Present crustal deformation and stress-strain fields of North China revealed from GPS observations and finite element modelling

Journal of Asian Earth Sciences 183 (2019) 103959

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Present crustal deformation and stress-strain fields of North China revealed from GPS observations and finite element modelling

T

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Wei Qua, , Yuan Gaoa, Qin Zhanga, Ming Haob, Qingliang Wangb a b

College of Geology Engineering and Geomatics, Chang’an University, Xian, Shaanxi, China Second Monitoring and Application Center, China Earthquake Administration, Xian, Shaanxi, China

A R T I C LE I N FO

A B S T R A C T

Keywords: North China Crustal deformation Stress-strain field Finite element method GPS Tectonic dynamics

North China is located on the N–S seismic belt of mainland China and is characterized by dense faults and intense seismicity. We analyzed the current regional crustal deformation using GPS observations from 1999 to 2007 and 2011–2017. We then established a dynamic finite element model based on the geological structure, geophysical parameters, and GPS velocity constraints to analyze the strain-stress features. Finally, we discuss the rationality of the simulation results, the variations in crustal activity, which may have been caused by the post-earthquake impact of the 2011 Mw 9.0 Tohoku and 2008 Mw 7.9 Wenchuan earthquakes, and the geodynamics of North China. Most parts of North China exhibited extensional stress in an approximately NW–SE direction during 2011–2017. In the two study periods, the maximum shear strain rates predominantly occurred in western North China; the central and eastern parts had relatively smaller values in 2011–2017. These characteristics indicate that the post-earthquake impact of the Tohoku earthquake significantly influenced most parts (central and eastern) of North China, whereas the Wenchuan earthquake mainly affected the western part. Our work quantitatively described the variations in current crustal movement velocities, stress-strain fields, and fault activity rates in North China. These characteristics indicate that the unique tectonic environment, intense crustal activity, and earthquake-prone nature of North China require continuous research attention. The results obtained in this study not only portray the current tectonic activity deformations but also reveal recent geodynamic processes in North China.

1. Introduction North China is located in northeastern China, with the Qinling and Dabie Mountains to the south, Yin and Yan Mountains to the north, Ordos Block to the west, and Yellow and Bo Seas to the east (Lin et al., 2017). It forms part of the famous N–S seismic belt in mainland China, where large historical and recent earthquakes have occurred, e.g., Huaxian (1556, Mw 8.5) and Tangshan (1976, Mw 7.5). Its frequent seismicity, intense crustal activity, and unique tectonic location make North China an important “natural laboratory” for studying active tectonic deformation in East Asia (Lin et al., 2017). Geodetic, geological, and geophysical studies have revealed important aspects of the tectonic activity in North China, e.g., by determining the temporal evolution (Menzies and Xu, 1998), using seismological monitoring networks and discontinuous deformation analysis methods to explore strong earthquakes (Li et al., 1993; Chen et al., 2003), using integrated receiver function imaging techniques and teleseismic surface wave tomography to image the lithospheric structure

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(Zheng et al., 2006; Tang et al., 2013), using large-scale surface gravity and teleseismic data to study the crustal structure and seismogenic mechanism (Jiang et al., 2014; Wu et al., 2018), analyzing the topography of the mantle transition zone from recorded teleseismic P waveforms (Si et al., 2016), and calculating crustal strain rates based on the GPS velocity of North China (Yao et al., 2015). GPS technology has been particularly useful for studying crustal deformation and geodynamic processes. Although GPS data have been used to describe the general characteristics of crustal motion in North China, detailed studies on the temporal variations in crustal deformation, stress-strain fields, and fault activity—specifically, the postearthquake influence of nearby strong earthquakes (e.g., the 2008 Mw 7.9 Wenchuan earthquake (Li et al., 2018) and 2011 Mw 9.1 Tohoku earthquake (Fukahata et al., 2012)—are lacking. To address this gap in the literature, we first used relatively new and more long-term GPS observations of two periods (1999–2007 and 2011–2017) obtained from the Crustal Movement Observation Network Of China to describe the temporal variability of crustal movement in

Corresponding author. E-mail address: [email protected] (W. Qu).

https://doi.org/10.1016/j.jseaes.2019.103959 Received 12 February 2019; Received in revised form 31 July 2019; Accepted 10 August 2019 Available online 12 August 2019 1367-9120/ © 2019 Elsevier Ltd. All rights reserved.

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the 1556 Mw 8.5 Huaxian earthquake and the 1303 Mw 8.0 Hongtong earthquake. The NCPB, bounded by Yin and Yan Mountain Blocks to the north, the Dabie Mountain fracture zone to the south, the TLF to the east, and the SR to the west, is moving in an ESE direction at a speed of ~3.0 mm/a (Zhang et al., 2011). More than 17 earthquakes of Mw > 7.0 have occurred in this region (Zhang et al., 1989), such as the 1679 Mw 8.0 Sanhe–Pinggu earthquake and the 1976 Mw 7.5 Tangshan earthquake (Ran et al., 1997; Guo et al., 2011). The LSB, to the east of the TLF, is also moving in an ESE direction but at a slightly greater speed than the NCPB (Deng et al., 2003).

