Distinguishing Tapered and Non-Tapered Gutenberg–Richter Distributions

ABSTRACT The magnitude–frequency distribution (MFD), which quantifies the relative frequency of large versus small earthquakes, is commonly used in seismic hazard assessment studies and is thought to characterize earthquake dynamics. The classic Gutenberg–Richter (GR) model posits that earthquake frequency decays exponentially with magnitude. The tapered Gutenberg–Richter (TGR) model is a variant that assumes a further reduced frequency of larger earthquakes. Distinguishing which of these two distributions better fits observations is important not only for a better understanding of earthquake physics but also for robust forecasting of earthquake magnitudes. Therefore, we evaluate methods used to differentiate these two distributions and their statistical significance given a set of observations. We find the likelihood-ratio test to be the most effective approach. It rarely misclassifies a GR distribution as a TGR distribution, whereas a TGR distribution can be misclassified as GR when the tail of the MFD is insufficiently sampled. We demonstrate that the probability of correctly identifying a TGR model exceeds 90% when the corner magnitude is one unit smaller than the maximum magnitude predicted by the GR distribution. Furthermore, we introduce an objective framework aimed at detecting potential temporal shifts between the two distributions. We apply this framework to global seismicity and two observational cases of induced seismicity. The MFD of global seismicity shows transitions between GR and TGR distributions over time, which might be explained by either inherent temporal variation in behavior or by the random sampling of a bilinear GR model with a larger b value for M > 7.6. Regarding the induced seismicity cases, we demonstrate significant and persistent TGR distributions in seismicity induced by geothermal well stimulations at Otaniemi, Finland. Furthermore, we find that earthquakes in the Coso geothermal field (California) exhibit TGR behavior during a specific period, likely influenced by the type of magnitude scale used.