Abstract A new composite model is suggested for the frequency–magnitude relation of the earthquakes. The new model statistically reasonably describes the distribution in the range of weak and moderate events (the Gutenberg–Richter law) and in the range of strongest events (generalized Pareto law—one of the limiting laws in the extreme value theory). By the example of Japan and Kuriles, based on the GCMT catalog, it is shown that the model fairly adequately describes the seismicity in the circles containing at least 80 main shocks in the range of the reliably detected events m ≥ 5.3. The restriction on the number of the events imposes a statistical limitation on the resolution of the proposed model. In the case of the studied regions, this limitation allows reliable estimation of seismicity parameters for the areas with a radius of 300 km on a 2° × 2° grid. The use of this model in our previously designed statistical method for seismic risk assessment (Pisarenko and Rodkin, 2007; 2010; 2013) provides a theoretical basis for developing this technique towards more robust results and a better spatial resolution approaching the scale of the general seismic zoning maps.

中文翻译：

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频幅关系的稳定修正及其在地震区划中的应用前景

摘要 提出了一种新的地震频率-震级关系复合模型。新模型在统计上合理地描述了弱事件和中等事件范围（Gutenberg-Richter 定律）和最强事件范围（广义帕累托定律——极值理论中的限制定律之一）的分布。以日本和千岛群岛为例，基于 GCMT 目录，表明该模型相当充分地描述了在可靠检测到的事件 m ≥ 5.3 范围内包含至少 80 个主震的圆圈中的地震活动。对事件数量的限制对所提出模型的分辨率施加了统计限制。在研究区域的情况下，这一限制允许在 2° × 2° 网格上对半径为 300 公里的区域进行地震活动参数的可靠估计。在我们之前设计的地震风险评估统计方法中使用该模型（Pisarenko 和 Rodkin，2007 年；2010 年；2013 年）为开发该技术以取得更稳健的结果和更好的空间分辨率提供了理论基础，接近一般地震分区地图。