North China, instead of using only GPS velocity to describe the general characteristics of crustal activity of North China over a certain period. Secondly, considering the actual stratigraphic structure and the significant influence of fault activity and tectonic environment on crustal deformation, we established a dynamic finite element model (FEM), rather than simply using a mathematical method, to study the stressstrain fields under the displacement boundary constraints of GPS velocity combined with geological and geophysical results. Finally, we discuss the rationality of the simulation results under the different fault geometries and elastic modules to determine the parameter settings, the variation in the stress-strain fields and fault activity (which may have been caused by the post-earthquake impact of the 2011 Mw 9.0 Tohoku and 2008 Mw 7.9 Wenchuan earthquakes), and the geodynamics of North China.

3. Distribution of GPS velocity fields The GPS data used in this study were obtained from the Crustal Movement Observation Network Of China. The GPS horizontal velocity solutions were obtained from the Second Monitoring and Application Center of the China Earthquake Administration, who processed the GPS data based on the methods used by Shen et al. (2005), Wang (2009), and SMCCEA et al. (2013). The GPS data were processed in four steps. First, GAMIT software (King and Bock, 1995) was used to obtain the loosely constrained daily solutions for satellite orbits and positions of regional stations by solving the GPS baseline with the International GPS Service precise ephemerides. Second, GLOBK (Herring, 1998) was used to combine the solutions with the daily loosely constrained solutions of the global International GPS Service network produced by the Scripps Orbit and Permanent Array Center (http://sopac.ucsd.edu) and output the loosely constrained solutions for the station coordinates, polar motion, and satellite orbits with their full variance–covariance matrices. Third, QOCA software (http://gipsy.jpl.nasa.gov/qoca/) was used to calculate the velocity of each GPS station with respect to the International Terrestrial Reference Frame 2008 (Altamimi et al., 2011). To analyze the interior crustal deformation of mainland China, we calculated the block rotational motion by directly adopting the Eurasian Pole of Eurasian Plate in the International Terrestrial Reference Frame 2008 provided by Altamimi (2011). Finally, the GPS velocities were transformed with respect to the Eurasian Plate reference frame. GPS velocities with obviously inconsistent motion trends with surrounding points, especially non-tectonic movement caused by local pumping in North China, were removed. In addition, co-seismic displacement models (Wang et al., 2011) were used to deduce the coseismic effect of the 2011 Mw 9.0 Tohoku earthquake. Hence, GPS velocities from two periods (1999–2007 and 2011–2017) were used to analyze variations in crustal deformation (SMCCEA et al., 2013). The horizontal components of GPS velocities in North China during the two periods are shown in Fig. 2a and b. Comparing the GPS velocity fields of 1999–2007 (Fig. 2a) and 2011–2017 (Fig. 2b), we found that North China predominantly moves in a SE direction with respect to the stable Eurasian Plate. This fit with the geodynamic setting of the study area (Wang et al., 2013). The main difference is that the overall magnitude of the GPS velocity field increased in 2011–2017. Nevertheless, overall crustal movement in western North China remained strong, and that in the central and eastern parts increased in 2011–2017. These features indicated that crustal movement in North China was generally continuous during the observation period, despite some changes in magnitude.

2. Geological background North China formed during the Archean and completed cratonization at the end of the Neoarchean (Kusky et al., 2007). In the Paleoproterozoic, reconstruction occurred in North China, and collision between the western and eastern blocks resulted in the formation of the Trans-North China Orogen and final amalgamation of North China (Kusky et al., 2007; Zhao et al., 2005). From the Mesoproterozoic, North China entered an evolutionary stage and remained stable for more than one billion years (Zhai et al., 2008). In the Mesozoic, tectonic activation and lithospheric thinning began because of stretching in the southern and northern margins of eastern North China (Menzies and Xu, 1998; Nicolas et al., 2011), forming the Tanlu Fault (TLF) and Zhangjiakou-Bo Sea Fault (ZBSF) (Zhu et al., 2009; Wan et al., 1996; Xu et al., 2000; Guo et al., 2015). The TLF is an important active tectonic deformation zone in eastern China with a total length of more than 3500 km and a NE strike. It is a right-lateral strike-slip thrust fault controlled by tectonic movement of the Pacific and East Asian Plates (Zhu et al., 2009; Wan et al., 1996; Xu et al., 2000). The ZBSF is another important active zone in North China, measuring ~700 km in length and striking NW. It has characteristics of a normal left-lateral strike-slip and a complex structure due to its intersection with several faults (Gao et al., 2001). The Shanxi Rift (SR), an important feature of North China, formed in the Late Pliocene, is Sshaped, and has a length of ~1040 km and a NE strike (Guo et al., 2004). The SR presently has predominantly right-lateral extensional characteristics and is one of the most active seismic belts in North China (Guo et al., 2004; Shi et al., 2015). The Tangshan–Cixian Fault (TCF), located in central North China, with a length of ~600 km and a NE strike, is a relatively new seismic tectonic belt that developed after the Late Tertiary and exhibits right-lateral movement (Xu et al., 1996). The above faults have played an important role in controlling the structural evolution of North China (Fig. 1). The Yilan–Yitong fault (YYF), located in northeastern North China, with a length of ~1000 km and a NE strike, is a seismic tectonic belt that developed after the Holocene and exhibits right-lateral movement (Yu et al., 2014). The Liaocheng–Lankao Fault (LLF), located in the center of the TCF and TLF, is an old normal fault that developed after the Late Paleozoic (Xiang et al., 2000). The dip angles of these major faults in North China ranges from 70 to 90° (Zhan et al., 2011). Specific information of the major faults are shown in Table 1. North China comprises the Ordos Block, SR, Yin Mountain Block, Yan Mountain Block, Yan Mountain–Bo Sea Block (YMBB), North China Plain Block (NCPB), and Ludong–Yellow Sea Block (Deng et al., 2003). The Ordos Block, with the Hetao Basin to the north, the Weihe Basin and Qinling Mountain Orogenic Belt to the south, the SR to the east, and the Yinchuan–Jilantai Basin to the west, is moving in an ESE direction at a speed of ~5.4 mm/a (Qu et al., 2017; Cui et al., 2016). The Ordos Block is relatively tectonically stable but intense in peripheral areas (Cui et al., 2016). Nineteen earthquakes of Mw > 7.0 have occurred in the area surrounding the Ordos Block (Guo et al., 2017), e.g.,

