Lower Crustal Flow and Its Relation to the Surface Deformation and Stress Distribution in Western Sichuan Region, China

Journal of Earth Science, Vol. 5, No. 4, p. 630 637, August 014 ISSN 1674-487X Printed in China DOI: 10.1007/s1583-014-0467-x Lower Crustal Flow and Its Relation to the Surface Deformation and Stress Distribution in Western Sichuan Region, China Yujiang Li* 1,, Lianwang Chen 1, Pei Tan 1, Hong Li 3 1. Key Laboratory of Crustal Dynamics, Institute of Crustal Dynamics, China Earthquake Administration, Beijing 100085, China. School of the Earth Sciences and Resources, China University of Geosciences, Beijing 100083, China 3. Earthquake Administration of Beijing Municipality, Beijing 100080, China ABSTRACT: The channel flow model was gradually being accepted with the more important multidisciplinary evidences from geology and geophysics, but how the lower crustal flow influenced the surface deformation quantitatively was unknown. Here, we develop a three-dimensional viscoelastic model to explore the mechanical relations between the lower crustal flow and the surface deformation in western Sichuan. Based on numerous tests, our results show that the modeled results fit well with the observed GPS data when the lower crust flows faster than the upper crust about 11 mm/a in the rhombic block, which can be useful to understand the possible mechanism of the surface deformation in western Sichuan. Moreover, taking the Xianshuihe fault as an example, we preliminarily analyze the relation between the active fault and stress field, according to the boundary constraints that deduced from the best model. The results show that the maximum shear stress on the Xianshuihe fault zone is mainly located in the fault terminal, intersections and the bend of the fault geometry, the stress level on the northwestern segment that has the high slip rate is relatively high. Additionally, with the reduction of the Young s modulus in the fault zone, it s conducive to generate the greater strain distribution, hence forming the high stress level. KEY WORDS: western Sichuan region, lower crustal flow, surface deformation, stress distribution, numerical simulation. 0 INTRODUCTION Located at the southeast border of the Tibetan Plateau, the western Sichuan region and its vicinity was a transitional zone between the Tibetan Plateau and the stable South China Block, which formed the special Y -shaped tectonic system. Due to the enormous gravitational potential energy that from the intense collision, the Tibetan Plateau demonstrated the mass extension in the eastward direction (Zhang et al., 003; England and Molnar, 1997; Zhong and Ding, 1996). There were also several faults including the Xianshuihe, Anninghe, Zemuhe and Longmenshan faults, which not only subdivided the western Sichuan and its vicinity into three active blocks such as the rhombic block, Barkam Block and South China Block, but also controlled the local stress division (Cui et al., 006; Wang et al., 1998). Since the 1970s, Molnar and Tapponnier (1975) had proposed the kinematics characteristics and dynamics mechanism of the lateral extrusion from the collision between India and Eurasia Plate, also the modern GPS data in the objective zone display the crustal rotation about the eastern syntaxis of the *Corresponding author: toleeyj@gmail.com China University of Geosciences and Springer-Verlag Berlin Heidelberg 014 Manuscript received September 8, 013. Manuscript accepted January 1, 014. Himalaya (Gan et al., 007; Shen et al., 005; Wang et al., 001). Recently, with the more important multidisciplinary evidences from geology and geophysics, the lower crustal flow is gradually accepted, which plays a crucial role in the surface deformation. Clark and Royden (000) compared the regional topographic gradients surrounding the Tibetan Plateau to the modeled results for flux of a Newtonian fluid through a lower crustal channel of uniform thickness, and found that the large-scale morphology of eastern plateau reflected the fluid flow within the lower crust. Flesch et al. (005) analyzed the GPS data, geologic data and the shear-wave splitting data in Central Asia, and demonstrated that the lower crust was so weak that the upper crustal deformation was decoupled from the motion of the underlying mantle, which made the relative velocity between crust-mantle reach 30 mm/a in Yunnan region, and finally controlled the clockwise rotation pattern in Sichuan- Yunnan region (Royden et al., 1997; Royden, 1996). Bai et al. (010) presented magnetotelluric data that imaged two major zones or channels of high electrical conductivity at a depth of 0 40 km in eastern Himalayan syntaxis. The channels extended horizontally from the Tibetan Plateau into Southwest China. Wang and He (01) employed the numerical methods to explore the relations between the lower crustal channel flow and the tectonic geomorphologic formation around the eastern Tibetan Plateau. The results showed that when the viscosity changed significantly from the eastern Tibetan Plateau to the stable Sichuan Basin, the tectonic geomorphologic features Li, Y. J., Chen, L. W., Tan, P., et al., 014. Lower Crustal Flow and Its Relation to the Surface Deformation and Stress Distribution in Western Sichuan Region, China. Journal of Earth Science, 5(4): 630 637. doi:10.1007/s1583-014-0467-x

