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D.L. Turcotte, B.D. Malamud, and G. Morein (Department of Geological Sciences,
Snee Hall, Cornell University, Ithaca, NY 14853 USA)
These simple classes of models have been proposed that exhibit "self-organized criticality". These are "sand-pile" models, slider-block models, and forest-fire models. Although these models are extremely simple, they appear to be representative of the behavior of common natural hazards. In the case of the "sand-pile" models the application is to landslides. Both the models and several landslide data sets satisfy power-law (fractal) statistics to a good approximation. Similarly the behavior of slider-block models can be associated with earthquakes and the behavior of forest-fire models with forest and wild fires. In the models the smaller events "prepare" the systems so that they "self-organize" and exhibit fractal statistics. The frequency of occurrence of smaller events can be extrapolated to estimate the frequency of occurrence of the larger events. Despite all the problems of weather and climate, the great varieties of combustible materials, and attempts to extinguish wild fires, the frequency-magnitude statistics of wild fires are fractal to a good approximation under a wide variety of circumstances. It has long been recognized that earthquakes obey fractal frequency-magnitude statistics. The fractal dimension is simply twice the b-value. The a-value is a measure of the intensity of the regional seismicity. It is shown for southern California that the a-value is the same for each year over a fifteen year period when aftershock sequences are removed. World-wide maps of a-value have been prepared and can be used to estimate the global seismic hazard.
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