## ON SIMILARITY IN THE SPATIAL DISTRIBUTION OF SEISMICITYV. G. Kosobokov and S. A. MazhkenovAbstract 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. Back to |