horizontally free; and the surface of the model keeps free. This paper focuses on simulating the influence of fault structure on cross-fault short-leveling and deep stress distribution, ignoring the influence of elevation change on the eastern margin of the Qinghai-Tibetan Plateau and the Longmenshan area, but taking into account the effect ofgravitational potential energy. The model under the regional gravity equilibrium state is taken as the initial stress state of the model, and on this basis, the boundary load with a time step of 6, 000 years is applied, and finally, the stress, strain and the surface cross-fault leveling displacement of the model are obtained.

3 SIMULATION RESULTS AND ANALYSIS 3.1 Comparison Between the Simulation and Observation Results

Through simulation, the results of average annual deformation rate of cross-fault short-leveling of the six models in the model 1 (red histogram in Fig. 5(a)) and model 2 (blue histogram in Fig. 5(a)) are obtained and compared with the observation value of average annual deformation rate over the years of the Guanxian, Shuanghe and Qipangou sites (the green histogram in Fig. 5(b)). In order to eliminate the post-earthquake impact of the Wenchuan earthquake, the deformation rate of observation site before 2008 is calculated. It can be seen that the average annual deformation rate of the three cross-fault leveling sites is 0.17-0.25mm/a, and the average annual rate in model 1 is increased from 0.09mm/a to 0.23mm/a in the range of 5-15km, then it stabilized at 0.25mm/a. The average annual deformation rate of model 2, which is closer to the actual fault structure, increases continuously with increased projection distance, especially at the horizontal projection distance of about 20km to the Longmenshan fault (Xu Xiwei et al., 2008; Wang Qi et al., 2011), the average annual deformation rate of faults obtained from simulation is 0.14-0.22mm/a, which is equivalent to the observation results, suggesting that the whole model is relatively reasonable and accurate in parameter selection and friction coefficient setting between faults.

Fig. 5 The simulation (a) and observation (b) results of average annual deformation rate of cross-fault short-leveling
3.2 Analysis of the Displacement

The cumulative displacements of the cross-fault short-leveling of model 1 and model 2 under different horizontal projection distances are obtained by model simulation, as shown in Fig. 6, where the solid blue line is the result of model 1 (the annotated angle is the dip angle of the fault plane), the red solid line is the results of model 2, and the black dashed line is the fitted trend line. The simulation results show that when the dip angle is fixed (model 1), the cumulative displacement on the hanging wall gradually increases with the increased horizontal projection distance, but when the horizontal projection distance is greater than 20km, the cumulative displacement gradually becomes stable, that is, for a dip-fixed single fault plane model, the cumulative displacement increases gradually with the decrease of the dip angle, but the influence of the decrease of the fault dip angle on the cumulative displacement in the Longmenshan area is significantly reduced when the dip angle is less than 45°. The trend fitting line of model 1 is divided into two parts: within the projection distance of 5-15km, every increase of 1km will lead to an increase of 81mm of the cumulative displacement; when the projection distance is within 20-30km, the cumulative displacement is maintained at about 1.5m.

Fig. 6 Cumulative displacements of cross-fault short-leveling

The simulation results of model 2 show that with the increase of horizontal projection distance, the cumulative displacement increases continuously. The fitting result shows that when the projection distance is within 5-20km, the cumulative displacement rate is about 42mm/km, which is only equivalent to half of the variation rate of model 1. However, when the projection distance exceeds 25km, the cumulative displacement rate of the surface leveling increases significantly, reaching 92mm/km, and the cumulative displacement reaches 1.75m. That is, when the horizontal projection distance is less than 20km, the "listric" structure hinders the sliding of the fault plane. The change of the fault structure leads to more deficiency in reflecting the regional stress enhancement from the cross-fault short-leveling. The ability of demonstrating the information is significantly weakened, and because the horizontal projection distance in the Longmenshan area is mostly between 10-20km, this may be the reason why the average annual deformation rate of the cross-fault short-leveling in the Longmenshan fault zone is significantly lower than other areas. However, when the horizontal projection distance reaches 25km, the low dip angle and the far projection distance are favorable to overcoming the fault friction and accumulating strain, and the high dip angle shape of the fault near the surface is more conducive to uplift of the hanging wall.

