This work proposes a new approach, based on Bayesian updating and extreme value statistics to determine the maximum magnitudes for truncated magnitude-frequency distributions such as the Gutenberg Richter model in the framework of Probabilistic Seismic Hazard Analyses. Only the maximum observed magnitude and the associated completeness period are required so that the approach is easy to implement and there is no need to determine and use the completeness periods for smaller events. The choice of maximum magnitudes can have a major impact on hazard curves when long return periods as required for safety analysis of nuclear power plants are considered. Here, not only a singular value but a probability distribution accounting for prior information, data and uncertainty is provided. Moreover, uncertainties related to magnitude frequency distributions, including the uncertainty related to the maximum observed magnitude are discussed and accounted for. The accuracy of the approach is validated based on simulated catalogues with various parameter values. Then the approach is applied to French data for a specific region characterized by high-seismic activity in order to determine the maximum magnitude distribution and to compare the results to other approaches.

中文翻译：

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基于极值分布的最大震级 mmax 的贝叶斯估计用于概率地震危害分析

这项工作提出了一种新方法，基于贝叶斯更新和极值统计来确定截断的震级频率分布的最大震级，例如概率地震危害分析框架中的 Gutenberg Richter 模型。只需要观测到的最大震级和相关的完整性周期，因此该方法易于实施，并且不需要为较小的事件确定和使用完整性周期。当考虑到核电厂安全分析所需的长重现期时，最大震级的选择会对危险曲线产生重大影响。在这里，不仅提供了奇异值，而且提供了考虑先验信息、数据和不确定性的概率分布。此外，与幅度频率分布相关的不确定性，包括与最大观测震级相关的不确定性进行了讨论和说明。基于具有各种参数值的模拟目录验证了该方法的准确性。然后将该方法应用于以高地震活动为特征的特定区域的法国数据，以确定最大震级分布并将结果与​​其他方法进行比较。