Quantitative Analysis of Seismicity Before Large Taiwanese Earthquakes Using the G-R Law

Seismicity has been identified as an example of a natural, nonlinear system for which the distribution of frequency and event size follow a power law called the “Gutenberg–Richter (G-R) law.” The parameters of the G-R law, namely b- and a-values, have been widely used in many studies about seismic hazards, earthquake forecasting models, and other related topics. However, the plausibility of the power law model and applicability of parameters were mainly verified by statistical error σ of the b-value, the effectiveness of which is still doubtful. In this research, we used a newly defined p value developed by Clausetet al. (Power-Law Distributions in Empirical Data, SIAM Rev. 51, 661–703, 2009) instead of the statistical error σ of the b-value and verified its effectiveness as a plausibility index of the power-law model. Furthermore, we also verified the effectiveness of K–S statistics as a goodness-of-fit test in estimating the crucial parameter (Formula presented.) of the power-law model.