Lower Crustal Flow and Its Relation to the Surface Deformation and Stress Distribution in Western Sichuan Region, China 631 could be best explained. Moreover, the previous simulation results also indicated that the drag force of the lower crust on the upper crust was not negligible (Cao et al., 009; Wang et al., 007; Zhu and Shi, 004). However, it remains unclear as how the lower crustal flow may influence the surface deformation. To address these questions, we developed a threedimensional viscoelastic finite element model for western Sichuan and its adjacent region, according to the multidisciplinary data including geology, geophysics and geodesy. We first use this model to investigate the crustal deformation characteristics and local stress pattern in different boundary constraints. Then, referencing the results from the optimization model, and taking the Xianshuihe fault as an example, we preliminarily investigate how the active fault may impact on the local stress pattern. 1 THREE-DIMENSIONAL FINITE ELEMENT MODEL 1.1 Model Description According to the previous research about the active blocks, the Sichuan-Yunnan region can be divided into four first-order blocks, which are the Barkam Block, Sichuan-Yunnan Rhombic Block, western Yunnan Block and South China Block. Moreover, the Sichuan-Yunnan Rhombic Block can be further divided into the western Sichuan and the middle Yunnan blocks due to the northeastern trending Lijiang-Xiaojinhe fault. The finite element model encompasses most of the first-order faults as shown in Fig. 1. In order to minimize the artificial boundary effects, the model domain is determined as follows: from 98.5º to 105.5º in longitude, and 5º to 33º in latitude. The model includes 15-km upper crust, 15-km middle crust with an elastic medium, and the 10-km viscoelastic layer representing the lower crust. All the faults in the model are described as the weaken zone with width less than 3 km, they have a dip angle of 90º, except the Longmenshan and Lijiang- Xiaojinhe faults, the former has the listric shape including a high dip angle of 70º near surface and low angle of 30º at depth, the latter has a dip angle of 60º (Zhang et al., 008; Xu et al., 003). Finally, the finite element model is composed entirely of 0-node viscoelastic elements, which consists of 17 617 elements with 154 458 active nodes (Fig. ). 1. Material Properties Wang et al. (00) established the three-dimensional velocity structure of crust and upper mantle in Sichuan-Yunnan region by using the first arrival P and S data of regional earthquakes recorded at local disperse stations. Huang et al. (003) presented a tomographic study on the S wave velocity of China and adjacent regions basing the robust Occam s inversion method. Referencing the relationship between Young s modulus, wave velocity, density and the Poisson s ratio (Wang R et al., 1980), we determine the mean values of Young s modulus after Huang s work. The effective viscosities are followed by Shi and Cao (008). The details are as follows in Table 1. Additionally, we assume the Young modulus in the fault as one third of the ambient medium, and the Poisson ratio as 0.6. Most previous studies related to the visco-elastic analysis used the Maxwell body, the relaxation and creep characteristics of the Maxwell body have shown a similar fluid property in which the stress reduces to zero, or the strain increases infinitely versus time. However, the real crustal rheological characteristics still have the seismogenic ability in the unlimited time, not the fluid material; this body may not match the fact (Li et al., 01). So we choose the Prony model in this article, also this model face the uneasy convergence and need high computational cost, the constitutive equation can be written as Figure 1. Sketch geological model in western Sichuan and its adjacent region. ANHF. Anninghe fault; DLSF. Daliangshan fault; LJF. Lijiang-Xiaojinhe fault; LMSF. Longmenshan fault; LTDWF. Litang-Dewu fault; MBF. Mabian fault; XSHF. Xianshuihe fault; YNXF. Yunongxi fault; ZMHF. Zemuhe fault. Figure. Three-dimensional finite element model.