4. Model and analysis Previous studies have shown that the GPS velocity field can reveal crustal deformation, which may be affected by the reference frame. However, the stress-strain rate is independent of the reference frame. Moreover, the stress-strain rate field can numerically describe ongoing geodynamic processes, reflect the response of the internal mechanism (s) of crustal deformation, and reveal local strain accumulation rates and their possible correlation to seismicity (Ward 1994; Riguzzi et al., 2012). The tectonic dynamic environment and fault activity also 2

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Fig. 1. Location of North China and its surrounding areas. Red rectangle outlines the study area in mainland China (a). Thin red solid lines represent the major faults in North China (Zhang et al., 2005a). Bold dashed lines represent the boundaries of major blocks in North China (b). Black circles represent different seismic activity levels after 1900 (M > 6.0). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

The elastic parameters of each layer were determined based on deep reflection detection data (Li et al., 2006; Liu, 2007):

significantly impact crustal activity in North China. Therefore, we used GPS velocities as displacement boundary constraints to establish our FEM (England and Dan, 1982) for further analysis of strain-stress features. Additionally, the short-term crustal deformation revealed by GPS observations was considered homogeneous isotropic elastic deformation. Subsequently, a three-dimensional (3D) FEM of North China was established (Fig. 3).

E=

VS2 ρ (3VP − 4VS2) VP2 − VS2

(1)

ν=

VP2 − 2VS2 2VP2 − 2VS2

(2)

where E is the elastic modulus, ν is Poisson’s ratio, ρ is the density of the crustal medium, and VS and VP are the S-and P-wave velocities of the medium, respectively. The calculated parameters are shown in Table 2. The elastic modulus of the faults is one tenth of the surrounding area. Considering the computational efficiency, simulation feasibility, and actual fault distribution, the major faults in North China were treated vertically to penetrate the bottom of the lower crust in the 3D FEM model. This simplified method has been proven reasonable by previous studies (Lu et al., 2011; Lu et al., 2012; Fan et al., 2012; Li et al., 2017). The meshing not only met the requirements of GPS velocity constraints but also guaranteed the convergence and accuracy of the simulated results. We adopted tetrahedral elements to divide the grids, and the mesh around the fault was encrypted (Fig. 3). The rationality of the boundary conditions plays an important role

4.1. Model Considering the integrity of the major geological units in North China, we constructed a 3D FEM for 108–124°E and 34–42°N. The actual distribution of dominant faults was applied to the model, and the faults were treated as weak zones embedded within the crust (Parsons, 2002). Considering the computational efficiency, simulation feasibility, and actual stratigraphic structure, the vertical distribution of the crustal medium was processed into uniform and horizontal layers (Parsons, 2002). The model was divided into seven vertical layers: upper crust, middle crust, lower crust, and four mantle layers. The thicknesses of the upper, middle, and lower crust were 11 km each, and those of the four mantle layers were 17, 17, 17, and 16 km from top to bottom. The total depth of the 3D FEM was ~100 km (Wang, 2017). Table 1 Major active faults in North China. Fault

Abbreviation

Strike

Depth (km)

Activity

Reference

Tanlu Fault Zhangjiakou–Bo Sea Fault Shanxi Rift Tangshan–Cixian Fault Yilan–Yitong Fault Liaocheng–Lankao Fault

TLF ZBSF SR TCF YYF LLF

NE NW NE–NNE NE NE NE–NNE

30–40 15–26 20–40 30–36 30–40 7–15

Right lateral Left lateral Right lateral Right lateral Right lateral Normal fault

Wan et al. (1996) Guo et al. (2015)Suo et al. (2013) Guo et al. (2004)Zhang et al. (2005b) Zhou et al. (2013)Liu et al. (2011) Yu et al. (2014)Wan et al. (1996) Xiang et al. (2000)

3

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Fig. 2. GPS velocities (mm/a) in North China during 1999–2007 (a) and 2011–2017 (b). Blue arrows are the predicted velocities based on the finite element model at each GPS station, and red arrows are the observed GPS velocities with respect to the Eurasian Plate based on the International Terrestrial Reference Frame 2008. White lines represent major faults. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

