地震b值的估计方法及其标准误差--应用蒙特卡罗方法估计b值精度
ON THE METHOD OF ESTIMATING B-VALUE AND ITS STANDARD ERRORThe Monte Carlo Method of Estimating the Accuracy of b-value
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摘要: 近年在地震预报问题的探索中, 不少人企图使用震级频数法则去寻找大震前兆, 讨论 b 值的时空变化.随之出现一个新问题, 为适应预报需要资料所取范围越来越小, 时段越来越短, 这样估计 b 值时使用的地震个数大大减少, 至使估计 b 值时误差增加.本文从古登堡、李希特的震级频数法则出发, 讨论了 b 值的各种估计方法.其中有极大似然估计、矩估计, 线性简单最小二乘估计和非线性简单最小二乘估计等.给出 b 值各种估计的精度, 从而比较各种方法的优劣.文中应用蒙特卡罗(Monte-Carlo)方法计算了一个 b 值误差表, 供计算 b 值时参考.Abstract: In attempting to stuty the problem of earthquake prediction, the law of magnitude and frequency of earthquakes has recently been employed to search for precursors of large earthquakes and to examine the variation with time and space of the b-value. A question arises that in order to comply with the requirements of earthquake prediction, the time length of earthquake data chosen, should be short. As a consequence, the number of earthquakes used will be greatly reduced, giving rise to increased error in the estimation of the b-value.Based on the law, of magnitude and frequency of earthquakes of Gutenberg and Richter, various methods for estimating b-value have been discussed in this paper, namely the maximum likehood estimate, the moment estimate, the simple linear and non-linear least square estimates ect., of which the respective accuracies are given and compared for their adequacy. Included in this paper for reference is an error chart for b-value estimation, computed by the Monte Carlo Method.
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[1] 石本已四雄, 飯田汲事.微動計による地震溉测(一)地震動の大さ, 空简的分布, Bulletin of the Earthquake Research Institute Tokyo Imperial University, 17, 443——478, 1939.
[2] B. Gutenberg, & C. F. Richter, Seismicity of the Earth and Associated Phenomena, Princeton University Press, 1949.
[3] 李全林, 于禄, 陈锦标, 郝柏林, b值时空扫描, 地球物理学报, 21, 2, 1978.
[4] 马鸿庆, 华北地区几次大震前的b值异常变化, 地球物理学报, 21, 2, 1978.
[5] 张建中, 蒙特卡罗方法(I) (II), 数学的实践与认识, 1, 2, 1974.
[6] 中国科学院计算中心概率统计组编著, 概率统计计算, 科学出版社, 1979.[1] 石本已四雄, 飯田汲事.微動計による地震溉测(一)地震動の大さ, 空简的分布, Bulletin of the Earthquake Research Institute Tokyo Imperial University, 17, 443——478, 1939.
[2] B. Gutenberg, & C. F. Richter, Seismicity of the Earth and Associated Phenomena, Princeton University Press, 1949.
[3] 李全林, 于禄, 陈锦标, 郝柏林, b值时空扫描, 地球物理学报, 21, 2, 1978.
[4] 马鸿庆, 华北地区几次大震前的b值异常变化, 地球物理学报, 21, 2, 1978.
[5] 张建中, 蒙特卡罗方法(I) (II), 数学的实践与认识, 1, 2, 1974.
[6] 中国科学院计算中心概率统计组编著, 概率统计计算, 科学出版社, 1979.
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