稳健估计b值及中强震异常特征研究
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摘要
利用Ｍ估计的稳健回归方法，选取ψ函数为正态密度型函数，计算震级－频度 关系中的ｂ值。对基于随机泊松分布的模拟地震样本及天然地震样本，用稳健估计方法 与最小二乘方法计算ｂ值后进行比较得出，对于天然地震样本，稳健估计得到的ｂ值更 加符合震级－频度关系。作为应用实例，将最小二乘估计法ｂ值与稳健估计ｂ值的偏离 度作为中强震的前兆判定指标，对新疆地区ｂ值进行时间扫描。在对北天山及南天山东 段Ｍs≥５级、南天山西段Ｍs≥６级地震前异常特征进行讨论后，认为该指标作为中短期 地震预报指标具有一定的实用性。
In this paper, using robust regression and choosing a function as normal density type function, we calculate b value in the relation between magnitude and frequency. After compared the earthquake samples from simulated Poisson distribution and natural earthquake samples, we think that b value calculated by robust estimation is accordant with reality. As an application example, difference (Db) between b value by least square estimation and by robust estimation is used as a discriminating index for precursor of moderate and strong earthquake. After discussing anomalies before earthquake with MS > 5 occurred in the North Tianshan and the east of South Tianshan zone, earthquake MS > 6 occurred in the west of South Tianshan zone, we also think that Db is certain practicable predicting index for moderate and strong earthquakes.
In this paper, using robust regression and choosing a function as normal density type function, we calculate b value in the relation between magnitude and frequency. After compared the earthquake samples from simulated Poisson distribution and natural earthquake samples, we think that b value calculated by robust estimation is accordant with reality. As an application example, difference (Db) between b value by least square estimation and by robust estimation is used as a discriminating index for precursor of moderate and strong earthquake. After discussing anomalies before earthquake with MS > 5 occurred in the North Tianshan and the east of South Tianshan zone, earthquake MS > 6 occurred in the west of South Tianshan zone, we also think that Db is certain practicable predicting index for moderate and strong earthquakes.
引文
[1] 李国英.稳健统计的发展[J].数理统计与应用概率,1987,2(3):369-384.
[2]Huber PJ.Robust estimation of location parameter[J].Math statist,1964,35(1):73-101.
[3]戴梁,王文均.洪水频率稳健估计研究状况[J].武汉水运工程学院学报,1989,3(13):85-93.
[4] 严尊国,陈俊华,郑文衡,等.地震震级—频度G-R关系的偏离度[J].地震,1995,15(4):328-332.
[5]李全林,于渌,郝柏林,等.地震频度—震级关系的时空扫描阳[M].北京:地震出版社,1979.
[6] 杨马陵,曲延军.b值的稳健估计及其在地震预报中的应用[J].地震,1999,19(3):253-260.
[2]Huber PJ.Robust estimation of location parameter[J].Math statist,1964,35(1):73-101.
[3]戴梁,王文均.洪水频率稳健估计研究状况[J].武汉水运工程学院学报,1989,3(13):85-93.
[4] 严尊国,陈俊华,郑文衡,等.地震震级—频度G-R关系的偏离度[J].地震,1995,15(4):328-332.
[5]李全林,于渌,郝柏林,等.地震频度—震级关系的时空扫描阳[M].北京:地震出版社,1979.
[6] 杨马陵,曲延军.b值的稳健估计及其在地震预报中的应用[J].地震,1999,19(3):253-260.
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