63 Yujiang Li, Lianwang Chen, Pei Tan and Hong Li Table 1 Physical parameters of the finite element model Blocks Layer Young modulus (10 4 MPa) Barkam Western Sichuan Middle Yunnan South China Poisson ratio Density (kg m -3 ) Viscosity (Pa s) Upper crust 7.6 0.5 650 10 1 Middle crust 7.6 0.5 700 10 0 Lower crust 8.0 0.6 750 10 0 Upper crust 7.4 0.5 650 10 1 Middle crust 7.0 0.5 700 10 19 Lower crust 7.7 0.6 750 10 19 Upper crust 7.5 0.5 650 10 1 Middle crust 7. 0.5 700 10 19 Lower crust 7.8 0.6 750 10 19 Upper crust 8. 0.5 700 10 3 Middle crust 8.5 0.5 750 10 Lower crust 8.8 0.6 800 10 1 t de t dδ Gt ( ) d I Kt ( ) d 0 d 0 d where σ=cauchy stress, e=deviatoric part of the strain, Δ=volumetric part of the strain, G(t)=shear relaxation kernel function, K(t)=bulk relaxation kernel function, t=current time, τ=past time, and I=unit tensor. For the elements solid 186, the kernel functions are represented in terms of Prony series, which assumes that n G t G= G Gi exp - G i=1 i nk t K= K Ki exp - K i=1 i In respect, G, G i =shear elastic moduli; K, K i =bulk elastic moduli; τ i G, τ i K =relaxation times for each Prony component; and n G, n K = number of Prony unit 1.3 Boundary Conditions and Loads The GPS observation is widely used which reveals the movement of tectonic deformation. Here, we employ the data of the two periods in 004 and 007, through the cubic spline interpolation, the annual velocities are determined, as shown in Fig. 3. Then, with the computation time into consideration, the boundary conditions are determined in the end. The upper surface is fully deformable, the bottom of the model domain is free horizontally but fixed vertically, as shown in Table in detail. Table Model Definition of the boundary conditions during the numerical tests Boundary conditions The lower crust flow Constitutive relation 1 Uniform in vertical No Prony series Uniform in vertical Yes Prony series 3ºN 6º 8º 30º 10 mm/a 98º 100º 10º Kunming Chengdu 104ºE Figure 3. Annual velocity of the finite element model. All modeling presented here was conducted using the ANSYS finite element program. The ANSYS employs the Newton-Raphson approach to solve nonlinear problems. In this method a load is subdivided into a series of increments applied over several steps. Before each solution this method evaluates the out of balance load vector. If the convergence criteria is not satisfied, the load vector is reevaluated, the stiffness matrix is updated, and a new solution is obtained until the problem converges.

