基于广义帕累托分布的地震震级分布尾部特征分析

极值理论在地震危险性分析中有着重要应用， 发震震级超过某一阈值的超出量分布可以近似为广义帕累托分布. 基于广义帕累托分布给出了若干地震活动性参数的估计公式， 包括强震震级分布、 地震复发周期和重现水平、 期望重现震级、 地震危险性概率和潜在震级上限等； 以云南地区震级资料为基础数据， 讨论了阈值选取、 模型拟合诊断和参数估计； 在此基础上计算了该地区的地震活动性参数. 结果表明， 广义帕累托分布较好地刻画了强震震级分布， 通过超阈值(POT)模型计算的复发周期与实际复发间隔统计基本一致， 高分位数估计在一定阈值范围内表现稳定， 为工程抗震中潜在震级上限的确定提供了一种途径. 

Characterization of tail distribution of earthquake magnitudes via generalized Pareto distribution

Extreme value theory in seismic risk analysis has important application, and the excess of earthquake magnitude distribution over a threshold can be approximated by generalized Pareto distribution. Based on the generalized Pareto distribution, we developed several estimation formulas of seismic activity parameters, including strong earthquake magnitude distribution, earthquake recurrence period and return level, expected recurrence magnitude, probability of seismic risk and maximum earthquake magnitude; then, based on historical seismic data in Yunnan region, we discussed how to choose the threshold value, model fitting diagnosis and parameter estimation. Finally we calculated seismicity parameters in the region. The results show that generalized Pareto distribution characterized strong earthquake magnitude distribution quite satisfactorily, the recurrence periods by POT (peaks over threshold method) model agree with the actual recurrence interval statistics, and the high quantile is stable within a specific threshold range. So the generalized Pareto distribution is a possible approach to determining the potential upper limit earthquake magnitude in engineering seismology.