A model of seismic focus and related statistical distributions of earthquakes

A growth model for accumulating seismic energy in a localized seismic focus is described, which introduces a fractional parameter r on geometrical grounds. The model is employed for deriving a power-type law for the statistical distribution in energy, where the parameter r contributes to the exponent, as well as corresponding time and magnitude distributions for earthquakes. The accompanying seismic activity of foreshocks and aftershocks is discussed in connection with this approach, as based on Omori distributions, and the rate of released energy is derived.