Numerical simulation of coseismic and postseismic deformation through a node-splitting algorithm: A case study of the Wenchuan earthquake
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摘要: 大地震导致的同震及震后效应，对于分析不同地震之间的相互影响及区域地震危险性等有着重要的作用。文中开发了模拟地震同震及震后效应的三维黏弹性有限元程序，通过计算走滑断层震例（概念性模型）引起的同震及震后效应，并与解析/半解析解进行对比，验证了程序的可靠性。同时基于概念性模型，分析了不同介质参数对同震及震后的地表变形的影响。研究表明，地球介质的横向不均匀性对地震同震位移有显著的影响，而中下地壳上地幔的黏度对震后效应起着主要控制作用。最后将该程序应用于青藏高原东缘，计算分析了2008年MW7.9汶川大地震导致的同震及震后库仑应力变化对2013年MW6.6芦山地震及2017年MW6.5九寨沟地震的影响。结果显示，汶川地震导致的库仑应力变化在芦山地震震源附近（0.013 MPa）及九寨沟地震震源附近（0.009 MPa）都为正值，说明汶川地震可能使得两次地震提前发生。Abstract: The coseismic and postseismic effects are crucial elements in analyzing fault interactions and the regional seismic risk. In this paper, we developed a three-dimensional viscoelastic finite element code to simulate the coseismic and postseismic deformation. We calculated the coseismic and postseismic deformations caused by the strike-slip fault with a conceptual model, and compared the results with the analytic and semi-analytic solutions so as to verify the reliability of the code. Meanwhile, we also analyzed the influence of different parameters on the coseismic and postseismic deformation, uncovering a significant effect of the earth's lateral heterogeneity on the coseismic displacement. And the viscosity of the middle-lower crust and upper mantle plays a major role in controlling the postseismic displacement. At last, we used the three-dimensional viscoelastic model to calculate the changes of the coseismic and postseismic Coulomb stress caused by the 2008 MW7.9 Wenchuan earthquake, and analyzed the subsequent effect on the 2013 MW6.6 Lushan earthquake and the 2017 MW6.5 Jiuzhaigou earthquake. The calculation results show that the Coulomb stress changes caused by the Wenchuan earthquake is positive near the hypocenters of the Lushan earthquake (0.013 MPa) and the Jiuzhaigou earthquake (0.009 MPa), indicating the Wenchuan earthquake might have triggered both the Lushan earthquake and Jiuzhaigou earthquake.
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图 1 分裂节点法的一维有限元示意图
箭头表示地震断层错动方向；U2a=-ΔU1b，表示地震断层的同震位移；数字表示单元节点号
Figure 1. 1-Dimensional finite element model with the node-splitting algorithm
The arrows show the direction of the fault slip. ΔU2a=-ΔU1b represents coseismic slip. The numbers represent the nodes
图 2 走滑断层的有限元模型
白色箭头表示模型的断层为右旋走滑；AA′为剖面位置
Figure 2. Conceptual finite element model with single strike-slip fault
The white arrows indicate a right-lateral strike-slip fault. AA′ is the profile location in Fig. 4.
图 3 走滑断层的地表同震位移分布图
图中白色线段表示断层位置；Ux，Uy，Uz分别表示x方向、y方向和z方向的同震位移分布
a—x方向同震位移分布图；b—y方向同震位移分布图；c—z方向同震位移分布图Figure 3. Surface coseismic slip distribution of the strike-slip fault. (a) Coseismic slip along the x-direction. (b) Coseismic slip along the y-direction. (c) Coseismic slip along the z-direction
The white line shows the location of fault in the model. Ux, Uy, and Uz represent the coseismic slip along the x-direction, y-direction, and z-direction, respectively.
图 4 地震同震及震后在剖面AA′上沿着断层走向(y方向)的位移分布图(剖面AA′的位置见图 2)
a—地震同震位移分布(实线表示有限元模型的结果，虚线为Okada模型计算得到的结果)；b—不同算例的地震同震位移；c—震后200年剖面同震位移变化图；d—同震和震后200年的位移总变化量
Figure 4. Coseismic and postseismic along-strike slip on the profile AA′. The location of the profile AA′ in the model is shown in Fig. 2
(a) Coseismic slip. The solid lines show the results of the finite element model. The dashed lines show the calculation results using the Okada model. (b) Coseismic slip of difference cases. (c) Postseismic slip after 200 years. (d) Total slip (Coseismic and postseismic slip after 200 years) on the profile AA′.
图 5 青藏高原东缘构造背景
(震源机制解数据来自于GCMT；https://www.globalcmt.org/)
Figure 5. Tectonic background of the eastern margin of the Tibetan Plateau.
(Focal mechanism solutions from GCMT; https://www.globalcmt.org/)
图 6 青藏高原东缘的三维有限元模型及汶川地震同震破裂模型
a—青藏高原东缘的三维有限元模型；b—汶川地震同震破裂模型
Figure 6. Three-dimensional finite element model of the eastern margin of the Tibetan Plateau (a) and coseismic rupture model of the Wenchuan earthquake (b).
图 7 汶川地震发生后芦山地震震源附近及九寨沟地震震源附近应力随时间的变化
a—汶川地震发生后芦山地震震源附近的应力随时间的变化；(应力投影方向为芦山地震震源机制，走向212°、倾角42°、滑动角100°)；b—汶川地震发生后芦山地震震源附近及九寨沟地震震源附近的应力随时间的变化(应力投影方向为九寨沟地震震源机制，走向150°、倾角78°、滑动角-13°)
Figure 7. Stress evolution near the hypocenter of the Lushan earthquake and that of the Jiuzhangou earthquake after the Wenchuan earthquake.
(a) Stress evolution near the hypocenter of the Lushan earthquake after the Wenchuan earthquake. The stress is projected to the plane determined by the focal mechanism of the Lushan earthquake (strike: 212°, dip: 42°, rake: 100°). (b) Stress evolution near the hypocenter of the Jiuzhaigou earthquake after the Wenchuan earthquake. The stress is projected to the plane determined by the focal mechanism of the Jiuzhaigou earthquake (strike: 150°, dip: 78°, rake: -13°).
表 1 单断层有限元模型的部分材料参数
Table 1. Material parameters of the finite element model with single fault
杨氏模量/Pa 黏度/(Pa·s) 断层左侧上地壳 断层右侧上地壳 中下地壳上地幔 算例1 8.75×1010 8.75×1010 1×1020 算例2 1.75×1011 8.75×1010 1×1020 算例3 4.375×1010 8.75×1010 1×1020 算例4 8.75×1010 8.75×1010 1×1018 算例5 8.75×1010 8.75×1010 1×1019 算例6 8.75×1010 8.75×1010 1×1021 
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表 2 青藏高原东缘有限元模型的参数设置
Table 2. Material parameters set for the finite element model of the eastern margin of the Tibetan Plateau
华南块体 其他块体 深度/km E/Pa υ η/(Pa·s) 深度/km E/Pa υ η/(Pa·s) 上地壳 0~20 8.5×1010 0.25 - 0~20 8.1×1010 0.25 - 中地壳 20~30 1.2×1011 0.26 1×1022 20~35 1.1×1011 0.25 1×1019 下地壳 30~40 1.5×1011 0.25 1×1022 35~50 1.5×1011 0.25 1×1019 上地幔 40~100 1.6×1011 0.28 1×1022 50~100 1.5×1011 0.30 1×1020 其他块体包括青藏高原东北缘、川滇块体和巴颜喀拉块体；上地壳的平均密度设置为2800 kg/m3，中下地壳上地幔的平均密度设置为3200 kg/m3
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