2005). The dynamic environments caused by tectonic movements of the surrounding blocks and faults are the driving forces for crustal tectonic activity in North China. Therefore, according to the simulated dynamic environments and their characteristics, which are reflected by the GPS monitoring data, the displacement conditions of the four boundaries of the 3D FEM were all set as free loads, determined by the GPS velocity fields (as shown in Fig. 3 from the GPS observations from 1999 to 2007). To avoid local boundary effects and stress-strain concentration, which would have affected the analysis, the FEM boundary ranges were

in the reliability of the simulated results. The Ordos Block exhibits longterm, slow, counter-clockwise motion because of the eastward movement of the Tibetan Plateau, resulting in the compression of western North China (Qu et al., 2016) Subduction of the Eurasian Plate by the Pacific Plate directly affects eastern North China (Xu et al., 1994). The South China Block in the south of North China is moving in an ESE direction at a certain speed every year (Deng et al., 2003). The SR, ZBSF, TCF, YYF, and TLF are important zones of tectonic activity in the study area, and their activity features were considered (Zhang and Hu, 4

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Mountain Block presented significant compressional stress in an approximately NW–SE direction in 1999–2007 (Fig. 4a), with a mean compressional stress of ~153 Pa/a. During 2011–2017 (Fig. 4b), this region showed extensional stress in an approximately NW–SN direction and compressional stress in a NE–SW direction, with mean extensional and compressional stress rates of ~100 and ~115 Pa/a, respectively. During 1999–2007 (Fig. 4a), the western YMBB exhibited significant compressional stress in an approximately NW–SE direction, with a mean compressional stress rate of ~152 Pa/a. During 2011–2017 (Fig. 4b), this region mainly presented extensional stress in an approximately NW–SE direction and compressional stress in a NE-SW direction, with mean extensional and compressional stress rates of ~107 and ~117 Pa/a, respectively. We compared the principal FEM-simulated stress results with those of previous studies. The stress-strain results calculated by the kinetic model (Qu et al., 2016) and 2D FEM (Zhang et al., 2012a) indicated that the principal stress vectors around the Ordos Block and adjacent areas were predominantly compressional stress-strain with an approximately NE–SW orientation and some extensional stress-strain in a NW–SE direction. The integrated focal mechanism solution from the seismic data for 2001–2013 also suggests that the current principal stress of the NCPB was mainly controlled by tensile stress in a NW–SE direction (Wang, 2017). The magnitude of the maximum shear strain rate reflects the degree of crustal deformation; a larger maximum shear strain rate indicates more crustal activity. Fig. 4a shows that the maximum shear strain rates predominantly occur in three regions. First, it occurs along the peripheral areas of the Ordos Block, with a mean value of 1.05 × 10−8/a. Second, it is located in most parts of the NCPB where the faults intersect, with a mean value of 0.74 × 10−8/a. Third, it appears in the western YMBB, with a mean value of 0.61 × 10−8/a. However, differences in the maximum shear strain rate exist between the two periods. During 2011–2017, only two regions in North China presented significant maximum shear strain rates: the peripheral areas of the Ordos Block (western North China), where the average magnitude increased from 1.05 × 10−8/a (1999–2007) to 1.27 × 10−8/a (Fig. 4a and b), and the eastern Yan Mountain Block, with a mean value of ~0.55 × 10−8/a. Higher rates of strain accumulation were generally associated with more frequent earthquakes (Fig. 4a and b). Therefore, these areas with intense crustal activity and high stress-strain rate in North China require continuous research attention. However, most (central and eastern) parts of North China had relatively smaller maximum shear strain rates. For example, the maximum shear strain rates in the western YMBB decreased from 0.61 × 10−8/a (1999–2007) to 0.48 × 10−8/a (Fig. 4a and b); those of the eastern NCPB also decreased from 0.63 × 10−8/a (1999–2007) to 0.23 × 10−8/a (Fig. 4a and b).

Fig. 3. Three-dimensional finite element model of North China. The origin of the coordinates is point O. The E-axis represents the eastern direction, the Uaxis is the vertical direction, and the N-axis is perpendicular to the surface UOE, constituting the right-handed system. Black vectors represent the boundary conditions of the model, determined by GPS velocity fields (1999–2007). Table 2 Elastic parameters of the three-dimensional finite element model. Stratum medium Upper crust Middle crust Lower crust Mantle

