The problem considered in this study is that of unrealistic ground motion estimates, which arise in the Cornell-McGuire method when the seismic hazard curve is calculated for extremely low annual probabilities of exceedance. This problem stems from using the normal distribution in the modelling of the variability of the logarithm of ground motion parameters. In this study, the database of the strong-motion seismograph networks of Japan was used to examine the distribution of the logarithm of peak ground acceleration (PGA). The normal distribution and the generalised extreme value distribution (GEVD) models were considered in the analysis, with the preferred model being selected based on statistical criteria. The results of the analysis demonstrated the superiority of the GEVD in the vast majority of considered examples. The estimates of the shape parameter of the GEVD were negative in every considered example, indicating the presence of a finite upper bound of PGA. Therefore, the GEVD provides a model that is more realistic for the scatter of the logarithm of PGA, and the application of this model leads to a bounded seismic hazard curve.

Probabilistic seismic hazard analysis (PSHA) is a regularly applied practice that precedes the construction of important engineering structures. The Cornell-McGuire procedure is the most frequently applied method of PSHA. This paper examines the fundamental assumption of the Cornell-McGuire procedure for PSHA, namely, the log-normal distribution of the residuals of the ground motion parameters. Although the assumption of log-normality is standard, it has not been rigorously tested. Moreover, the application of the unbounded log-normal distribution for the calculation of the hazard curves results in non-zero probabilities of the exceedance of physically unrealistic amplitudes of ground motion parameters. In this study, the distribution of the residuals of the logarithm of peak ground acceleration is investigated, using the database of the Strong-motion Seismograph Networks of Japan and the ground motion prediction equation of Zhao and co-authors. The distribution of residuals is modelled by a number of probability distributions, and the one parametric law that approximates the distribution most precisely is chosen by the statistical criteria. The results of the analysis show that the most accurate approximation is achieved with the generalized extreme value distribution for a central part of a distribution and the generalized Pareto distribution for its upper tail. The effect of replacing a log-normal distribution in the main equation of the Cornell-McGuire method is demonstrated by the calculation of hazard curves for a simple hypothetical example. These hazard curves differ significantly from one another, especially at low annual exceedance probabilities.

Abstract—The magnitude of completeness $${{M}_{c}}$$ of the earthquakes above which 100% of events are thought to be reliably detected is a vital parameter characterizing the completeness of seismic data. A known fact is that to obtain correct estimates of the parameters of seismicity, it is compulsory to take into account $${{M}_{c}}$$ variations in space and time. In this work, we compare six modern methods for estimating $${{M}_{c}}$$. To compare the methods, we use event samples from real instrumental earthquake catalogs and synthetic catalogs generated based on the three models of magnitude distribution. We analyze the dependences of the two first moments of the distributions of $${{M}_{c}}$$ estimates on the shape of magnitude distributions and the sample size. We use three models corresponding to sample distributions that occur in the analysis of instrumental earthquake catalogs. Based on the obtained results, we formulate recommendations on selecting the suitable method for estimating the magnitude of completeness $${{M}_{c}}$$.

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