Study on the influence of local mountainous topography to fault dynamic rupture
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摘要: 基于曲线网格有限差分方法研究了垂直走滑断层在不同山体地形情况下的动力学破裂传播，分析并讨论了局部山体地形对断层破裂过程及相应地面地震动的影响，得到了各模型断层面的动力学破裂过程及相应的地表峰值速度特征。研究结果表明，山体地形尺度（山体高度及底部延展距离等）对断层动力学破裂过程影响较大，进而影响到相应的地面地震动分布。当山体地形处于自由地表上亚剪切向超剪切转换的位置附近时，山体地形会阻碍断层面上自由地表超剪切的产生。一般而言，对于具有一定埋深的断层，当山体地形底部延展距离一定时，山体高度越高，其对自由地表超剪切的阻碍程度越大；当山体高度一定时，地形底部延展距离越大，越会阻碍自由地表超剪切的产生，这种破裂过程的变化会导致相应地面地震动呈现不同特征的分布。此外，还探讨了断层破裂过程及相应地震动对成核区外初始剪切应力变化的响应，结果显示，当初始剪切应力较高时，高应力降引起的超剪切破裂会对断层破裂及相应的地震动分布起主导作用。Abstract: In this study, the curved grid finite-difference method was implemented to investigate the effect of local irregular topography on the dynamic rupture process of a vertical strike-slip fault and the resultant strong ground motions. The rupture propagation and ground motions were simulated with different irregular topography in a three-dimensional homogeneous half-space. Our results show that the scale of ridge topography including its height and bottom extension size has great impact on the dynamic rupture process, and then will affect the distribution of ground motions. The mountainous topography will obstruct the generation of super-shear induced by free surface when it is located near the subshear-to-supershear transition position on free surface. Generally, for the faults with a certain buried depth, with the same size of topography bottom extension, the higher the mountain height is, the stronger prevention it has on the generation of super-shear. In addition, when the mountain height is fixed, the larger extension of mountain bottom size has more obstacles to the generation of the super-shear induced by free surface. The variation of fault rupture process will make different distribution of ground motions. Furthermore, the response of dynamic rupture process and the corresponding ground motion to the change of initial shear stress outside the nucleation area was discussed. Our result shows that with the high initial shear stress, the super-shear induced by high stress drop also plays an important role in dynamic rupture and distribution of the resultant ground motion.
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图 1 三维断层及地形模型 （a）与断层面所在垂直剖面 （b）示意图
蓝色矩形表示埋深为200 m的垂直走滑断层，黄色方形表示成核区，灰色区域表示包含吸收边界的高强度区
Figure 1. Three dimensional fault and topography model （a） and vertical profile along fault plane （b）
The blue rectangle depicts the 3-D vertical strike-slip fault，the yellow square indicates the nucleation area and the grey are aindicates a high strength area including absorbing boundary
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图 2 成核区外初始剪切应力为5 MPa时各模型断层面上的破裂起始时间等值线分布
图（a）为水平自由地表模型；图（b）−（f）为山体地形高度分别为400，600，800，1 000和1 100 m时的模型
Figure 2. Initial time contours of ruptures on fault plane for different models with initial shear stress 5 MPa outside the nucleation area
Fig. （a） is for flat free surface model；Figs. （b）−（f） are for Gaussian hill models with height 400，600，800，1 000 and 1 100 m，respectively
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图 3 成核区外初始剪切应力为5 MPa时各模型断层面上峰值滑动速率分布
图（a）为水平自由地表模型；图（b）−（f）为山体地形高度分别为400，600，800，1 000和1 100 m时的模型
Figure 3. Distribution of peak slip rate on fault plane for different models with initial shear stress 5 MPa outside of the nucleation area
Fig. （a） flat free surface model；Figs. （b）−（f） are for Gaussian hill models with height 400，600，800 ，1 000 and 1 100 m，respectively
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图 4 成核区外初始剪切应力为5 MPa时各模型地表峰值速度的平行断层面水平分量分布