3.3 The Equivalent Stress Results

The change of the cross-fault short-leveling is the most intuitive representation of the deep fault stress adjustment on the surface, and its essence is the response to the stress result of deep fault. Therefore, the equivalent stress distribution results of the six models in model 1 and model 2 are calculated. Through the simulation, the stress state change at the model's midpoint of model 1 and model 2 under the same displacement load condition are obtained respectively, and then the influence of fault structure on the regional tectonic stress in the Longmenshan area is analyzed. The equivalent stress is calculated as follows (Zhu Shoubiao et al., 2010):

$ {\sigma _{\rm{s}}} = \frac{{\sqrt 2 }}{2}\sqrt {({{({\sigma _1} - {\sigma _2})}^2} + {{({\sigma _2} - {\sigma _3})}^2} + {{({\sigma _3} - {\sigma _1})}^2})} $ (2)

where, σ1, σ2 and σ3 are the first principal stress, the second principal stress and the third principal stress, respectively

The paper simulated the equivalent stress results of model 1 and model 2, and calculated the difference between model 2 and model 1 under the same horizontal projection. The results are shown in Fig. 7 (blue solid line shows the maximum equivalent stress results of model 1; red solid line shows the maximum equivalent stress results of model 2; green solid line shows the results of model 2 minus model 1; black solid line is the fitting trend line of model 1). The simulation results show that the maximum equivalent stress value in model 1 increases with the increase of horizontal projection distance, and the whole process changes linearly. The equivalent stress reaches the maximum of 18.5MPa at the projection distance of 30km, which proves that the smaller the fault dip angle is, the more likely the stress accumulates at the bottom of the fault plane. The maximum equivalent stress obtained by model 2 is significantly higher than that of model 1 at the same horizontal projection distance, and the "listric" structure is more likely to accumulate stress at the bottom of the fault. And it can be seen from the simulation results that the whole process can be divided into three stages: the maximum equivalent stress has a steep rise at 10km, which is 6.5Mpa higher than 11.3MPa at 5km, but when the distance increases from 10km to 20km, the maximum equivalent stress is maintained at around 18.0MPa. However, as the projection distance increases further, the rate of variation of the maximum equivalent stress increases again, reaching to 0.9MPa every 5km, and reaches the maximum of 20.1MPa at 30km. The change of green curve in the Fig. 7 shows that the listric fault structure can make model 2 accumulate higher equivalent stress in the projection distance of 5-20km compared to the fixed dip angle fault models, but when the projection distance is greater than 25km, the difference between the maximum equivalent stress value of model 1 and model 2 is gradually reduced influenced by the farther projection distance, that is, the influence of the "listric" fault structure is reduced somewhat.

Fig. 7 Results of the maximum equivalent stress of the models

In order to further analyze the distribution of the equivalent stress values around the fault in the model 1 and model 2, the equivalent stress distribution results of the six models are shown in Fig. 8. As the effect of fault structure on equivalent stress is mainly in the Longmenshan and its surrounding areas, Fig. 8 only exhibits the influence area of the model with a perimeter of about 200km around the fault (the red solid line is the fault location, and the maximum equivalent stress value is marked at the bottom of the fault). The simulation results show that the equivalent stress of the model is mainly concentrated at the bottom of the fault, which is roughly consistent with the results of a large amount of slip at the depth of 15-22km obtained by Chen Qifu et al. (2015) and Wang Qi et al. (2011). However, due to the influence of fault structure, the equivalent stress distribution pattern of model 1 and model 2 is quite different. The high equivalent stress area in model 1 is mainly concentrated at the bottom of the fault plane, and the low stress concentration zone is formed at the top of the fault. However, in the model 2, the low stress concentration zone is concentrated mainly along the fault plane with lower dip angle, the high stress concentration zone is more favorable to form at the bottom of the fault as well as the surface with high dip angle, and then forming a high-low stressdifference zone near the bottom of the fault plane and near the high-low dip transition zone. However, the high-low stress difference zone at the bottom of the fault plane is more significant, once the bottom of fault plane overcomes the fault friction to produce slip, and high stress accumulation is more likely to extend to the low stress region along the fault plane.

