地震震级－频度关系b值参数的稳健估计
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摘要
文中依据古登堡－里克特（Ｇ－Ｒ）震级－频度公式，结合实例说明了参数ｂ值的稳健估计方法，并将其与最小二乘法及最大似然法比较。结果表明，一般情况下，稳健估算结果与实际数据分布较吻合，并且可以在不剔除低震级段和大震级段的偏离分布值的情况下，取得与选取合理震级上下限后最小二乘法一致的结果。此外，稳健估计结果的余差分析同样也得到地震震级－频度关系不是简单的对数线性关系的结果，而原始Ｇ－Ｒ公式需加二次以上的高次项才能较好地描述该特性。
In this paper,we use the relationship Log N =a - b M between magnitude and frequency. The method of robust estimation of the b-value is expounded by an examle. In general, the estimation resule can correspond with the distribution of the real data. The robust estimation result is compared with by the least squares method and by the maximum likelihood method. When we use the robust estimation method, not reject the section of small or great magnitude,and the estmation result is corresponded with by the least squares method after selecting an upper and a lower limit of magnitude reasonably.In addition,the result of residual analysis shows that a relation of magnitude-frequency can not be a simple logarithm straight relationship, it is necessary for adding higher order items to the Gutenberg-Richter magnitude-frequency relation.
In this paper,we use the relationship Log N =a - b M between magnitude and frequency. The method of robust estimation of the b-value is expounded by an examle. In general, the estimation resule can correspond with the distribution of the real data. The robust estimation result is compared with by the least squares method and by the maximum likelihood method. When we use the robust estimation method, not reject the section of small or great magnitude,and the estmation result is corresponded with by the least squares method after selecting an upper and a lower limit of magnitude reasonably.In addition,the result of residual analysis shows that a relation of magnitude-frequency can not be a simple logarithm straight relationship, it is necessary for adding higher order items to the Gutenberg-Richter magnitude-frequency relation.
引文
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