Stable Modification of Frequency–Magnitude Relation and Prospects for Its Application in Seismic Zoning

Abstract

A new composite model is suggested for the frequency–magnitude relation of the earthquakes. The new model statistically reasonably describes the distribution in the range of weak and moderate events (the Gutenberg–Richter law) and in the range of strongest events (generalized Pareto law—one of the limiting laws in the extreme value theory). By the example of Japan and Kuriles, based on the GCMT catalog, it is shown that the model fairly adequately describes the seismicity in the circles containing at least 80 main shocks in the range of the reliably detected events m ≥ 5.3. The restriction on the number of the events imposes a statistical limitation on the resolution of the proposed model. In the case of the studied regions, this limitation allows reliable estimation of seismicity parameters for the areas with a radius of 300 km on a 2° × 2° grid. The use of this model in our previously designed statistical method for seismic risk assessment (Pisarenko and Rodkin, 2007; 2010; 2013) provides a theoretical basis for developing this technique towards more robust results and a better spatial resolution approaching the scale of the general seismic zoning maps.