Lower Crustal Flow and Its Relation to the Surface Deformation and Stress Distribution in Western Sichuan Region, China RESULTS In this article, we adopt 100 years as one sub-step, boundary constraints increase with time step, and we calculate 10 sub-steps in all. Since the total computation time is shorter than the relaxation time of the upper and middle crust, and longer than that of the lower crust, so the model in fact describe the motion and deformation of elastic upper and middle crust which underling by the viscoelastic lower crust. Displacement Fields In order to investigate the influence of the lower crust flow of the rhombic block on the deformation, we calculated the displacement in the two models. The Fig. 4 depicts the crustal motion image and comparison between the observed and modeled results in two different models. The two models unanimously show that the crustal deformation rotates about the eastern Himalaya syntaxis, but also the differences between the modeled and GPS observations in different subdivisions, as shown in Fig. 5 in detail. In the Model 1, the special geological background of the region is ignored, so the difference between them is conspicuous, the error statistics show that for the Barkam Block, the mean misfits is 0.91 mm/a in east-west direction and 0.78 mm/a in north-south direction; for the western Sichuan Block, the mean is.01 mm/a in east-west direction and 3.94 mm/a in north-south direction; for the middle Yunnan Block, the mean is 1.57 mm/a in east-west direction and 3.80 mm/a in north-south direction; and for the South China Block, the mean is 0.74 mm/a in east-west direction and 1.19 mm/a in north-south direction; also the orientation mean error reaches 7º. But in the Model, the lower crust of the rhombic block is faster than the upper crust about 11 mm/a, then the modeled and observed fit well than the Model 1. For the Barkam Block, the mean misfits is 0.49 mm/a in east-west direction and 0.40 mm/a in north-south direction; for the western Sichuan Block, the mean is 0.53 mm/a in east-west direction and 0.78 mm/a in 633 north-south direction; for the middle Yunnan Block, the mean is 0.58 mm/a in east-west direction and 0.83 mm/a in north-south direction; and for the South China Block, the mean is 0.36 mm/a in east-west direction and 0.68 mm/a in north-south direction; the orientation mean error reaches 3º. To qualify the agreement between the modeled and observed data, we further calculate the chi-square merit function χ.1 i i i i 1 N ( X Mod X GPS ) (YMod YGPS ) N i 1 ( X i ) ( Y i ) GPS GPS In respect, XModi, YModi and XGPSi, YGPSi are two velocity components of the modeled and GPS data along the east and north direction. ΔXGPSi and ΔYGPSi are the GPS data error, N is the number of GPS data. The χ test is a statistical approach that represents the deviation degree between the actual observation and the theoretical value, the small value explains the good accordance between them. From Fig. 5 we can conclude that, the modeled and observed data fit well when the lower crust flow is included, especially in the rhombic block.. Stress Fields From the analysis above, we can conclude that the modeled and the observed correspond well when the lower crust flow faster than the upper crust about 11 mm/a. In order to further investigate the influence of lower crust flow on the stress pattern, we compare the modeled crust stress field in Model with the previous results. As shown in Fig. 6, the maximum principal compressional stress presents the near EW or NWW direction in Barkam and northwestern Sichuan region; it rotates the SEE direction in middle Yunnan region; and finally the NNW or near NS direction in north Yunnan region. In general, the stress trend rotates from the near EW direction Figure 4. Comparison between the modeled and observed results in two models.

634 Yujiang Li, Lianwang Chen, Pei Tan and Hong Li in the north region to the NWW-SEE in the central and NNW-SSE or near NS direction in the south region. Briefly, the characteristics are coincident well with the previous researches (Cui et al., 006; Xu et al., 1987; Kan et al., 1977)..3 Active Fault and Stress Field in the Xianshuihe Fault Zone The Xianshuihe fault was a highly active left-lateral strike-slip fault in the late quaternary, which was frequently prone to major earthquakes that had ruptured various segments of this fault in the past (Wen et al., 008; Allen et al., 1991). Consequently, we employ the three dimensional precise finite element model of Xianhuihe fault to explore the relation between stress field and active fault, according to the results in Model as the boundary condition. Moreover, we preliminary analysis the stress pattern in different Young modulus of the fault gauge. In previous research, the Young modulus in the fault gauge was commonly regarded as the ratio of 1/3 or 1/10 to the surrounding rock (Chen et al., 008; Xu and Chao, 1997). In order to explore how the Young modulus change will influence the stress pattern, we discuss the maximum shear stress change in different ratios of 1/, 1/5 and 1/10. From Figs. 7a to 7c, we can demonstrate that the high stress is mainly located in the fault terminal, intersections and the bend of the fault geometry. Also the stress shows the increase tendency as the ratio decreases. That is to say, with the reduction of the Young s modulus in the fault zone, it s conducive to generate the greater strain distribution, hence forming the high stress level. Moreover, in order to depict the relative size among these high stress regions, we assume the highest as one, and the relations among them is clearly shown in Fig. 7d, the highest stress pattern is independent of the ratio change. 3 CONCLUSIONS AND DISCUSSIONS The lower crustal flow is gradually accepted, and it plays a crucial role in the surface deformation in the western Sichuan. So in this study, we employ a three dimensional finite element model to explore how the lower crustal flow may influence on it. Then, taking the Xianshuihe fault as an example, we further Mean misfit of velocity in E-W direction (mm/a) 3 1 0 Model 1 Model Mean misfit of velocity in N-S direction (mm/a) 0 BB WSB MYB SCB BB WSB MYB SCB 4 3 1 Model 1 Model 10 5 Mean misfit of orientation angle (º) 8 6 4 Model 1 Model Chi-square test 4 3 1 Model 1 Model 0 0 BB WSB MYB SCB BB WSB MYB SCB Figure 5. Comparison between the modeled velocity and the GPS observation in two models. BB. Barkam Block; WSB. western Sichuan Block; MYB. Middle Yunnan Block; SCB. South China Block.