Density (kg·m3) 2750 2800 3200 3300

Elastic modulus (Pa) 10

7.71 × 10 9.41 × 1010 1.21 × 1011 1.85 × 1011

Poisson’s ratio 0.25 0.25 0.25 0.33

larger than those of the GPS coverage. The relatively stable GPS stations close to the edge of the study area were selected, and those near the faults were excluded. The velocity of each node of the boundaries was calculated by linear interpolation and used as boundary displacement constraints. We assumed that the boundary displacement constraints did not change with depth (Li et al., 2006) (Fig. 3). 4.2. Stress-strain results and analysis The distribution of principal stress vectors and maximum shear strain rates over the two study periods were stimulated by the FEM (Fig. 4a and b). Comparing the principal stress results during the two periods, we observed significant differences between 1999–2007 and 2011–2017 around the eastern Ordos Block, eastern Yin Mountain Block, NCPB, southern margin of the Yan Mountain Block, and western YMBB. During 1999–2007 (Fig. 4a), the principal stress vectors around the eastern Ordos Block predominantly exhibited compressional stress rates in an approximately NE–SW direction and extensional stress in a NW–SE direction, with a mean compressional stress of ~220 Pa/a. However, for 2011–2017 (Fig. 4b), the principal stress vectors of this region exhibited extensional stress in an approximately NW–SE direction, with a mean extensional stress rate of ~181 Pa/a. Similar variations in principal stress vectors were observed in the eastern Yin Mountain Block, NCPB, southern margin of the Yan Mountain Block, and western YMBB. During 1999–2007, the eastern Yin Mountain Block exhibited significant compressional stress in an approximately NE–SW direction and some extensional stress in a NW–SE direction, with a mean compressional stress of ~218 Pa/a. During 2011–2017 (Fig. 4b), this region exhibited relatively significant extensional stress in an approximately NW–SE direction, with a mean extensional stress of ~119 Pa/a. The NCPB was dominated by compressional stress in a NE–SW direction and some extensional stress in the NW–SE direction during 1999–2007 (Fig. 4a), with a mean compressional stress of ~162 Pa/a. In 2011–2017 (Fig. 4b), the compressional stress of NCPB exhibited a decreasing trend, whereas the extensional stress increased, with a mean extensional stress rate of ~105 Pa/a. The southern margin of the Yan

5. Discussion 5.1. Model validation The reliability of the simulated results depends on the validity of the model. Thus, we analyzed the characteristics of residual errors between the observed and FEM-predicted values at GPS observation stations. Fig. 2 compares observed GPS velocities with model predictions based on the FEM. The root mean square error (RMSE) values are 1.62 and 1.60 mm/a, respectively. The histogram results (Fig. 5) indicate that the residual distribution satisfies the requirements for normality and lack of bias. The residuals around the central and northern NCPB and western YMBB are larger. This may be due to the complex geological characteristics of these areas. The fault geometry and elastic module are important factors in the simulation results. Therefore, to analyze the influence of different fault geometries and elastic modules on the modeling results, nine models were constructed with GPS velocities from 1999 to 2007 as examples 5

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Fig. 4. Vector maps of the principal stress rates (Pa/a) superimposed on contour maps of the maximum shear strain rates (10−8/a) of North China for 1999–2007 (a) and 2011–2017 (b). The different sizes of the grey circles represent the distribution of seismicity over the different periods. Black crossed arrows indicate the principal stress rate vectors, where the length and direction of the arrow represent the magnitude and principal direction of the principal stress rate, respectively. The opposite arrow represents the extensional principal stress rate, and the crossed arrow represents the compressional principal stress rate. n

(Table 3). The RMSE between the measured and simulated GPS velocities was used to evaluate the rationality of the models (Fig. 6):

RMSE =

∑1 [(VSE − VME )2 + (VSN − VMN )2] n

(3)

where n is the number of GPS stations, and VSE , VSN and VME , VMN 6

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Fig. 5. Histograms of residuals between observed and predicted velocities based on the finite element model in the E–W and N–S components for 1999–2007 (a1 and a2) and 2011–2017 (b1 and b2).

that Model 3 has the smallest RMSE value, which suggests that this model is optimal. These results are also supported by Table 3. It should be emphasized that although we discuss the validity of the model, the 3D FEM of North China established in this study is a relatively simple model. The actual geological conditions, fault activity characteristics, physical deformation of strata at different depths, and uncertainty of the observations may cause differences between reality and simulations (England and Dan, 1982; Parsons, 2002; Zhang et al., 2012a). In addition, the faults in North China are well-developed and complex. We therefore considered the main faults that influence tectonic activities in North China (Zhu et al., 2009; Wan et al., 1996; Xu et al., 2000; Gao et al., 2001; Guo et al., 2004; Xu et al., 1996; Wang, 2017). Moreover, we focused on the spatial distribution of large-scale crustal deformation and stress-strain fields of North China. We modeled the major faults via the 3D FEM because their activities significantly impact the crustal activity in North China, but we did not focus on other features of the fault, such as the dip or rake angle. On the other hand, the regional geodynamics are complex and occur over long periods, which complicates explanations or predictions with a single model or method. GPS observations can provide accurate and large-scale information of the crustal movement. This information reflects the present-day activity level of the crustal active deformation, but this remains “short-term” in terms of geological timescales. Nevertheless, the observations over 14 years provided a good indication of the present crustal movement. We further obtained the temporal variations in crustal deformation and stress-strain fields. Specifically, the variations in these crustal characteristics caused by nearby strong earthquakes, the

Table 3 Fault parameters and geometry settings of different models. Model Model Model Model Model Model Model Model Model Model

Fault parameter and depth 1 2 3 4 5 6 7 8 9

EMF/EMSA = 1/5, FLB EMF/EMSA = 1/15, FLB EMF/EMSA = 1/10, FLB EMF/EMSA = 1/5, FMB EMF/EMSA = 1/15, FMB EMF/EMSA = 1/10, FMB EMF/EMSA = 1/5, FUB EMF/EMSA = 1/15, FUB EMF/EMSA = 1/10, FUB

