Spatio-temporal clustering of earthquakes based on distribution of magnitudes

It is expected that the pronounced decrease in b -value of the Gutenberg–Richter law for some region during some time interval can be a promising precursor in forecasting earthquakes with large magnitudes, and thus we address the problem of automatically identifying such spatio-temporal change points as several clusters consisting of earthquakes whose b -values are substantially smaller than the total one. For this purpose, we propose a new method consisting of two phases: tree construction and tree separation. In the former phase, we employ one of two different declustering algorithms called single-link and correlation-metric developed in the field of seismology, while in the later phase, we employ a variant of the change-point detection algorithm, developed in the field of data mining. In the later phase, we also employ one of two different types of objective functions, i.e., the average magnitude which is inversely proportional to the b -value, and the likelihood function based on the Gutenberg–Richter law. Here note that since the magnitudes of most earthquakes are relatively small, we formulate our problem so as to produce one relatively large cluster and the other small clusters having substantially larger average magnitudes or smaller b -values. In addition, in order to characterize some properties of our proposed methods, we present a method of analyzing magnitude correlation over an earthquake network. In our empirical evaluation using earthquake catalog data covering the whole of Japan, we show that our proposed method employing the single-link strategy can produce more desirable results for our purpose in terms of the improvement of weighted sums of variances, average logarithmic likelihoods, visualization results, and magnitude correlation analyses.