Abstract. Crucial to the development of earthquake forecasting schemes is the manifestation of spatiotemporal correlations between earthquakes as highlighted, for example, by the notion of aftershocks. Here, we present an analysis of the statistical relation between subsequent magnitudes of a recently proposed self-similar aftershock rates model of seismicity, whose main distinguishing feature is that of interdependence between trigger and triggered events in terms of a time-varying frequency–magnitude distribution. By means of a particular statistical measure, we study the level of magnitude correlations under specific types of time conditioning, explain their provenance within the model framework and show that the type of null model chosen in the analysis plays a pivotal role in the type and strength of observed correlations. Specifically, we show that while the variations in the magnitude distribution can give rise to large trivial correlations between subsequent magnitudes, the non-trivial magnitude correlations are rather minimal. Simulations mimicking southern California (SC) show that these non-trivial correlations cannot be observed at the 3σ level using real-world catalogs for the magnitude of completeness as a reference. We conclude that only the time variations in the frequency–magnitude distribution might lead to significant improvements in earthquake forecasting.

中文翻译：

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地震活动性自相似余震率模型中的震级相关性

摘要。地震预报方案发展的关键是地震之间时空相关性的表现，例如，余震的概念。在这里，我们对最近提出的地震活动自相似余震率模型的后续震级之间的统计关系进行了分析，该模型的主要区别在于触发事件和触发事件之间在时变频率-震级分布方面的相互依赖性. 通过特定的统计测量，我们研究了特定类型时间条件下的幅度相关性水平，在模型框架内解释了它们的出处，并表明分析中选择的空模型类型在类型和强度中起着关键作用观察到的相关性。具体来说，我们表明，虽然幅度分布的变化会导致后续幅度之间存在较大的无关紧要的相关性，但非无关紧要的幅度相关性相当小。模拟南加州 (SC) 的模拟表明，使用真实世界目录的完整性程度作为参考，无法在 3σ 级别观察到这些非平凡的相关性。我们得出结论，只有频率-震级分布的时间变化可能会导致地震预测的显着改进。模拟南加州 (SC) 的模拟表明，使用真实世界目录的完整性程度作为参考，无法在 3σ 级别观察到这些非平凡的相关性。我们得出结论，只有频率-震级分布的时间变化可能会导致地震预测的显着改进。模拟南加州 (SC) 的模拟表明，使用真实世界目录的完整性程度作为参考，无法在 3σ 级别观察到这些非平凡的相关性。我们得出结论，只有频率-震级分布的时间变化可能会导致地震预测的显着改进。