EMF: elastic modulus of the fault; EMSA: elastic modulus of the surrounding area; FLB: fault penetrates the bottom of the lower crust; FMB: fault penetrates the bottom of the middle crust; FUB: fault penetrates the bottom of the upper crust.

represent the simulated and measured GPS velocity in the E–W and N–S components, respectively. Compared with the other six models, Models 1, 2, and 3 have smaller RMSE values (Fig. 6). In these three models, the faults were set to penetrate the bottom of the lower crust; the setting of fault geometry was relatively reasonable. Furthermore, in the same fault geometry setting (FLB, FMB, and FUB), Models 3, 6, and 9 had smaller RMSE values (Fig. 6). Compared with the other six models, Models 3, 6, and 9 had their elastic modulus all set as one tenth of the surrounding area (Fig. 6), which is relatively reasonable. More importantly, Fig. 6 shows 7

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Fig. 6. Root mean square errors (RMSEs) of the constructed nine models. The Xaxis represents different models, and the Y-axis represents the RMSE value.

activity features of the major faults, and dynamic tectonic characteristics are relevant to a deeper understanding of the current tectonic deformations and geodynamic processes of North China. 5.2. Variations in stress-strain fields The 2008 Mw 7.9 Wenchuan earthquake occurred in the Longmenshan fault in southwestern North China (Zhang et al., 2009). A comparison of the stress-strain fields during 1999–2007 (Fig. 4a) and 2011–2017 (Fig. 4b) revealed a relative increase (from 1.05 × 10−8/a to 1.27 × 10−8/a) in maximum shear strain in the peripheral areas of the Ordos Block. The principal stress vectors in these two regions exhibited variations from 1999–2007 to 2011–2017 (Fig. 4a and b). In 1999–2007, the principal stress vectors around the Ordos Block indicated mainly compressional stress in a NE–SW direction and extensional stress in a NW–SE direction. Clear extensional stress (especially in northern North China) in a NW–SE direction and some compressional stress in a NE–SW direction was observed in 2011–2017. Furthermore, in the two periods, higher rates of the maximum shear strain presented in the peripheral areas of the Ordos Block, indicating intense crustal activity. These features suggest that the post-earthquake effect of Wenchuan earthquake also had some impact on shear strain accumulation and stress variations around the Ordos Block and its surroundings. The 2011 Mw 9.0 Tohoku earthquake that occurred in northeast North China was caused by the subduction of the Pacific Plate under the Eurasian Plate (Liang et al., 2018). The Tohoku earthquake released accumulated compressional stress-strain energy because of the plate subduction effect, which led to extensional stress in an approximately NW–SN direction and some compressional stress in a NE–SW direction (Wang et al., 2011; Zhang et al., 2012b; Tan et al., 2015). Therefore, this dynamic process resulted in the present tectonic stress field pattern in North China. As shown in Fig. 4b, most parts, especially in central and eastern North China, show extensional stress in an approximately NW–SN direction and some compressional stress in a NE–SW direction, such as the NCPB, western YMBB, eastern Yan Mountain Block, and western Ludong–Yellow Sea Block. The magnitudes of the extensional stress vectors in a NW–SN direction significantly increased in northeastern North China. On the other hand, the maximum shear strain in the central and eastern parts of North China decreased (Fig. 4b and a). The seismicity in central and eastern North China were also weakened after the Tohoku earthquake (Fig. 4b and c). This feature corresponds to the Coulomb stress variations after the Tohoku earthquake calculated by Feng et al. (2013). The variations in stress-strain fields during the two study periods indicate that the 2008 Mw 7.9 Wenchuan earthquake had some influence on the western margin of North China, especially in the peripheral areas of the Ordos Block, whereas the 2011 Mw 9.0 Tohoku earthquake affected most parts of North China (especially the central and eastern parts). We also analyzed the influence of different fault geometries and

Fig. 7. Rose diagrams of the third principal stress in the polar coordinate system. W, N, E, and S represent the western, northern, eastern, and southern directions, respectively. The length of each bar represents the magnitude of the compressional stress. The direction adopts the azimuth of the third principal stress, namely the angle between the bar and northern direction.

