Abstract—The issues concerning the relationship between two self-similarity parameters—the Gutenberg–Richter b- and Omori p-values—in the aftershock sequences are explored. In the laboratory experiments, under fracture initiation in the rock by sharp jumps in the axial stress, a correlation between the p- and b-values is revealed in the fracture relaxation regimes similar to aftershocks. The correlation observed in the experiments on water-saturated sandstone samples with the preliminarily formed faults is negative and clearly pronounced. The correlation in the case of dry samples of migmatite and concrete proved to be positive but its statistical significance is lower than for the wet samples. The analysis of the literature data on detecting the connection between parameters p and b in the natural aftershock sequences shows that the reported results are heterogeneous. Some authors conclude that these parameters are connected and that both positive and negative correlation is noted between them. Other authors present evidence suggesting the absence of any correlation. Our study of the natural aftershocks based on the data of regional earthquake catalogs has shown that the statistical estimates of the Gutenberg–Richter and Omori parameters are fairly sensitive to the quality and homogeneity of the input data. The key factors affecting the estimation quality of these parameters are established, and the procedure for selecting the aftershock catalogs for subject analysis is developed. The results of statistical estimating the Gutenberg–Richter and Omori parameters in the aftershock processes in the regions with different types of the tectonic regimes—subduction zones and regions of shear transform faults—have shown that that the correlation of these parameters in the subduction zones can be positive and negative either. In the zones of the transform faults, the connection between these parameters is not detected. Our study generalizes K. Scholtz’s idea that the Omori law can be explained by the superimposition of the relaxation processes having different relaxation times. According to the generalized model, the different sign of the correlation between the self-similarity parameters in the aftershock processes correspond to the different relaxation mechanisms with different types of the dependence of the relaxation time on the “size” of the relaxator. It is currently unclear which particular mechanisms are implemented in the aftershock processes. The relationship between the Omori and Gutenberg–Richter parameters revealed by our laboratory experiments and field studies (positive correlation, negative correlation, or lack of correlation) may indicate the implementation of different relaxation mechanisms in some or other particular conditions.

中文翻译：

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余震序列中大森参数与古腾堡-里希特参数的关系

摘要——探讨了余震序列中两个自相似参数（Gutenberg-Richter b 值和 Omori p 值）之间的关系问题。在实验室实验中，在轴向应力急剧跳跃导致岩石破裂的情况下，在类似于余震的破裂松弛状态中揭示了 p 值和 b 值之间的相关性。在含水饱和砂岩样品与初步形成的断层的实验中观察到的相关性是负的并且很明显。混合岩和混凝土的干样品的相关性被证明是正相关的，但其统计显着性低于湿样品。对检测自然余震序列中参数 p 和 b 之间联系的文献数据的分析表明，报告的结果是异质的。一些作者得出结论，这些参数是相互关联的，并且在它们之间注意到了正相关和负相关。其他作者提供的证据表明不存在任何相关性。我们基于区域地震目录数据对自然余震的研究表明，Gutenberg-Richter 和 Omori 参数的统计估计对输入数据的质量和均匀性相当敏感。建立了影响这些参数估计质量的关键因素，并制定了选择余震目录进行主题分析的程序。对具有不同类型构造制度的区域——俯冲带和剪切转换断层区——余震过程中的古腾堡-里希特和大森参数的统计估计结果表明，这些参数在俯冲带中的相关性可以要么是积极的，要么是消极的。在变换故障区域中，未检测到这些参数之间的联系。我们的研究概括了 K. Scholtz 的观点，即大森定律可以通过具有不同弛豫时间的弛豫过程的叠加来解释。根据广义模型，余震过程中自相似参数之间相关性的不同符号对应于不同的弛豫机制，弛豫时间对弛豫“尺寸”的依赖性不同。目前尚不清楚在余震过程中采用了哪些特定机制。我们的实验室实验和实地研究揭示的 Omori 和 Gutenberg-Richter 参数之间的关系（正相关、负相关或缺乏相关）可能表明在某些或其他特定条件下不同松弛机制的实施。