b值的稳健估计及其在地震预报中的应用
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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，并讨论了稳健估计方法与最小二乘估计所得结果的差异。认为由稳健估计得到的 ｂ 值更加符合震级频度关系中的大小比例，可作为可靠的背景值使用。作为应用实例对新疆地区ｂ 值进行空间及时间扫描，并定义最小二乘估计ｂ 值与稳健估计ｂ 值的偏差，以此为中强震的前兆判定指标，对喀什－ 巴楚地区 ８０ 年代以来 ６ 级以上地震前的异常进行讨论，认为该指标间接地反映了地震前的降维过程，且具有一定的实用性。
b value in the relation between magnitude and frequency is calculated by using robust regression of M estimation and choosing function ψ as normal density type function. The difference between the results obtained by the methods of robust estimation and least square estimation is also discussed in the paper. It is considered that the b value obtained by robust estimation is more suitable for the dimension proportion in the relation between magnitude and frequency, and it can be used as a reliable background value. As an application example, the b value of Xinjiang region has been scanned spatially and temporally, and the difference between b value of least square estimation and robust estimation is defined and used as a discriminant index for precursors of moderate and strong earthquakes. Through discussion on anomalies appeared before earthquakes with M ≥6 which have occurred in Karshi Barchu area since 1980, we think that the index indirectly reflects the dimension declining process and has certain practical meaning.
b value in the relation between magnitude and frequency is calculated by using robust regression of M estimation and choosing function ψ as normal density type function. The difference between the results obtained by the methods of robust estimation and least square estimation is also discussed in the paper. It is considered that the b value obtained by robust estimation is more suitable for the dimension proportion in the relation between magnitude and frequency, and it can be used as a reliable background value. As an application example, the b value of Xinjiang region has been scanned spatially and temporally, and the difference between b value of least square estimation and robust estimation is defined and used as a discriminant index for precursors of moderate and strong earthquakes. Through discussion on anomalies appeared before earthquakes with M ≥6 which have occurred in Karshi Barchu area since 1980, we think that the index indirectly reflects the dimension declining process and has certain practical meaning.
引文
1 傅征祥.中国大陆地震活动性力学研究.北京:地震出版社,1997
2 吴今培.实用时序分析.长沙:湖南科学技术出版社,1989
3 李国英.稳健统计的发展概况.数理统计与应用概率,1987,2(3):369～384
4 Huber P J. Robust estim ation of location param eter. M ath statist, 1964,35(1):73～101
5 戴梁,王文均.洪水频率稳健估计研究状况.武汉水运工程学院学报,1989,3(13):85～93
6 李全林,于渌,郝柏林,等.地震频度震级关系的时空扫描.北京:地震出版社,1979
7 严尊国,陈俊华,郑文衡,等.地震震级频度 G R 关系的偏离度.地震,1995,15(4):328～332
8 宇津德治.地震のマダニチユ—ド分布式のパラメタ- の推定:最大地震のマダニチユ- ドを含む场合.地震,1978,31(4)
9 梅世蓉,冯德益,张国民,等.中国地震预报概率.北京:地震出版社,1993
2 吴今培.实用时序分析.长沙:湖南科学技术出版社,1989
3 李国英.稳健统计的发展概况.数理统计与应用概率,1987,2(3):369～384
4 Huber P J. Robust estim ation of location param eter. M ath statist, 1964,35(1):73～101
5 戴梁,王文均.洪水频率稳健估计研究状况.武汉水运工程学院学报,1989,3(13):85～93
6 李全林,于渌,郝柏林,等.地震频度震级关系的时空扫描.北京:地震出版社,1979
7 严尊国,陈俊华,郑文衡,等.地震震级频度 G R 关系的偏离度.地震,1995,15(4):328～332
8 宇津德治.地震のマダニチユ—ド分布式のパラメタ- の推定:最大地震のマダニチユ- ドを含む场合.地震,1978,31(4)
9 梅世蓉,冯德益,张国民,等.中国地震预报概率.北京:地震出版社,1993
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