ON SIMILARITY IN THE SPATIAL DISTRIBUTION OF SEISMICITYV. G. Kosobokov and S. A. Mazhkenov
The basic law of seismicity, the Gutenberg-Richter recurrence relation, is suggested in a modified form involving a spatial term: $\log N(M,L) = A - B (M-5) + C \log L$, where $N(M,L)$ is the expected annual number of mainshocks of a certain magnitude $M$ within an area of linear size $L$. Using the original algorithm tested on a number of model catalogs, estimates of similarity coefficients, $A,\;B$, and $C$ were obtained for seismic regions of FSU and other countries worldwide, as well as for global seismic belts of the Earth. The coefficient $C$ reflects spatial similarity of a set of epicenters. Making appropriate assumptions of homogeneity and self-similarity, it can be referred to as the fractal dimension of the set. The actual values of $C$ vary from 1.0 to 1.5 and correlate with the geometry of tectonic features: High values of $C$ for regions of complex dense patterns of faults of different strikes, and low values of $C$ for regions with a predominant linear fault zone. The coefficients provide an insight into scaling properties of actual seismicity and are of specific interest to seismologists working on seismic zonation and risk assessment.