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Since the year 1973, more than 54,000 M ≥ 3.0 earthquakes have occurred around Taiwan, and their magnitude-frequency relationship was found following with the Gutenberg-Richter recurrence law with b value equal to 0.923 from the least-square calculation. However, using this b value with the McGuire-Arabasz algorithm results in some disagreement between observations and expectations in magnitude probability. This study introduces a simple approach to optimize the b value for better modeling of the magnitude probability, and its effectiveness is demonstrated in this paper. The result shows that the optimal b value can better model the observed magnitude distribution, compared with two customary methods. For example, given magnitude threshold = 5.0 and maximum magnitude = 8.0, the optimal b value of 0.835 is better than 0.923 from the least-square calculation and 0.913 from maximum likelihood estimation for simulating the earthquake's magnitude probability distribution around Taiwan. [ABSTRACT FROM AUTHOR]

Statistical studies on earthquake recurrence time probabilities have frequently been applied to seismic hazard analyses. In Taiwan, an instrumental catalog provides a good opportunity to examine statistical attributes of earthquakes around the study region, with the objective to evaluate the seismic risk and earthquake potential for hazard mitigation. With the completeness of recordings, seismic rates for small-to-moderate magnitudes can be obtained. An elimination of aftershocks was performed using a double-link cluster analysis method. The time intervals between a series of events (the inter-occurrence periods) are stationary with an identical temporal distribution. Based on the goodness-of-fit testing between a few models and observation, we suggested the use of the Gamma distribution in modeling this variable, earthquake inter-occurrence periods, for the study region. Accordingly, unified relationship was constructed, and statistical limitations of sparse sampling for devastating earthquakes (such as M ≥ 6.0 or 7.0) could be resolved. The empirical result evaluated by introducing the conditional probability indicates that the recurrence probability of a M ≥ 7.0 earthquake is 78.8 % within 10 years in Taiwan region. [ABSTRACT FROM AUTHOR]