Three‐dimensional spontaneous rupture propagation and implications for the earthquake source mechanism
Three‐dimensional spontaneous rupture propagation and implications for the earthquake source mechanism
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三维自发破裂传播及其对震源机制的影响
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发表时间：
1981
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通讯作者：
Shamita Das
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作者：
Shamita Das
摘要
我们把无限介质中断层面上的自生裂缝看作是一种现实的震源模型。用DAS中描述的边界积分方程法计算了裂纹面上的位移和应力。对于在屈服强度不变的无限平面上对称地扩展到所有四个象限的断层，我们发现纯反平面破裂方向的终端破裂速度VIIICR由VIIICR<；β给出。在纯面内破裂扩展方向上，根据屈服强度的不同，最终破裂速度VIICR由VIICR<；α或VIICR<；0.5α给出。我们还发现，纯反平面方向的裂纹扩展不影响纯平面内方向的裂纹扩展，反之亦然。
对于无限长的有限宽的剪切裂纹，在从较近的裂纹边缘绕射的剪切波到达后，一点的滑移增长较慢。在进一步裂隙边缘的剪切到达后，滑移实际上停止了。这意味着对于这样的断层，滑动是由断层宽度控制的。对于无限大介质中的矩形断层，我们最终的动态解与EShelby的静态椭圆裂纹解比与Chinnery的静态矩形“位错模型”解更接近。我们发现在这种半宽的矩形断层上的平均滑动ū和平均动应力降τe之间的关系为τe=Cμ(ū/W)，其中c˜0.7。对于比宽度大得多的断层，内点的滑动再次受到断层宽度的控制，因此滑动可以在断裂过程完成之前断层开始的区域停止。这意味着两个长度不同但宽度相同的矩形断层在相同的平均应力降下具有相同的滑动，这一事实显然与沿同一断层发生的大地震的断层滑动随地震规模增加的观测结果相矛盾。如果更大的地震的应力降也更大，这个矛盾就会得到解决。
Summary
We consider spontaneous cracks spreading out areally over a fault plane in an infinite medium as a realistic earthquake source model. The boundary integral equation technique described in Das is used to determine the displacements and stresses everywhere on the crack plane. For faults spreading out symmetrically in all four quadrants over infinite planes of constant yield strength, we find that the terminal rupture velocity VIIICR in the direction of purely anti-plane rupture is given by VIIICR < β. In the purely in-plane direction of rupture propagation, we find the terminal rupture velocity VIICR to be given by VIICR < α or VIICR < 0.5α, depending on the yield strength. We also find that crack propagation in the purely antiplane direction does not influence crack propagation in the purely in-plane direction and vice versa.
For infinitely long shear cracks of finite width, the slip at a point is found to grow more slowly after the arrival of a shear wave diffracted from the nearer crack edge. The slip virtually ceases after the shear arrival from the further crack edge. This implies that for such faults the slip is controlled by the fault width. For a rectangular fault in an infinite medium, our final dynamic solution is in closer agreement with the static elliptical crack solution of Eshelby than with the static rectangular ‘dislocation model’ solution of Chinnery. We find the relationship between the average slip ū and average dynamic stress drop τe on such a rectangular fault of half-width W to be τe= Cμ(ū/W), where c ˜ 0.7. The slip at an interior point is again controlled by the fault width for faults that are much longer than wide so that the slip may stop in the region where the fault initiated before the completion of the rupture process. This implies that two rectangular faults of varying lengths but of the same width have the same slip for the same average stress drop, a fact clearly contradicted by observations that fault slip increases with earthquake size for great earthquakes occurring along the same fault. This contradiction is resolved if stress drops are also bigger for bigger earthquakes.