Fig. 8 Equivalent stress distribution of the models
4 CONCLUSION AND DISCUSSION

In this paper, aiming at the influence of thrust fault structure on the cross-fault short-leveling, a two-dimensional finite element model perpendicular to the Longmenshan area is constructed, by designing the flat straight fault plane model with different projection distances and the "listric" fault model. The influence on the cumulative displacement of the surface and the regional tectonic stress is analyzed. According to the simulation results, the following conclusions are obtained:

(1) In the model 1, with the increase of the horizontal projection distance, the cumulative displacement of the surface increases gradually, but when the horizontal projection distance is greater than 20km, the influence of the fault dip angle on the cumulative displacement decreases greatly, and the cumulative displacement is maintained at about 1.5m. In the model 2, with the increase of horizontal projection distance, the cumulative displacement increases continuously. On the contrary, when the horizontal projection distance is greater than 25km, the cumulative displacement increases significantly, with the maximum leveling displacement reaching 1.75m.

(2) The trend fitting results of cumulative displacement shows that the cumulative displacement variation rate of the surface short-leveling is about 42mm/km within the projection distance range of 5-20km of the model 2, which is only equivalent to half of that in model 1 at the same projection distance, and when the projection distance exceeds 25km, the cumulative displacement variation rate of surface short-leveling increases significantly, reaching 92mm/km, which is greater than the cumulative variation rate of displacement in any stage of model 1, indicating that when the projection distance is less than 20km, the listric structure, whose dip angle has translate from a low angle of 20° to a high dip angle of 80°, hinders the sliding on the fault plane. The change of the fault structure leads to a weaker ability of reflecting the regional stress enhancement by cross-fault leveling, and the information revealing ability is significantly weakened. But when the horizontal projection distance becomes bigger than 25km, the low dip angle and the farther projection distance are favorable for overcoming the fault friction and accumulating strain. The shape of high dip angle near the surface is more conducive to uplift of the hanging wall, which in turn leads to greater surface displacement.

(3) The equivalent stress results of the model show that the maximum equivalent stress value in the model 1 increases with the increased horizontal projection distance, but that of the model 2 has a sharp rise at 10km, and subject to the "listric" fault structure, higher equivalent stress is accumulated at the projection distance between 5-20km, and then the high-low stress difference area is formed at the bottom of the fault plane and near the high-low dip angle transition zone, especially the high-low stress difference zone formed at the bottom of the fault plane is the most significant. Once the bottom of the fault plane overcomes the fault friction, slip would occur, and the high stress accumulation is more likely to extend to the low stress region along the fault plane.

Model 1 discusses the influence of the dip angle change of the flat straight fault model on the variation of cross-fault short-leveling. The simulation results show that the better anomaly response of the cross-fault short-leveling sites before several strong earthquakes, such as Yongsheng and Xiaguan, may be related to the higher sensitivity of the low dip angle (less than 40°) faults (Zhang Xinghua et al., 1997) to the process of stress enhancement. Cross-fault short-leveling can easily capture the differential movement of faults caused by stress enhancement. Model 2 simulates the variation of surface cross-fault short-leveling with "listric" fault structure underunilateral displacement loading. The results show that the listric structure which is steep in the upper part and gentle in the lower part, as well as a projection distance of 10-20km which is similar to the faults on the Longmenshan fault zone, can more likely to hinder the cross-fault short-leveling displacement, at the same time, resulting in more stress accumulating at the bottom of the fault and weakening of the ability of cross-fault short-leveling to reflect the regional stress enhancement. This may be the reason why few number of abnormalities observed by the cross-fault short-leveling sites in the near-field of the Longmenshan fault zone before several strong earthquakes. The model mainly considers the influence of thrust fault structure on the cross-fault short-leveling. To control the number of influencing factors, the fault model only considers the influence of a single fault. The study on influence of multiple complex faults on the regional short-leveling will be the direction of future research.

