Generalizing the Gutenberg-Richter scaling law

The evident heterogeneity of seismic distribution in space and time requires special approaches. The patterns of seismic dynamics are apparently scalable to smaller magnitudes according to the generalized Gutenberg-Richter recurrence law that takes into account the fractal nature of faults and fault zones. We revisit the results of global analysis of the distribution of earthquake size, which takes into account the spatial similarity of the set of epicentres at a given location, to conclude that (i) a seismic region, in a wide range of magnitudes and sizes, can be characterized by the following recurrence law: Log N(M,L) = A - B (M - 5) + C Log L, where N(M,L) is the expected annual number of main shocks of magnitude M within an area of liner size L; (ii) C ranges from under 1 to 1.6 and correlate with the geometry of tectonic features; (iii) an estimate of the local earthquake recurrence depends on the size of the territory that is used for averaging. We draw a comparison between the Generalized Gutenberg-Richter Law (Kossobokov and Mazhkenov, 1988), GGRL, and the Unified Scaling Law for Earthquakes (Bak et al, 2002), USLE, and apply them in a simplistic approximation of the Global Seismic Risk Assessment. The confirmed multiplicative scaling changes the view of traditional mechanics on the recurrence of earthquakes in an epicenter zone and has serious implications for estimation of seismic hazard, as well as for earthquake prediction.