Distribution of the largest aftershocks in branching models of triggered seismicity: theory of the universal Båth law.
Distribution of the largest aftershocks in branching models of triggered seismicity: theory of the universal Båth law.
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触发地震活动分支模型中最大余震的分布：普遍巴斯定律理论。
DOI：
10.1103/physreve.71.056127
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发表时间：
2005
期刊：
影响因子：
--
通讯作者：
D. Sornette
中科院分区：
文献类型：
--
作者：
A. Saichev;D. Sornette
使用触发地震活动的触发型余震序列（ETAS）分支模型，我们应用生成概率函数的形式主义，精确地计算了主震震级与其最大余震震级之间的平均差值。根据经验，这个平均震级差与主震震级无关，等于1.2，这是一个普遍的现象，被称为巴斯定律。我们的理论表明，Båth定律仅在足够接近ETAS分支过程的临界状态下成立。考虑到Båth常数值在1.2附近的误差线为+/- 0.1，我们对Båth定律的精确分析处理提供了对生产率指数α和分支比n的新约束：0.9约<α <或=1。我们提出了一种方法来测量α的基础上预测的重整化的古腾堡-里克特分布的最大余震的震级。我们还介绍了“前震的巴斯第二定律“：主震成为前震的概率不取决于它的震级ρ。
Using the epidemic-type aftershock sequence (ETAS) branching model of triggered seismicity, we apply the formalism of generating probability functions to calculate exactly the average difference between the magnitude of a mainshock and the magnitude of its largest aftershock over all generations. This average magnitude difference is found empirically to be independent of the mainshock magnitude and equal to 1.2, a universal behavior known as Båth's law. Our theory shows that Båth's law holds only sufficiently close to the critical regime of the ETAS branching process. Allowing for error bars +/- 0.1 for Båth's constant value around 1.2, our exact analytical treatment of Båth's law provides new constraints on the productivity exponent alpha and the branching ratio n: 0.9 approximately < alpha < or =1. We propose a method for measuring alpha based on the predicted renormalization of the Gutenberg-Richter distribution of the magnitudes of the largest aftershock. We also introduce the "second Båth law for foreshocks:" the probability that a main earthquake turns out to be the foreshock does not depend on its magnitude rho.