Finite element method simulation of the earthquake preparation, occurrence, and recurrence cycles
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摘要:
强震孕育发生及其复发过程的定量研究对于预测预报地震有着重要的科学意义；合理连续地计算地震孕育、同震破裂过程及其复发循环特征将有助于我们更好地认识强震发生的时空分布规律.为此，本文基于Newmark隐式时间积分法，根据模拟孕震-同震循环过程的特殊要求，发展了一种新的有限单元计算方法.新方法具有以下特点：（1）在不改变时间积分方法的情况下，实现对时间步长进行自动平滑地缩放，进而可以连续的模拟准静态、动态不同力学状态下的孕震-同震循环过程；（2）模型的初始应力场非人为指定，计算时通过施加重力及缓慢的构造加载获得；（3）地震破裂的成核区域及成核方式等亦非人为给定，模拟中破裂成核是自然形成的，这样更加符合实际地震地质情况.通过大量的模型计算，其结果表明，新的计算方法可以连续稳定的模拟断层孕震-同震及其循环过程，计算结果不仅可以给出强震的复发间隔，同时还可以给出地震时断层破裂行为的详细过程.此外，本文还考察了摩擦系数对地震准周期性的影响，发现断层上的静、动摩擦系数差值直接影响着断层的强震复发周期，两者差值越小，复发周期越短；差值越大，复发间隔越长.
Abstract:The study of the quasi-periodic recurrence behavior of strong earthquakes is important for predicting and mitigating earthquake disasters. Reasonably and continuously simulating the interseismic-coseismic cycle process is the key to researching the spontaneous earthquake sequences. Based on the finite element dynamic implicit algorithm, this work develops a new methodology for simulating the interseismic-coseismic cycle processes. Our approach has the following advantages:(1) Continuously simulate the interseismic-coseismic cycle process without switching algorithms, and the time step size is automatically and smoothly scaled between quasi-static and dynamic states. (2) The stress field of the calculation model can be obtained under slow tectonic loading and gravity without artificially assigned. (3) The nucleation process of each earthquake event is formed slowly and naturally, and does not need to be given artificially. The simulation results show that the new methodology can continuously and steadily simulate the fault interseismic-coseismic cycle behavior, recurrence interval of strong earthquake, and the detailed coseismic rupture process. In addition, we study the influence of friction coefficient on the recurrence interval of strong earthquake. It turns out that the difference between the static and dynamic friction coefficients on the fault directly affect the recurrence interval of strong earthquake. The smaller the difference, the shorter the recurrence period is.
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图 2
断层上盘上的典型点(中间点)的位移随时间的变化曲线
Figure 2.
Displacements change with time at the typical point on the hanging wall of the fault
图 3
断层典型点位置上下盘之间的位错随时间的变化曲线
Figure 3.
Sliding distance at the typical point on the fault vary with time
图 4
孕震期间和同震期间的自动增量步时间的变化
Figure 4.
The change of the automatic time increments during interseismic and coseismic periods
图 5
每次地震事件断层上各点滑移随时间的变化
Figure 5.
Snapshots of the slip profiles at every node along the fault vary with time in each event
图 6
地震事件五中不同时刻断层周边介质的振动速度云图
Figure 6.
Contour distributions of particle velocities at different times around the fault in event 5
图 7
重力作用下，垂直于地表方向应力云图
Figure 7.
The vertical stresses of the models under applying gravity
图 8
不同摩擦系数下，断层典型点位置上下盘之间的位错随时间的变化
Figure 8.
Slip between hanging wall and footwall at the typical point on the fault vary with time in different models in which friction coefficients are different
表 1
显式算法和隐式算法的优缺点
Table 1.
Advantages and disadvantages of explicit and implicit algorithms
算法 优点 缺点 中心差分法(显式) 不需要平衡迭代，不存在收敛性问题每步计算成本低 有条件稳定，时间步长Δt必须小于Δtcr=L/(E/ρ)1/2(式中L为模型中尺度最小单元的最小边长) Newmark法(隐式) 无条件稳定，即时间步长Δt不影响解的稳定性 处理非线性问题时，需要平衡迭代，存在收敛性问题.每步计算成本高 
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表 2
模型参数
Table 2.
Model parameters
参数 值 P波速度 6000 m·s-1 S波速度 3464 m·s-1 泊松比 0.25 密度 2670 kg·m-3 构造载荷 15 mm·a-1 静摩擦系数 0.49 动摩擦系数 0.47 特征滑移距离 0.1 m
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