ACKNOWLEDGEMENT

The author would like to express their gratitude to Research Professor Liu Xia at the First Monitoring and Application Center of China Earthquake Administration for her guidance and suggestions in the preparation of the manuscript.

REFERENCES
Aagaard B.T., Hall J.F., Heaton T.H.Aagaard B.T., Hall J.F., Heaton T.H. Effects of fault dip and slip rake angles on near-source ground motions: Why rupture directivity was minimal in the 1999 Chi-Chi, Taiwan, Earthquake[J]. Bulletin of the Seismological Society of America, 2004, 94(1): 155-170. DOI:10.1785/0120030053
Burchfiel B.C., Royden L.H., van der Hilst R.D., Hager B.H., Chen Z., King R.W., Li C., Lü J., Yao H.Burchfiel B.C., Royden L.H., van der Hilst R.D., Hager B.H., Chen Z., King R.W., Li C., Lü J., Yao H. A geological and geophysical context for the Wenchuan earthquake of 12 May 2008, Sichuan, the People's Republic of China[J]. GSA Today, 2008, 18(7): 4-11. DOI:10.1130/GSATG18A.1
Byerlee J.O.Byerlee J.O. Friction of rocks[J]. Pageoph, 1978, 116(4/5): 615-626.
Chen Jiuhui, Liu Qiyuan, Li Shunceng, Guo Biao, Li Yu, Wang Jun, Qi ShaohuaChen Jiuhui, Liu Qiyuan, Li Shunceng, Guo Biao, Li Yu, Wang Jun, Qi Shaohua. Seismotectonic study by relocation of the Wenchuan MS8.0 earthquake sequence[J]. Chinese Journal of Geophysics, 2009, 52(2): 390-397 (in Chinese with English abstract). DOI:10.1002/cjg2.1359
Chen Qifu, Hua Cheng, Li Le, Cheng JinChen Qifu, Hua Cheng, Li Le, Cheng Jin. Viscoelastic simulation of deep tectonic deformation of the Longmenshan fault zone and its implication for strong earthquakes[J]. Chinese Journal of Geophysics, 2015, 58(11): 4129-4137 (in Chinese with English abstract).
Chen Qifu, Li LeChen Qifu, Li Le. Deep deformation of the Longmenshan fault zone related to the 2008 Wenchuan earthquake[J]. Chinese Science Bulletin, 2018, 63(19): 1917-1933. DOI:10.1360/N972018-00362
Hubbard J., Shaw J.H.Hubbard J., Shaw J.H. Uplift of the Longmen Shan and Tibetan plateau, and the 2008 Wenchuan (M=7.9) earthquake[J]. Nature, 2009, 458(7235): 194-197. DOI:10.1038/nature07837
Hubbard J., Shaw J.H., Klinger Y.Hubbard J., Shaw J.H., Klinger Y. Structural setting of the 2008 MW7.9 Wenchuan, China, earthquake[J]. Bulletin of the Seismological Society of America, 2010, 100(5B): 2713-2735. DOI:10.1785/0120090341
Jiang Zaisen, Fang Ying, Wu Yanqiang, Wang Min, Du Fang, Ping JianjunJiang Zaisen, Fang Ying, Wu Yanqiang, Wang Min, Du Fang, Ping Jianjun. The dynamic process of regional crustal movement and deformation before Wenchuan MS8.0 earthquake[J]. Chinese Journal of Geophysics, 2009, 52(2): 505-518 (in Chinese with English abstract).
Li Yuan, Liu Xia, Liu Xikang, Zhou Wei, Zheng Zhijiang, Zhang Licheng, Du Xuesong, Shen XiaoqiLi Yuan, Liu Xia, Liu Xikang, Zhou Wei, Zheng Zhijiang, Zhang Licheng, Du Xuesong, Shen Xiaoqi. Activity analysis of faults around Qilianshan before the 2016 Menyuan MS6.4 earthquake[J]. Journal of Geodesy and Geodynamics, 2016, 36(4): 288-293 (in Chinese with English abstract).
