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资助的（公法111-5）。了解高频范围（1Hz）内的地震地面运动对工程界具有重大意义，因为大多数人造结构的共振频率都在该范围内。在该频率范围内，地面运动相对不相干，所有频率都存在，这表明一个激发所有波长波的源过程。本计画探讨地震破裂在粗糙断层上的传播，并假设由粗糙度所引起的不规则传播可能是产生观测到的高频辐射的原因。特别是，自然断层被很好地描述为自相似分形表面：粗糙度是目前在所有尺度和与特定波长的粗糙度的幅度是成比例的波长。非平面断层上的滑动扰动了局部应力场，导致传播破裂的局部加速和减速以及地震波的发射。除了对高频地面运动的具体关注外，本项目还研究了非平面断层上地震动力学的一般特征。这些研究问题将通过非平面断层上动态破裂的直接数值模拟来解决。在实验室实验中观察到，在同震滑动速率下，断层受速率和状态摩擦定律支配，具有极端的速度弱化行为。断层外响应被建模为Drucker-Prager弹塑性材料（类似于Mohr-Coloumb材料）的速率无关或粘塑性方程，不规则几何形状采用坐标映射技术处理，控制方程采用高阶有限差分数值逼近。特定的数值方法具有几种机制（上旋和自适应选择的有限差分stenetrance），防止寄生振荡的发展，否则会污染的解决方案在感兴趣的高频率。

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.