elastic modulus on the stress results by calculating the compressional stress vector of the nine models described in Section 5.1 and plotting them in stress rose diagrams (Fig. 7). Fig. 7 shows that the different fault geometry and elastic modulus settings resulted in different stress results. These differences were manifested in the magnitude and azimuth angle of the principal compressional stress. Taking the NCPB as an example, the mean stress ranged from −124 to −152 Pa/a. The largest difference in stress value (28 Pa/a) was between Models 2 and 8. In addition, the mean azimuth angle of the NCPB ranged from NE 71° to NE 76°. The largest difference in azimuth angle (5°) was between Models 5 and 6. The results suggested that different fault geometries and elastic modulus caused differences in stress simulation results, but the trend characteristics of principal stress in the nine models showed similar features. This further demonstrated that the numerical simulation method that considered physical properties, stratigraphic structure, and fault distribution is effective for studying regional crustal deformation and stress-strain fields (Lei et al., 2010; Liu et al., 2016; Li et al., 2017). To further analyze the differences in maximum shear strain with increasing depth (Fig. 8), a NW–SE profile was established across North China (red line in Fig. 9). Fig. 8a and b shows that the high values of the maximum shear strain are concentrated near the SR, TCF, LLF, and TLF fault zones, indicating intense crustal activity (Zhu et al., 2009; Guo et al., 2004; Xu et al., 1996; Xiang et al., 2000). The average values of maximum shear strain in the SR and TCF were approximately 132 × 10−10/a and 90 × 10−10/a in 1999–2007 and slightly increased to 150 × 10−10/a and 93 × 10−10/a in 2011–2017, respectively. However, the affection depth of maximum shear strain in the SR and TCF was ~65 and ~55 km in 1999–2007 and decreased to ~50 and ~40 km in 2011–2017, respectively. The variation value and affection depth of maximum shear strain may indicate that the post-earthquake impact of the 2008 Mw 7.9 Wenchuan earthquake on the two fault zones has persisted. The average values of maximum shear strain in the LLF and TLF were ~87 × 10−10/a and ~105 × 10−10/a in 1999–2007 and decreased to ~55 × 10−10/a and ~56 × 10−10/a in 2011–2017, respectively. The affection depth of maximum shear strain in the LLF 8

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indicating that the SR had right-lateral movement characteristics (Fig. 10(a11)–(a22)). Similar right-lateral movement features were observed in the TCF (Fig. 10(b11)–(b22)) and TLF (Fig. 10(c1) and (c2)). However, section lines D1-D1′ and D2-D2′ showed higher activity rates for the upper wall of the ZBSF than for the footwall, indicating that the ZBSF had left-lateral movement characteristics (Fig. 10(d11)–(d22)). Similar left-lateral movement features were found in the YYF (Fig. 10(e1) and (e2)). These features are consistent with previous geological and geophysical results (Che and Fan, 1999; Zhou et al., 2013; Gao et al., 2001; Ding, 1984; Yu et al., 2014; Jiang et al., 2000). Fig. 10 shows that the magnitudes of all fault activity rates increased in 2011–2017. For example, the activity rate of the nodes across the TLF was 3.79 mm/a in 1999–2007 and 4.74 mm/a in 2011–2017 (Fig. 10(c1) and 10(c2)). However, the relative activity rate of the TLF decreased from 0.036 mm/a in 1999–2007 (Fig. 10(c1)) to 0.025 mm/a in 2011–2017 (Fig. 10(c2)). The mean relative activity rate of the TCF simulated by the FEM is consistent with the slip rate revealed by geological analysis (Che and Fan, 1999). Taking the YYF, which is located in northeastern North China, as another example, the activity rate of the nodes across the YYF was 1.86 mm/a in 1999–2007 and reached 3.39 mm/a in 2011–2017 (Fig. 10(e2) and (e1)). However, the relative activity rate of the YYF decreased from 0.13 mm/a in 1999–2007 (Fig. 10(e1)) to 0.04 mm/a in 2011–2017 (Fig. 10(e2)). Similar activity features were found in other faults, except for the southern SR (section line A2-A2′). The activity rate of the nodes across section line A2-A2′ was 5.71 mm/a in 1999–2007 but decreased to 5.48 mm/a in 2011–2017 (Fig. 10(a22) and (a21)). Conversely, the relative activity rate of section line A2-A2′ increased from 0.17 mm/a in 1999–2007 (Fig. 10(a21)) to 0.36 mm/a in 2011–2017 (Fig. 10(a22)). The abnormal activity of section line A2-A2′ may have been caused by the post-earthquake impact of the 2008 Mw 7.9 Wenchuan earthquake, whereas the decreased relative activity rate of most faults in North China may relate to the release of stress-strain energy caused by coseismic and post-earthquake impacts of the 2011 Mw 9.0 Tohoku earthquake. To further analyze the influence of different fault geometries and elastic modulus on the fault activity, we calculated and plotted the relative activity rate of the faults between the nine models described in Section 5.1 (Fig. 11). Fig. 11 shows that the relative activity rates of these models varied. Model 7, whose activity rate was much smaller than that of the other eight models, had the highest RMSE value, suggesting the poorest simulation results (Fig. 6). This may be attributed to the difference between the setting of physical and geometric parameters and the actual characteristics. However, the overall differences between the other eight models were small. The difference in the relative activity rate of section line A2-A2′ between Models 2 and 8 was the largest (0.12 mm/a). More importantly, despite the differences between the nine models, the simulation results of the motion characteristics of the major faults were consistent.

Fig. 8. Maximum shear strain distribution of the profile (red line in Fig. 9) in the depth direction for 1999–2007 (a) and 2011–2017 (b). LLF: Liaocheng–Lankao Fault; SR: Shanxi Rift; TCF: Tangshan–Cixian Fault; TLF: Tanlu Fault.