Li Yujiang, Chen Lianwang, Liu Shaofeng, Yang Shuxin, Jing YanLi Yujiang, Chen Lianwang, Liu Shaofeng, Yang Shuxin, Jing Yan. Impact of the Lushan earthquake on the surrounding faults: insights from numerical modeling[J]. Acta Geoscientica Sinica, 2014, 35(5): 627-634 (in Chinese with English abstract).
Lian Weiping. Rupture Characteristics of the Listric Thrust Fault and the Parallel Thrust Faults: Results from FEA Models Based on the Profile in the Middle of the Longmenshan Fault Zone[D]. Beijing: Institute of Geophysics, China Earthquake Administration, 2014 (in Chinese with English abstract).
Liu Chang, Dong Peiyu, Shi YaolinLiu Chang, Dong Peiyu, Shi Yaolin. Recurrence interval of the 2008 MW7.9 Wenchuan earthquake inferred from geodynamic modelling stress buildup and release[J]. Journal of Geodynamics, 2017, 110: 1-11. DOI:10.1016/j.jog.2017.07.007
Ran Yongkang, Xu X.W., Chen W., Chen L., Dong S., Wang H. Paleoearthquake and large earthquakes recurrence interval along Yingxiu-Beichuan fault of the Longmenshan fault zone, Sichuan, China. In: American Geophysical Union, Fall Meeting 2009. Washington: AGU, 2009.
Ran Yongkang, Wang Hu, Yang Huili, Xu LiangxinRan Yongkang, Wang Hu, Yang Huili, Xu Liangxin. Key techniques and several cases analysis in paleoseismic studies in mainland China (4): Sampling and event analysis of paleoseismic dating methods[J]. Seismology and Geology, 2014, 36(4): 939-955 (in Chinese with English abstract).
Shi Yaolin, Cao JianlingShi Yaolin, Cao Jianling. Effective viscosity of China continental lithosphere[J]. Earth Science Frontiers, 2008, 15(3): 82-95 (in Chinese with English abstract). DOI:10.1016/S1872-5791(08)60064-0
Song HongbiaoSong Hongbiao. The comprehensive interpretation of geological and geophysical data in the orogenic belt of Longmen Mountains, China[J]. Journal of Chengdu Institute of Technology, 1994, 21(2): 79-88 (in Chinese with English abstract).
Su Qin, Xiang Heping, Qiu Guilan, Ma LingliSu Qin, Xiang Heping, Qiu Guilan, Ma Lingli. Cross-fault level and 8.0 earthquake aftershock monitoring[J]. Journal of Seismological Research, 2010, 33(4): 269-273 (in Chinese with English abstract).
Su Qin, Yang Yonglin, Zheng Bing, Wang Shuanghong, Li Feifei, Liu GuanzhongSu Qin, Yang Yonglin, Zheng Bing, Wang Shuanghong, Li Feifei, Liu Guanzhong. A review of the thinking and process about prediction of Lushan M7.0 earthquake on Apr. 20, 2013[J]. Seismology and Geology, 2014, 36(4): 1077-1093 (in Chinese with English abstract).
Wang Chunyong, Lou Hai, Lü Zhiyong, Wu Jianping, Chang Lijun, Dai Shigui, You Huichuan, Tang Fangtou, Zhu Lupei, Silver P.Wang Chunyong, Lou Hai, Lü Zhiyong, Wu Jianping, Chang Lijun, Dai Shigui, You Huichuan, Tang Fangtou, Zhu Lupei, Silver P. S-wave crustal and upper mantle's velocity structure in the eastern Tibetan Plateau-Deep environment of lower crustal flow[J]. Science in China Series D: Earth Sciences, 2008, 51(2): 263-274 (in Chinese). DOI:10.1007/s11430-008-0008-5
