A mechanical model for the statistics of earthquakes, magnitude, moment, and fault distribution

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Abstract
A mechanical model is presented to explain the Ishimoto Iida empirical law for earthquake statistics where n(M) dM is the number of earthquakes in the interval of magnitude M, M + dM. The model fits properly the statistics of earthquakes of all of the regions of the world for which exist reliable catalogs of earthquakes (Ranalli, 1974) although the mechanism of the model considered is specifically that of stick slip. The same model explains the empirical law for the statistics of the seismic moment Mo and explains also the scatter of the values in the empirical relation between Mo and M. Finally if one knows the rate at which the elastic energy is stored in a region of the Earth's crust, and if a catalog of earthquakes of the region is available, this model gives an estimate of the number and size of faults of the region, and also of the maximum magnitude and seismic moment possible in the region.