Numerical models of rupture dynamics provide great insights into the physics of fault failure. However, resolving stress interactions among multiple faults remains challenging numerically. Here, we derive the elastostatic Green’s functions for stress and displacement caused by arbitrary slip distributions along multiple parallel faults. The equations are derived in the Fourier domain, providing an efficient means to calculate stress interactions with the fast Fourier transform. We demonstrate the relevance of the method for a wide range of applications, by simulating the rupture dynamics of single and multiple parallel faults controlled by a rate‐ and state‐dependent frictional contact, using the spectral boundary integral method and the radiation‐damping approximation. Within the antiplane strain approximation, we show seismic cycle simulations with a power‐law distribution of rupture sizes and, in a different parameter regime, sequences of seismogenic slow‐slip events. Using the in‐plane strain approximation, we simulate the rupture dynamics of a restraining stepover. Finally, we describe cycles of large earthquakes along several parallel strike‐slip faults in three dimensions. The approach is useful to explore the dynamics of interacting or isolated faults with many degrees of freedom.

中文翻译：

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多平行断层准动态断裂的谱边界积分法

破裂动力学的数值模型提供了对断层破坏物理学的深刻见解。然而，解决多个断层之间的应力相互作用在数值上仍然具有挑战性。在这里，我们推导出由沿多个平行断层的任意滑动分布引起的应力和位移的弹性格林函数。这些方程是在傅立叶域中推导出来的，提供了一种使用快速傅立叶变换计算应力相互作用的有效方法。我们通过使用谱边界积分法和辐射阻尼近似来模拟由速率和状态相关摩擦接触控制的单个和多个平行断层的破裂动力学，证明了该方法在广泛应用中的相关性。在反平面应变近似内，我们展示了具有破裂尺寸幂律分布的地震周期模拟，以及在不同参数范围内的地震慢滑事件序列。使用面内应变近似，我们模拟了约束跨步的破裂动力学。最后，我们从三个维度描述了沿着几个平行的走滑断层的大地震的循环。该方法可用于探索具有许多自由度的相互作用或孤立断层的动力学。