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

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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.