by A. K. Nekrasova, V. G. Kossobokov, I. A. Parvez and X. Tao
The distribution of the number of seismic events by magnitudes—the Gutenberg–Richter frequency–magnitude relation—is of paramount importance for seismic hazard assessment of a territory. The generalization of the Gutenberg–Richter relation—the Unified Scaling Law for Earthquakes (USLE) proposed in 1988 makes it possible to take into account the pattern of epicentral distribution of seismic events when changing the spatial scale of the analysis. This is extremely important for adequate downscaling of the frequency of occurrence into a smaller area within the territory under study (e.g., in the megalopolis). In 2002, Per Buck suggested a dual formulation of USLE where, instead of the number of earthquakes over a certain period of time, the reciprocal of their frequency of occurrence—the time between seismic events—is used. The same year, the Institute of Earthquake Prediction Theory and Mathematical Geophysics of the Russian Academy of Sciences developed a modified algorithm for robust estimation of USLE parameters referred to as Scaling Coefficients Estimation (SCE) for producing seismic hazard maps of territories prone to seismic effects. This brief review is focused on the use of the USLE approach to the assessment of seismic hazard and associated risk.