Abstract

The problem of evaluation of the maximum possible regional earthquake magnitude (M_max) is reviewed and analyzed. Two aspects of this topic are specified: statistical, and historical and paleoseismic. The frequentist and the fiducial approaches used in the problem are analyzed and compared. General features of the Bayesian approach are discussed within the framework of the M_max problem. A useful connection between quantiles of a single event and maximum event in a future time interval T is derived. Various estimators of M_max used in seismological practice are considered and classified. Different methods of estimation are compared: the statistical moment method, the Bayesian method, the estimators based on the extreme value theory (EVT), the estimators using order statistics. A comparison of several well-known estimators of M_max in the framework of the truncated Gutenberg–Richer law is made. As a more adequate and stable alternative to M_max the quantiles Q_q(T) of maximum earthquake considered in future time horizon T are proposed and analyzed. These quantiles permit us to select a time horizon T and quantile level q for a reliable estimation of maximum possible magnitudes. The instability of M_max-estimates compared to Q_q(T)-estimates is demonstrated. The main steps of the Q_q(T)-quantile estimation procedure are highlighted. The historical and paleoseismic data are used, and an additional evidence of low robustness of M_max-parameter is found. The evidence of possibility of earthquake magnitudes well exceeding the M_max-value obtained for the truncated Gutenberg–Richter law is found also. The present situation in the domain of the M_max-evaluation is discussed.

中文翻译：

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解决最大可能地震震级 (Mmax) 问题的方法

摘要

回顾和分析了最大可能区域地震震级（M _{max ）的评估问题。}本主题的两个方面进行了说明：统计以及历史和古地震。分析和比较了问题中使用的常客和基准方法。在M _max问题的框架内讨论了贝叶斯方法的一般特征。导出了单个事件的分位数与未来时间间隔T中的最大事件之间的有用联系。M _max的各种估计器地震学实践中使用的。比较了不同的估计方法：统计矩法、贝叶斯方法、基于极值理论 (EVT) 的估计量、使用阶数统计的估计量。在截断的 Gutenberg-Richer 定律的框架内比较了几个著名的M _{max估计量。}作为M _max的更充分和稳定的替代方案，提出并分析了未来时间范围T中考虑的最大地震的分位数Q _q (T) 。这些分位数允许我们选择时间范围T和分位数水平q用于可靠估计最大可能幅度。与Q _q (T) -估计相比， M _max -估计的不稳定性得到证明。Q _q (T) -分位数估计过程的主要步骤被突出显示。使用了历史和古地震数据，并发现了M _max参数的低稳健性的额外证据。还发现了地震震级可能远远超过截断 Gutenberg-Richter 定律获得的M _{max值的证据。}讨论了M _max评估领域的现状。