2. China Earthquake Networks Center, Beijing 100045, China;
3. Survey Engineering Institute, Sichuan Earthquake Agency, Ya'an 625000, Sichuan, China
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 fixedpoint crossfault shortleveling/shortbaseline 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 crossfault 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 nearfield crossfault leveling sites (Zhang Licheng et al., 2009; Su Qin et al., 2010, 2014, Yue Chong et al., 2017), while the crossfault leveling data at the Yongsheng and Xiaguan sites in Yunnan had a good anomalous response before the west Menglian M_{S}7.3 and Lijiang M_{S}7.0 earthquakes (Zhang Xinghua et al., 1996, 1997; Wang Yong'an et al., 2004). Are these different responses of crossfault 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 ChiChi earthquake; Zhang Zhuqi et al. (2010) used twodimensional contact element model to analyze the influence of different fault dip angles on seismic activity and found that the movement of gentledip reverse fault at depth has an obvious promoting effect on the seismicity of high dip angle reverse fault in shallow areas. Using the existing seismogeological data, Wei Lianping (2014) obtained the optimal twodimensional simulated occurrence of the BeichuanYingxiu fault, and compared the rupture characteristics of different dip faults. However, there are few studies on the significant differences in crossfault leveling between different sites before the earthquake and the impact of fault occurrence on the crossfault shortbaseline and shortleveling survey. Therefore, this paper takes the thrust faults in the Longmenshan area as an example to construct the twodimensional 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 crossfault shortleveling 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 crossfault observation data.
1 DATA AND METHODSThis study focuses mainly on the influence of the structure of thrust faults on the crossfault shortleveling. The Longmenshan fault zone is a good representative site for this study, where crossfault shortleveling 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 M_{S}8.0 Wenchuan and M_{S}7.0 Lushan occurred. Therefore, the paper focuses on data from the three crossfault shortleveling 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 (MaoxianWenchuan) fault of the Longmenshan fault zone. The Guanxian and Shuanghe sites are located in the Qianshan (Anxianguanxian) fault. The measurement period is monthly, with a total of 12 times per year. From the original curves, we can see that the shortleveling curves of the three sites did not show significant shortterm 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.
In order to further analyze the crossfault leveling changes quantitatively, this paper calculates the change of intensity of fault activity at the crossfault 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 h_{i}^{t} denotes the ith observation value of the tth year. When the calculated average annual deformation rate v_{t}>0, it means uplift of the hanging wall of the fault, when v_{t} < 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 crossfault shortleveling 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 postearthquake 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 lowrate level like the rate before the Wenchuan earthquake.
Therefore, aiming at the low average annual deformation rate of the crossfault shortleveling 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 crossfault observation data more objectively.
2 MODEL'S GEOMETRY, PARAMETERS AND BOUNDARY CONDITIONS 2.1 GeometryCombined 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 highangle 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 1020km.
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 nearsurface, 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.
The longitudinally layered viscoelastic finite element model is built based on the stratification characteristics of the crustal medium in the SichuanYunnan 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 QinghaiTibetan 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 QinghaiTibetan 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 surfacesurface 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 crossfault 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.
There is a large uncertainty in the determination of quantitative parameters of longterm 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, 00010, 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 longterm 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 twodimensional model) is 35mm/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 fournode 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 crossfault shortleveling and deep stress distribution, ignoring the influence of elevation change on the eastern margin of the QinghaiTibetan 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 crossfault leveling displacement of the model are obtained.
3 SIMULATION RESULTS AND ANALYSIS 3.1 Comparison Between the Simulation and Observation ResultsThrough simulation, the results of average annual deformation rate of crossfault shortleveling 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 postearthquake 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 crossfault leveling sites is 0.170.25mm/a, and the average annual rate in model 1 is increased from 0.09mm/a to 0.23mm/a in the range of 515km, 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 0.140.22mm/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.
The cumulative displacements of the crossfault shortleveling 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 dipfixed 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 515km, every increase of 1km will lead to an increase of 81mm of the cumulative displacement; when the projection distance is within 2030km, the cumulative displacement is maintained at about 1.5m.
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 520km, 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 crossfault shortleveling. The ability of demonstrating the information is significantly weakened, and because the horizontal projection distance in the Longmenshan area is mostly between 1020km, this may be the reason why the average annual deformation rate of the crossfault shortleveling 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 ResultsThe change of the crossfault shortleveling 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, σ_{1}, σ_{2} and σ_{3} 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 520km 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.
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 1522km 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 highlow stressdifference zone near the bottom of the fault plane and near the highlow dip transition zone. However, the highlow 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.
In this paper, aiming at the influence of thrust fault structure on the crossfault shortleveling, a twodimensional 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 shortleveling is about 42mm/km within the projection distance range of 520km 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 shortleveling 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 crossfault 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 520km, and then the highlow stress difference area is formed at the bottom of the fault plane and near the highlow dip angle transition zone, especially the highlow 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 crossfault shortleveling. The simulation results show that the better anomaly response of the crossfault shortleveling 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. Crossfault shortleveling can easily capture the differential movement of faults caused by stress enhancement. Model 2 simulates the variation of surface crossfault shortleveling 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 1020km which is similar to the faults on the Longmenshan fault zone, can more likely to hinder the crossfault shortleveling displacement, at the same time, resulting in more stress accumulating at the bottom of the fault and weakening of the ability of crossfault shortleveling to reflect the regional stress enhancement. This may be the reason why few number of abnormalities observed by the crossfault shortleveling sites in the nearfield of the Longmenshan fault zone before several strong earthquakes. The model mainly considers the influence of thrust fault structure on the crossfault shortleveling. 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 shortleveling will be the direction of future research.
ACKNOWLEDGEMENTThe 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.
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