Applicability of gutenberg–richter law extrapolation to strong earthquakes: A case study of seismic source zones in Uzbekistan

Abstract

This study investigates the applicability of extrapolating the Gutenberg-Richter relationship, established from small-to-moderate earthquakes, to the magnitude range of strong earthquakes. Regional analysis of seismic source zones in Uzbekistan showed that, despite a stable linear relationship over the main part of the frequency-magnitude distribution, the high-magnitude tail may exhibit different behavior. Three contrasting seismic source zones were selected for statistical testing of these patterns. Catalog completeness and the stability of the b-value were assessed, and alternative declustering algorithms, bootstrap analysis, and exact Poisson tests with Holm correction were applied. For Zone 9, a statistically robust excess of strong earthquakes relative to the linear extrapolation was identified. For Zone 18, the interpretation of the initially observed deviation changed substantially after separating background and swarm seismicity. For Zone 20, no statistically significant deviations from the extrapolated Gutenberg-Richter relationship were detected. The results demonstrate that reliable estimation of the parameters of the main linear part of the frequency-magnitude distribution does not, by itself, justify extrapolation of the fitted relationship to the high-magnitude range. Therefore, when estimating the recurrence of rare strong earthquakes, the applicability of such extrapolation requires an independent statistical assessment.