Collaborative Research: Earthquakes on Nonplanar Faults: Rupture Dynamics and High Frequency Ground Motion

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。了解高频率范围（1Hz）的地震地面运动对工程界来说是非常重要的，因为大多数人造结构的共振频率都在这个范围内。在这个频率范围内，地面运动相对不连贯，所有频率都存在，这表明一个激发所有波长波的源过程。本项目探讨地震破裂在粗糙断层上的传播，工作假设是由粗糙度引起的不规则传播可能是产生观测到的高频辐射水平的原因。特别是，自然断层被很好地描述为自相似的分形表面：粗糙度存在于所有尺度上，并且与特定波长相关的粗糙度的振幅与该波长成正比。非平面断层上的滑动扰动了局部应力场，引起传播破裂的局部加减速和地震波的发射。除了特别关注高频地震动外，该项目还研究了非平面断层地震动力学的一般特征。这些研究问题将通过非平面断层动态破裂的直接数值模拟来解决。在实验室实验中观察到，断层受速率和状态摩擦定律控制，在同震滑动率下具有极端的速度减弱行为。非断层响应建模为德鲁克-普拉格弹塑性材料（类似于莫尔-科伦材料）在速率无关或粘塑性公式中的响应。利用坐标映射技术处理不规则几何形状，并利用高阶有限差分数值逼近控制方程。特定的数值方法具有几种机制（上绕和有限差分模板的自适应选择），可以防止假振荡的发展，否则会在感兴趣的高频处污染溶液。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).Understanding seismic ground motion in the high frequency range (1Hz) is of substantial interest to the engineering community since the resonance frequency of most man-made structures lies within it. In this frequency range, ground motion is relatively incoherent and all frequencies are present, suggesting a source process that excites waves of all wavelengths. This project explores earthquake rupture propagation on rough faults with the working hypothesis that the irregular propagation induced by roughness might be responsible for producing observed levels of high frequency radiation. In particular, natural faults are well described as self-similar fractal surfaces:roughness is present at all scales and the amplitude of the roughness associated with a particular wavelength is proportional to that wavelength. Slip on nonplanar faults perturbs the local stress field, causing local accelerations and decelerations of propagating ruptures and the emission of seismic waves. In addition to the specific focus on high frequency ground motion, the project investigates general characteristics of earthquake dynamics on nonplanar faults.These research questions will be addressed using direct numerical simulations of dynamic ruptures on nonplanar faults. The faults are governed by rate-and-state friction laws featuring extreme velocity-weakening behavior at coseismic slip rates, as observed in laboratory experiments. The off-fault response is modeled as that of a Drucker-Prager elastic-plastic material (similar to a Mohr-Coloumb material) in either a rate-independent or viscoplastic formulation.The irregular geometries are handled using a coordinate mapping technique and high order finite differences are used to approximate the governing equations numerically. The particular numerical method features several mechanisms (upwinding and the adaptive selection of finite difference stencils) that prevent the development of spurious oscillations that would otherwise contaminate the solution at the high frequencies of interest.