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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.
In the exploration of earthquake prediction in recent years, many people attempt to find the precursors of large earthquakes by using the rule of magnitude of frequency and discuss the spatiotemporal change of b value .A new problem ensues, and the scope of data acquisition needs to be smaller and smaller, The time period is shorter and shorter, so the number of earthquakes used in estimating b value is greatly reduced, so that the error increases when b value is estimated.This paper starts with the rule of frequency and frequency of Gutenberg and Richter, Which includes the maximum likelihood estimation, the moment estimation, the linear simple least squares estimation and the nonlinear simple least square estimation, etc. The accuracy of various estimation of b value is given to compare the advantages and disadvantages of various methods. A b-value error table was calculated using the Monte-Carlo method for reference when calculating the b-value.