Wang Fuyun, Zhao Chengbin, Feng Shaoying, Ji Jifa, Tian Xiaofeng, Wei Xueqiang, Li Yiqing, Li Jichang, Hua XinshengWang Fuyun, Zhao Chengbin, Feng Shaoying, Ji Jifa, Tian Xiaofeng, Wei Xueqiang, Li Yiqing, Li Jichang, Hua Xinsheng. Seismogenic structure of the 2013 Lushan MS7.0 earthquake revealed by a deep seismic reflection profile[J]. Chinese Journal of Geophysics, 2015, 58(9): 3183-3192 (in Chinese with English abstract).
Wang Qi, Qiao Xuejun, Lan Qigui, Freymueller J, Yang Shaomin, Xu Caijun, Yang Yonglin, You Xinzhao, Tan Kai, Chen GangWang Qi, Qiao Xuejun, Lan Qigui, Freymueller J, Yang Shaomin, Xu Caijun, Yang Yonglin, You Xinzhao, Tan Kai, Chen Gang. Rupture of deep faults in the 2008 Wenchuan earthquake and uplift of the Longmen Shan[J]. Nature Geoscience, 2011, 4(9): 634-640. DOI:10.1038/ngeo1210
Wang Yong'an, Liu Qiang, Wang Shiqin, Li YongliWang Yong'an, Liu Qiang, Wang Shiqin, Li Yongli. The typical characteristics of the trend anomaly of tilting deformation at the fixed observational sites before the occurrence of strong earthquakes in Yunnan[J]. Journal of Seismological Research, 2003, 26(S1): 126-132 (in Chinese with English abstract).
Wang Yong'an, Liu Qiang, Wang ShiqinWang Yong'an, Liu Qiang, Wang Shiqin. Variation characteristics of cumulative percentage of cross-fault deformation before M7.0 Lijiang earthquake[J]. Journal of Seismological Research, 2004, 27(1): 61-65 (in Chinese with English abstract).
Wu Jianping, Ming Yuehong, Wang ChunyongWu Jianping, Ming Yuehong, Wang Chunyong. Regional waveform inversion for crustal and upper mantle velocity structure below Chuandian region[J]. Chinese Journal of Geophysics, 2006, 49(5): 1369-1376 (in Chinese with English abstract).
Xu Xiwei, Wen Xueze, Ye Jianqing, Ma Baoqi, Chen Jie, Zhou Rongjun, He Honglin, Tian Qinjian, He Yulin, Wang Zhicai, Sun Zhaomin, Feng Xijie, Yu Guihua, Chen Lichun, Chen Guihua, Yu Shen'e, Ran Yongkang, Li Xiguang, Li ChenxiaXu Xiwei, Wen Xueze, Ye Jianqing, Ma Baoqi, Chen Jie, Zhou Rongjun, He Honglin, Tian Qinjian, He Yulin, Wang Zhicai, Sun Zhaomin, Feng Xijie, Yu Guihua, Chen Lichun, Chen Guihua, Yu Shen'e, Ran Yongkang, Li Xiguang, Li Chenxia. An Yanfen. The MS8.0 Wenchuan earthquake surface ruptures and its seismogenic structure[J]. Seismology and Geology, 2008, 30(3): 597-629 (in Chinese with English abstract).
Xu Xiwei, Chen Guihua, Yu Guihua, Cheng Jia, Tan Xibin, Zhu Ailan, Wen XuezeXu Xiwei, Chen Guihua, Yu Guihua, Cheng Jia, Tan Xibin, Zhu Ailan, Wen Xueze. Seismogenic structure of Lushan earthquake and its relationship with Wenchuan earthquake[J]. Earth Science Frontiers, 2013, 20(3): 11-20 (in Chinese with English abstract).
Xu Xiwei, WuXiyan, Yu Guihua, Tan Xibin, Li KangXu Xiwei, WuXiyan, Yu Guihua, Tan Xibin, Li Kang. Seismo-geological signatures for identifying M≡7.0 earthquake risk areas and their premilimary application in mainland China[J]. Seismology and Geology, 2017, 39(2): 219-275 (in Chinese with English abstract).
