A stochastic fault model: 1. Static case

The number-size distribution of earthquakes requires that irregularities exist on a fault at all length scales. The assumption of self-similar irregularity is used to formulate a stochastic description of the faulting process. A random irregularity is termed self similar if it remains statistically similar upon a change of length scale. Self-similar geometric irregularity of a fault surface is represented in this model by stress and friction functions that fluctuate self similarly on a plane. If the set of rupture areas of all earthquakes on the brittle portion of a fault plane is assumed to be self similar, then the number of ruptures with area greater than A is proportional to 1/A. If stress drop is independent of earthquake size, then the number of earthquakes with moment greater than M/sub 0/ is proportional to M/sub 0//sup -2/3/. The size of an earthquake is determined by spatial fluctuation of the initial stress and sliding friction functions. The spectrum of the stress function is related to both the average stress drop as a function of earthquake size and the number-moment distribution. A model of the slip and stress change functions of an earthquake is constructed in the Fourier transform domain. While the stressmore » function becomes smoother in an earthquake at the length scale of the rupture, it becomes rougher at shorter length scales to prepare the fault for future smaller earthquakes. Seismicity is a cascade of stored elastic energy from longer to shorter wavelengths.« less

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