Distribution research of recurrence interval for moderate-strong earthquake in the mainland of China
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摘要: 地震复发间隔的概率分布是计算地震发生概率的基础。利用我国历史地震目录资料，统计分析中国大陆中强地震归一化区域复发间隔，分析发现中国大陆中强地震活动兼具周期性和丛集性特点。采用对数正态分布与指数分布构建混合概率分布模型，通过最小二乘法拟合混合概率分布函数的最优参数。拟合结果的误差分析表明，混合概率分布模型更加符合中国大陆中强地震的活动特点。Abstract: Probability distribution of earthquake recurrence interval is the foundation of calculating the occurrence probability of earthquake. Based on the historical earthquake catalog data, the normalized local recurrence intervals of moderate-strong earthquake in the mainland of China are statistically analyzed. It is found that earthquake activity has both periodic and clustering characteristics. We construct a hybrid distribution model using lognormal distribution and exponential distribution, and the optimal parameters of the hybrid distribution model are estimated through least square method. The error analysis demonstrates that the hybrid probability distribution model is more consistent with the characteristic of moderate-strong earthquake activity in the mainland of China.
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图 1 中国大陆1960年以来MS4.7以上地震目录的完整性分析[18]
（a）震级—序号法给出的地震密度分布；（b）多统计方法定量分析给出的最小完整性震级Mc的时间变化
Figure 1. Completeness analysis of earthquake catalog (MS≥4.7) in mainland China since 1960[18]
（a） Seismic rate for different magnitudes in the index domain；（b） Completeness thresholds Mc estimated by three statistical methods
图 2 删除余震前后的累积频次曲线对比
Figure 2. Cumulative frequency curve before and after declustering
图 3 1960年以来中国大陆中强地震 （MS5.0—6.5）归一化区域复发间隔频率直方图
Figure 3. Normalized frequency histogram of moderate-strong (MS5.0—6.5) earthquake recurrence intervals in mainland China since 1960
图 5 1960年以来中国大陆中强地震（MS5.0—6.5）归一化区域复发间隔频率直方图及CDF曲线
Figure 5. Normalized frequency histogram and cumulative density function curve of moderate-strong (MS5.0—6.5) earthquake recurrence intervals in mainland China since 1960 and the curve of CDF
图 6 混合分布累积概率密度函数拟合结果。黑线为基于数据绘制的累积概率密度函数（CDF）曲线，绿线为拟合的CDF曲线，红线为基于估算得到的参数绘制的概率密度函数（PDF）曲线，相应的对数正态分布和指数分布函数曲线分别用黑色线段虚线和点虚线表示，蓝色柱状图为归一化区域地震复发间隔数据的统计频率直方图
Figure 6. Cumulative density function fitting result of hybrid distribution model. The solid black line is the estimated cumulative density function (CDF) curve based on recurrence data, the green solid line is the best-fitting CDF curve, the red line is the best-fitting probability density function (PDF) curve, the black dashed and dotted lines show the lognormal and exponential distribution functions, respectively. The blue histogram is the normalized frequency histogram of earthquake recurrence intervals
图 7 对数正态分布累积概率密度函数拟合结果。黑线为基于数据绘制的累积概率密度函数（CDF）曲线，绿线为拟合的CDF曲线，红线为基于估算得到的参数绘制的概率密度函数（PDF）曲线，蓝色柱状图为归一化区域地震复发间隔数据的统计频率直方图
Figure 7. Cumulative density function fitting result of lognormal distribution. The solid black line is the estimated cumulative density function (CDF) curve based on recurrence data, the green solid line is the best-fitting CDF curve, the red line is the best-fitting probability density function (PDF) curve, the blue histogram is the normalized frequency histogram of earthquake recurrence intervals
图 8 指数分布累积概率密度函数拟合结果。黑线为基于数据绘制的累积概率密度函数（CDF）曲线，绿线为拟合的CDF曲线，红线为基于估算得到的参数绘制的概率密度函数（PDF）曲线，蓝色柱状图为归一化区域地震复发间隔数据的统计频率直方图
Figure 8. Cumulative density function fitting result of exponential distribution. The solid black line is the estimated cumulative density function (CDF) curve based on recurrence data, the green solid line is the best-fitting CDF curve, the red line is the best-fitting probability density function (PDF) curve, the blue histogram is the normalized frequency histogram of earthquake recurrence intervals
表 1 参数估算与拟合误差结果
Table 1. Results of estimated parameters and fitting error
模型 参数估计 拟合误差 混合分布 a 0.569 0.00016 μ 0.291 σ 0.657 λ 4.291 对数正态分布 μ −0.515 0.00157 σ 1.382 指数分布 λ 1.012 0.00132 
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