Yue Chong, Yan Wei, Li Xiaofan, Niu Anfu, Zhao Jing, Yuan ZhengyiYue Chong, Yan Wei, Li Xiaofan, Niu Anfu, Zhao Jing, Yuan Zhengyi. Sichuan fault activity analysis and correlation study of Wenchuan & Lushan seismic activity[J]. Journal of Geodesy and Geodynamics, 2017, 37(9): 888-892 (in Chinese with English abstract).
Zhang Licheng, Yu Min, Sun DongyingZhang Licheng, Yu Min, Sun Dongying. Analysis on fault deformation anomaly of Longmenshan fault zone before Ms8.0 Wenchuan strong earthquake[J]. North China Earthquake Sciences, 2009, 27(1): 34-38 (in Chinese with English abstract).
Zhang Peizhen, Xu Xiwei, Wen Xueze, Ran YongkangZhang Peizhen, Xu Xiwei, Wen Xueze, Ran Yongkang. Slip rates and recurrence intervals of the Longmen Shan active fault zone and tectonic implications for the mechanism of the May 12 Wenchuan earthquake, 2008, Sichuan, China[J]. Chinese Journal of Geophysics, 2008, 51(4): 1066-1073 (in Chinese with English abstract).
Zhang Xinghua, Song JinlingZhang Xinghua, Song Jinling. Responses of cross fault deformation before the M7.3 west Menglian, Yunnan earthquake[J]. Chinese Journal of Geophysics, 1996, 39(2): 286 (in Chinese).
Zhang Xinghua, Song Jinling, Wang Qiongwei, Shao DeshengZhang Xinghua, Song Jinling, Wang Qiongwei, Shao Desheng. Crustal deformation and the M7.0 Lijiang earthquake in Yunnan[J]. Journal of Seismological Research, 1997, 20(1): 72-82 (in Chinese with English abstract).
Zhang Zhuqi, Zhang Peizhen, Wang QingliangZhang Zhuqi, Zhang Peizhen, Wang Qingliang. The structure and seismogenic mechanism of Longmenshan high dip-angle reverse fault[J]. Chinese Journal of Geophysics, 2010, 53(9): 2068-2082 (in Chinese with English abstract).
Zhu Aiyu, Zhang Dongning, Jiang Changsheng, Li MingZhu Aiyu, Zhang Dongning, Jiang Changsheng, Li Ming. The numerical simulation of the strain energy density changing rate and strong earthquake recurrence interval of the Sichuan-Yunnan block[J]. Seismology and Geology, 2015, 37(3): 906-927 (in Chinese with English abstract).
Zhu Aiyu, Zhang Dongning, Jiang ChangshengZhu Aiyu, Zhang Dongning, Jiang Changsheng. Numerical simulation of the segmentation of the stress state of the Anninghe-Zemuhe-Xiaojiang faults[J]. Science China Earth Sciences, 2016a, 59(2): 384-396. DOI:10.1007/s11430-015-5157-8
Zhu Aiyu, Zhang Dongning, Guo YingxingZhu Aiyu, Zhang Dongning, Guo Yingxing. The numerical simulation on the seismogenic mechanism of the Lushan MS7.0 earthquake constrained by deformation observation[J]. Chinese Journal of Geophysics, 2016b, 59(5): 1661-1672 (in Chinese with English abstract).
Zhu Shoubiao, Zhang PeizhenZhu Shoubiao, Zhang Peizhen. A study on the dynamical mechanisms of the Wenchuan MS8.0 earthquake, 2008[J]. Chinese Journal of Geophysics, 2009, 52(2): 418-427 (in Chinese with English abstract).
Zhu Shoubiao, Zhang PeizhenZhu Shoubiao, Zhang Peizhen. Numeric modeling of the strain accumulation and release of the 2008 Wenchuan, Sichuan, China, earthquake[J]. Bulletin of the Seismological Society of America, 2010, 100(5B): 2825-2839. DOI:10.1785/0120090351