Statistical distributions are investigated for magnetic storms, sudden commencements (SCs), and substorms to identify the possible amplitude of the one in 100-year and 1000-year events from a limited data set of less than 100 years. The lists of magnetic storms and SCs are provided from Kakioka Magnetic Observatory, while the lists of substorms are obtained from SuperMAG. It is found that majorities of events essentially follow the log-normal distribution, as expected from the random output from a complex system. However, it is uncertain that large-amplitude events follow the same log-normal distributions, and rather follow the power-law distributions. Based on the statistical distributions, the probable amplitudes of the 100-year (1000-year) events can be estimated for magnetic storms, SCs, and substorms as approximately 750 nT (1100 nT), 230 nT (450 nT), and 5000 nT (6200 nT), respectively. The possible origin to cause the statistical distributions is also discussed, consulting the other space weather phenomena such as solar flares, coronal mass ejections, and solar energetic particles.

中文翻译：

---

极端地磁活动：统计研究

调查了磁暴、突然开始 (SC) 和亚暴的统计分布，以从不到 100 年的有限数据集中确定 100 年和 1000 年事件的可能振幅。磁暴和 SC 的列表来自 Kakioka Magnetic Observatory，而亚暴的列表来自 SuperMAG。发现大多数事件本质上遵循对数正态分布，正如从复杂系统的随机输出所预期的那样。然而，不确定大振幅事件是否遵循相同的对数正态分布，而是遵循幂律分布。根据统计分布，可以估计磁暴、SCs 和亚暴的 100 年（1000 年）事件的可能振幅约为 750 nT（1100 nT），分别为 230 nT (450 nT) 和 5000 nT (6200 nT)。还讨论了导致统计分布的可能起源，参考了其他空间天气现象，如太阳耀斑、日冕物质抛射和太阳高能粒子。