A MODEL OF SEISMIC FOCUS AND RELATED STATISTICAL DISTRIBUTIONS OF EARTHQUAKES

摘要

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 magnitude distribution is applied to Vrancea earthquakes, in order to assess relevant statistical parameters for this seismic region. The accompanying seismic activity of foreshocks and aftershocks is also discussed in connection with this approach, the associated Omori distributions are derived, and the time dependence of the magnitudes and the rate of released energy are given. It is shown that Omori's distribution arises from a self-replication process of a generating distribution, the two distributions being inter-related by Euler's transform. The self-consistency of the process generating the accompanying seismic events requires an exponential law for the generating distribution. A generalization of Omori's law is also included.