Estimation of the Frequency–Magnitude Gutenberg–Richter b‐Value without Making Assumptions on Levels of Completeness
Estimation of the Frequency–Magnitude Gutenberg–Richter b‐Value without Making Assumptions on Levels of Completeness
复制标题
在不对完整性水平做出假设的情况下估计频率-幅度古腾堡-里克特 b 值
DOI：
10.1785/0220160177
复制
发表时间：
2017
影响因子：
3.3
通讯作者：
A. Smit
中科院分区：
文献类型：
--
作者：
A. Kijko;A. Smit
摘要经典的Aki-Utsu B-值估计的一个明显的弱点是它严重依赖于量值完备性水平m c，而对它的评估本身并不是一项简单的任务。本文提出了两个新的不依赖于完备性水平的Gutenberg-Richter B-值的估计量。蒙特卡罗模拟表明，当不完整的频率-幅度分布由三参数伽马分布建模时，矩量法（MM）和最大似然（ML）程序提出的估计量特别有效，三参数伽马分布逐渐弯曲并且只有一个最大值;也就是说，根据Mignan（2012）的分类，它属于IV类分布。在某些情况下，MM估计量与ML估计量相当，并且更容易计算。在应用的地震震级样本是完整的情况下，新导出的MM和ML B-值估计采用经典的阿基（1965）和宇津（1965）解的形式。为了说明的目的，新的程序被应用于估计南非地震最活跃（构造）地区Ceres-Tulbagh地区的B-值。
ABSTRACT A pronounced weakness of the classic Aki–Utsu b ‐value estimator is its heavy dependence on the level of magnitude completeness m c , of which the assessment itself is no trivial task. Two new estimators for frequency–magnitude Gutenberg–Richter b ‐value that are not dependent on the level of completeness are proposed in the present work. Monte Carlo simulations show that the proposed estimators by the method of moments (MM) and the maximum‐likelihood (ML) procedures are especially effective when the incomplete frequency–magnitude distribution is modeled by the three‐parameter gamma distribution, which curves gradually and has only one maximum; that is, it belongs to the distributions of category IV, according to the classification by Mignan (2012). In some instances, the MM estimator is comparable with its ML counterpart and is significantly easier to calculate. In instances where the applied sample of earthquake magnitudes is complete, the newly derived MM and ML b ‐value estimators take the form of the classic Aki (1965) and Utsu (1965) solutions. For the purpose of illustration, the new procedures were applied for estimating the b ‐value in the Ceres–Tulbagh area, the most seismically active (tectonic) area of South Africa.