Lower Crustal Flow and Its Relation to the Surface Deformation and Stress Distribution in Western Sichuan Region, China Figure 6. Characteristics of the maximum principal stress after Model. 635 investigate how the active fault may impact on the local stress pattern, according to the results from the optimization model as the boundary constraints. The results showed that the dynamic model in the western Sichuan and its adjacent region may be controlled by the special dynamics conditions, also when the lower crust flows faster than the upper crust about 11 mm/a in the rhombic block, the modeled results fit well with the GPS observation data. Wang et al. (007) employed the finite element model to discuss the influence deduced from the lower crustal flow on the upper crust deformation, the results showed that the modeled fit well with the observed data when the lower crust flow fast than the upper crust about 10 mm/a, and the viscosity in the lower crust was assumed to 1018 Pa s. Nonetheless, the vertical heterogeneity was ignored in the model. However, we include the horizontal and vertical heterogeneity, and the viscosity was assumed to 1019 Pa s, which is consistent with the previous conclusion that the lower crust has a low viscosity of 1019 100 Pa s (Shi and Cao, 008). The maximum shear stress on the Xianshuihe fault is mainly located in the fault terminal, intersections and the bend of the fault geometry. Moreover, with the reduction of the Young s modulus in the fault zone, it s conducive to generate Figure 7. Stress distribution in different ratio and the relative size among them.

636 Yujiang Li, Lianwang Chen, Pei Tan and Hong Li the greater strain distribution, hence forming the high stress level. The relative high stress regions are mainly concentrating on the segments, which have the straight strike and simple structure, especially in these regions following the Qianning, Luhuo and Ganzi. In the numerical methods, determination of the boundary condition is a crucial issue. Commonly, the uniform model is adopted, but in fact, the boundary constraint is unequal, especially in the vertical direction. Here, we propose a new way to determine the local boundary constraint, and apply it to the Xianshuihe fault to explore the relation between the active fault and the stress pattern. Previously, the mechanical parameters in the fault gauge are commonly given by experience. In order to explore how these change will influence the stress pattern, we discuss the maximum shear stress change in different Young s modulus. The results demonstrate that the stress shows the increase tendency as the Young s modulus decreases. That is to say, with the reduction of the Young s modulus in the fault zone, it s conducive to generate the greater strain distribution, hence forming the high stress level. However, the highest stress pattern is independent of the ratio between the fault gauge and surrounding rock. Meanwhile, it should be noted that we treat the faults as the weaken zone, so the frictional mechanism is ignored. In the following, we will treat the fault as Coulomb-type frictional surface to explore the relation between fault geometry and stress distribution, and make a comparison between them. Additionally, the viscosity is also considered as the key factor that influences the deformation, so we will discuss the differences in different viscosities of the lower crust. ACKNOWLEDGMENTS We sincerely thank Profs. 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