Iwata Daichi, Nanjo Kazuyoshi Z
OPT, Inc., Tokyu Bancho Bldg., 6 Yonbancho, Chiyoda-ku, Tokyo, 102-0081, Japan.
Global Center for Asian and Regional Research, University of Shizuoka, 3-6-1, Takajo, Aoi-ku, Shizuoka, 420-0839, Japan.
Sci Rep. 2024 Mar 5;14(1):4630. doi: 10.1038/s41598-024-54576-x.
Earthquakes follow an exponential distribution referred to as the Gutenberg-Richter law, which is characterized by the b value that represents a ratio of the number of large earthquakes to that of small earthquakes. Spatial and temporal variation in the b value is important for assessing the probability of a larger earthquake. Conventionally, the b value is obtained by a maximum-likelihood estimation based on past earthquakes with a certain sample size. To properly assess the occurrence of earthquakes and understand their dynamics, determining this parameter with a statistically optimal method is important. Here, we discuss a method that uses a state space model and a particle filter, as a framework for time-series data, to estimate temporal variation in the b value. We then compared our output with that of a conventional method using data of earthquakes that occurred in Tohoku and Kumamoto regions in Japan. Our results indicate that the proposed method has the advantage of estimating temporal variation of the b value and forecasting magnitude. Moreover, our research suggests no heightened probability of a large earthquake in the Tohoku region, in contrast to previous studies. Simultaneously, there is the potential of a large earthquake in the Kumamoto region, emphasizing the need for enhanced monitoring.
地震遵循一种被称为古登堡-里希特定律的指数分布，其特征是b值，该值代表大地震数量与小地震数量的比率。b值的时空变化对于评估更大地震的概率很重要。传统上，b值是通过基于具有一定样本量的过去地震的最大似然估计获得的。为了正确评估地震的发生并了解其动态，用统计上最优的方法确定这个参数很重要。在这里，我们讨论一种使用状态空间模型和粒子滤波器的方法，作为时间序列数据的框架，来估计b值的时间变化。然后，我们将我们的输出与使用日本东北和熊本地区发生的地震数据的传统方法的输出进行了比较。我们的结果表明，所提出的方法在估计b值的时间变化和预测震级方面具有优势。此外，与之前的研究相比，我们的研究表明东北地区发生大地震的概率没有增加。同时，熊本地区存在发生大地震的可能性，这强调了加强监测的必要性。