Fig. 9. Sketch map of the section lines across the faults in the finite element model (FEM). Black solid lines represent faults. White lines represent the section lines. A1-A1′ and A2-A2′ represent the section lines of the Shanxi Rift (SR). B1-B1′ and B2-B2′ represent the section lines of the Tangshan–Cixian Fault (TCF). C2-C2′ represents the section line of the Tanlu Fault (TLF). D2-D2′ and D3-D3′ represent the section lines of the Zhangjiakou–Bo Sea Fault (ZBSF). E1E2′ represents the section line of the Yilian–Yitong Fault (YYF). The red line across the NW–SE of the FEM is the profile for studying the maximum shear strain distribution in the depth direction. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

5.4. Dynamic tectonic characteristics

and TLF also significantly decreased in 2011–2017. These results may be due to the release of stress-strain energy caused by coseismic and post-earthquake impacts of the 2011 Mw 9.0 Tohoku earthquake (Zhang et al., 2012b; Wang et al., 2011; Tan et al., 2015).

Crustal deformation is fundamentally controlled by regional tectonic dynamics (Qu et al., 2018). Collision and continuous convergence of the Indian and Eurasian Plates is the main controlling factor in crustal tectonic activity in mainland China (Xu et al., 1994). Collision between the Indian and Eurasian Plates caused rapid uplift of the Tibetan Plateau and its expansion towards surrounding areas. Eastern expansion of the plateau material caused approximately ENE–WSWtrending extrusions on the southwest boundary of North China, leading to the counter-clockwise rotation of the Ordos block and overall NW–SE movement of North China (Chen et al., 2011). Another important controlling factor in mainland China tectonism is the subduction of the Eurasian Plate by the Pacific Plate and post-arc expansion of the Japanese Sea, which exerted thrust stress on mainland

5.3. Variations in fault activity We selected five major active faults or zones (namely the SR, TCF, TLF, ZBSF, and YYF) to further analyze the variations in fault activity in North China during the study periods. Eight section lines were used to analyze the variations in activity rate in these faults (Fig. 9). During the two study periods, section lines A1-A1′ and A2-A2′ exhibited lower activity rates for the upper wall of the SR than for the footwall, 9

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Fig. 10. Activity rate of the upper wall and footwall of the major faults during 1999–2007 and 2011–2017. The coordinate system is independent and established on each section line. The X-axis represents the length of the section line, and the Y-axis represents the activity rate of the nodes on the section line; the positive direction is the strike direction of the fault.

Plate caused strong magmatism (Zhu et al., 2010), which increased the melt content of the upper mantle in North China, resulting in large-scale thinning of the lower lithosphere. On the other hand, extension of the far-field back arc of the subduction plate with resistance from the

China in a SW direction (Xu et al., 1994). Subduction of the Pacific Plate beneath the Eurasian Plate caused instability of the lithosphere and a mantle convective system under eastern North China (Xu et al., 1994; Zhu et al., 2012). On the one hand, the subduction of the Pacific

Fig. 11. Comparison of the relative activity rate of faults between the nine constructed models. The X-axis represents the eight section lines. The Y-axis represents the relative activity rate of the faults. 10

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6. Conclusions In this study, a 3D FEM of North China was established to study the crustal tectonic activity of the region according to geological structure, geophysical parameters, and GPS velocity constraints. The current crustal deformation and stress-strain rates were analyzed during two periods (1999–2007 and 2011–2017). The post-earthquake influence of the 2011 Mw 9.0 Tohoku earthquake and 2008 Mw 7.9 Wenchuan earthquake on the crustal tectonic activity of North China is also discussed. The principal stress, maximum shear strain rates, and fault activity of most parts of North China exhibited significant changes during 2011–2017. These areas were characterized by extensional stress in an approximately NW–SE direction, smaller maximum shear strain rates and affection depths, and decreased relative activity rates along the peripheral areas of the eastern Yin Mountain Block, NCPB, southern margin of the Yan Mountain Block, and western YMBB. These regions are mainly located in central and eastern North China and may have been influenced by the release of stress-strain energy caused by coseismic and post-earthquake effects of the 2011 Mw 9.0 Tohoku earthquake. In the two study periods, higher rates of maximum shear strain occurred in the peripheral areas of the Ordos Block (western North China), signifying the post-earthquake impact of the 2008 Mw 7.9 Wenchuan earthquake. Our work quantitatively described the variations in current crustal movement velocities, stress-strain fields, and fault activity rates of North China. These characteristics indicate that the intense crustal activity and high stress-strain zones in North China require continuous research attention. Therefore, to further improve the resolution and accuracy of crustal activity and seismic monitoring in North China, future research should continue to monitor crustal tectonic activity in this region, using long-term GPS monitoring data and other advanced monitoring sensors, such as InSAR and gravity monitoring.

Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements The authors are grateful to surveyors who work hard around North China in a challenging environment to obtain GPS data. We thank the second high-tech research center monitoring room of China Seismological Bureau for providing the high precision GPS data. This study was supported by the National Key Research and Development Program of China (No: 2018YFC1503604), the Nature Science Fund of China (NSFC) (project Nos: 41674001, 41731066, 41874017, 41604001, and 41202189), Natural Science Basic Research Plan in Shaanxi Province of China (No. 2019JM-202), the Special Fund for Basic Scientific Research of Central Universities (No. CHD300102268204). Some Figures were prepared using the public domain Generic Mapping Tools GMT (Wessel and Smith, 1998). Constructive comments from editor and two anonymous reviewers improved the manuscript. We would like to thank Editage (www.editage. cn) for English language editing. 11

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