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

该奖项根据 2009 年美国复苏和再投资法案（公法 111-5）提供资金。了解高频范围 (1Hz) 内的地震地面运动引起了工程界的极大兴趣，因为大多数人造结构的共振频率都位于该范围内。在这个频率范围内，地面运动相对不相干，并且所有频率都存在，表明存在激发所有波长波的源过程。该项目探讨了粗糙断层上的地震破裂传播，其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幅度与该波长成正比。非平面断层上的滑动扰乱了局部应力场，导致传播破裂的局部加速和减速以及地震波的发射。除了特别关注高频地震动之外，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。正如实验室实验中所观察到的，断层受速率和状态摩擦定律的控制，该定律在同震滑移速率下具有极端的速度减弱行为。断层响应被建模为 Drucker-Prager 弹塑性材料（类似于 Mohr-Columb 材料）的速率无关或粘塑性公式。使用坐标映射技术处理不规则几何形状，并使用高阶有限差分对控制方程进行数值近似。特定的数值方法具有多种机制（迎风和有限差分模板的自适应选择），这些机制可以防止寄生振荡的发展，否则会在感兴趣的高频下污染解决方案。

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.