The geographic distribution of earthquake effects quantified in terms of macroseismic intensities, the so-called macroseismic field, provides basic information for several applications including source characterization of pre-instrumental earthquakes and risk analysis. Macroseismic fields of past earthquakes as inferred from historical documentation may present spatial gaps, due to the incompleteness of the available information. We present a probabilistic approach aimed at integrating incomplete intensity distributions by considering the Bayesian combination of estimates provided by intensity prediction equations (IPEs) and data documented at nearby localities, accounting for the relevant uncertainties and the discrete and ordinal nature of intensity values. The performance of the proposed methodology is tested at 28 Italian localities with long and rich seismic histories and for two well-known strong earthquakes (i.e., 1980 southern Italy and 2009 central Italy events). A possible application of the approach is also illustrated relative to a 16th-century earthquake in the northern Apennines.

中文翻译：

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用概率方法整合宏观地震强度分布：在意大利的应用

根据宏观地震强度量化的地震效应的地理分布，即所谓的宏观地震场，为多种应用提供了基本信息，包括仪器前地震的震源表征和风险分析。由于可用信息的不完整，从历史文献中推断出的过去地震的宏观地震场可能存在空间差距。我们提出了一种概率方法，旨在通过考虑强度预测方程 (IPE) 提供的估计值和附近地区记录的数据的贝叶斯组合来整合不完整的强度分布，考虑相关的不确定性以及强度值的离散和有序性质。所提出的方法的性能在 28 个具有悠久而丰富的地震历史的意大利地点和两次著名的强地震（即 1980 年意大利南部事件和 2009 年意大利中部事件）进行了测试。该方法的可能应用也以 16 世纪亚平宁山脉北部的地震为例进行了说明。