The Existence, Source, and Mechanical Significance of Hierarchical Fractal Structures in Fault Zones

9902901 SammisA最近对加利福尼亚州帕克菲尔德的小地震的研究发现，应力降随着震级的增加而减小（Nadeau和约翰逊，1998）。 可以解释这一观察结果的一个假设是，断层面被粗糙体的分形阵列锁定，使得每单位面积的粗糙体数量随着面积的增加而减少，从而减少了较大事件的表观应力降。这一假设得到了震源对相关函数的支持，发现这与粗糙的2-D康托尘埃一致（Sammis等人，1998年）。这一建议将进一步探讨断裂带中分级分形结构的几何学、来源和力学意义。 该项目将进一步分析帕克菲尔德地震数据，以确定作为震级函数的空间和时间分布是否也与康托尘埃假说一致。 关于分形层次的来源，我们提出了三个假说：1）断层被具有层次分形结构的粗糙体所锁定; 2）断层被具有层次分形结构的断层泥带中的“颗粒桥”所锁定; 3）地震发生在剪切局部化的嵌套层次上。 计划进行一系列的实验室调查，以检验每一种假设。 一个主要的目标是试图确定的条件下，离散的层次分形结构出现在剪切变形。

9902901SammisA recent study of small earthquakes at Parkfield, CA, has found that the stress drop decreases with increasing magnitude (Nadeau and Johnson, 1998). One hypothesis that can explain this observation is that the fault plane is locked by a fractal array of asperities, such that the number of asperities per unit area decreases with increasing area thereby reducing the apparent stress drop for larger events. This hypothesis is supported by the pair correlation function of the hypocenters, which were found to be consistent with a 2-D Cantor dust of asperities (Sammis et al., 1998). This proposal will further investigate the geometry, source, and mechanical significance of hierarchical fractal structures in fault zones. The project will further analyze Parkfield seismic data to determine if the spatial and temporal distributions as a function of magnitude are also consistent with a Cantor dust hypothesis. As to the source of the fractal hierarchy, we have formulated three hypotheses 1) the fault is locked by asperities which have a hierarchical fractal structure, 2) the fault is locked by "grain bridges" in the gouge zone which have a hierarchical fractal structure, and 3) earthquakes occur on a nested hierarchy of shear localizations. A series of laboratory investigations are planned to test each hypothesis. A primary objective is to try to identify the conditions under which discrete hierarchical fractal structure emerges in shear deformation.