图（a）为水平自由地表模型；图（b）−（f）为山体地形高度分别为400，600，800，1 000和1 100 m时的模型
Figure 4. Fault-parallel component of peak ground velocity distribution for different models with initial shear stress 5 MPa outsidethe nucleation area
Fig. （a） is for flat free surface model；Figs. （b）−（f） are for Gaussian hill models with height 400，600，800，1 000 and 1 100 m，respectively
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图 5 成核区外初始剪切应力为5 MPa时各模型地表峰值速度的垂直断层面水平分量分布
图（a）为水平自由地表模型；图（b）−（f）为山体地形高度分别为400，600，800，1 000和1 100 m时的模型
Figure 5. Fault-normal component of peak ground velocity distribution for different models with initial shear stress 5 MPa outside the nucleation area
Fig. （a）is for flat free surface model；Figs. （b）−（f） are for Gaussian hill models with height 400，600，800，1 000 and 1 100 m，respectively
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图 6 山体地形高度为800 m时不同山体地形底部延展距离a0下各模型断层面上的破裂起始时间分布
Figure 6. Initial time contours of rupture on fault plane for the models with different a0 when Gaussian hillheight is 800 m
（a） a0＝1 000 m；（b） a0＝1 500 m；（c） a0＝2 000 m
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图 7 山体地形高度为1 000 m时不同山体地形底部延展距离a0下各模型断层面上的破裂起始时间分布
Figure 7. Initial time contours of rupture on fault plane for the models with different a0 when Gaussian hillheight is 1 000 m
（a） a0＝1 000 m；（b） a0＝1 500 m；（c） a0＝2 000 m
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图 8 山体地形高度为800 m时不同山体地形底部延展距离a0下各模型的地表峰值速度的平行断层面水平分量分布
Figure 8. Fault-parallel component of peak ground velocity distribution for the models with different a0 when Gaussian hillheight is 800 m
（a） a0＝1 000 m；（b） a0＝1 500 m；（c） a0＝2 000 m
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图 9 山体地形高度为800 m时不同山体地形底部延展距离a0下各模型的地表峰值速度的垂直断层面水平分量分布
Figure 9. Fault-normal component of peak ground velocity distribution for the models with different a0 when Gaussian hillheight is 800 m
（a） a0＝1 000 m；（b） a0＝1 500 m；（c） a0＝2 000 m
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图 10 成核区外初始剪切应力为5.6 MPa时各模型断层面上破裂起始时间分布
图（a）为水平自由地表模型；图（b）−（f）为山体地形高度分别为400，600，800，1 000和1 100 m时的模型
Figure 10. Initial time contours rupture on fault plane for different models with initial shear stress 5.6 MPa outside the nucleation area
Fig. （a） is for flat free surface model；Figs. （b）−（f） are for Gaussian hill models with height 400，600，800，1 000and 1 100 m，respectively
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图 11 成核区外初始剪切应力为5.6 MPa时各模型地表峰值速度的平行断层面水平分量分布
图（a）为水平自由地表模型；图（b）−（f）为山体地形高度分别为400 ，600，800，1 000和1 100 m时的模型
Figure 11. Fault-parallel component of peak ground velocity distribution for different models with initial shear stress 5.6 MPa outside of the nucleation area
Fig. （a） is for flat free surface model；Figs. （b）−（f） are for Gaussian hill models with height 400，600，800，1 000 and 1 100 m，respectively
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图 12 成核区外初始剪切应力为5.6 MPa时各模型地表峰值速度的垂直断层面的水平分量分布
图（a）为水平自由地表模型；图（b）−（f）为山体地形高度分别为400，600，800，1 000和1 100 m时的模型
Figure 12. Distribution of fault-normal component of peak ground velocity for different models with initial shear stress 5.6 MPa outside the nucleation area
Fig. （a） is for flat free surface model；Figs. （b）−（f） are for Gaussian hill models with height 400，600，800，1 000 and 1 100 m，respectively
表 1 断层面的模型参数
Table 1 Model parameters on fault plane
区域 初始剪切应力σ0/MPa 剪切破裂强度σu/MPa 残余应力σr/MPa 临界滑动弱化距离Dc/m 断层成核区内 10.1 10.0 0 0 断层成核区外 5.0 10.0 0 0.2 断层外 5.0 200.0 0 20.0 
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