[论文解读] Dependence of the source deactivation factor on the earthquake magnitude

A. V. Guglielmi, О. Д. Зотов|arXiv (Cornell University)|Aug 5, 2021

earthquake and tectonic studies参考文献 16被引用 5

一句话总结

本文提出一个微分方程模型来描述余震衰减，引入了“源去活化因子”这一概念——即主震后地震源能量耗散速度的度量。该研究通过理论分析与实证数据表明，去活化因子随主震震级增大而单调递减，解决了奥莫里定律与能量守恒原理之间长期存在的矛盾。

ABSTRACT

Three fundamental laws of the physics of earthquakes, bearing the names of their discoverers Omori, Gutenberg, Richter and Bath, are widely used in original, review, monographic, and encyclopedic literature. In this paper, we have tried to look at laws from an unusual point of view. The idea behind our approach is as follows. Each of the three laws was established in the course of work on solving a specific research problem, and the result was expressed in a specific mathematical form. We asked ourselves whether it is possible to modify the statement of the problem, and/or modify the form of expression of the law in order to see new facets of a well-known scientific statement? The result was successful in relation to Omori's law, according to which the frequency of aftershocks hyperbolically decreases over time. The modified formulation of the problem was to find a differential equation describing the time evolution of aftershocks. We found a simple differential model, within the framework of which the concept of deactivation of the earthquake source is introduced. The question of dependence of the deactivation factor on the magnitude of main shock is analyzed theoretically and experimentally. A monotonic decrease in the deactivation factor with an increase in the magnitude of the main shock has been reliably established. Other possible applications of the proposed methodological technique are considered. In particular, it is indicated how to overcome the contradiction between the Omori law and the law of energy conservation. Keywords: Omori law, Gutenberg-Richter law, Bath law, main shock, aftershock, deactivation factor, Omori epoch, differential equation of evolution.

研究动机与目标

• 将余震衰减的奥莫里定律重新表述为微分方程框架，以模拟地震能量释放的时间演化。
• 引入并定义“去活化因子”，作为衡量地震源丧失产生余震能力速率的指标。
• 从理论与实证两方面研究去活化因子与主震震级的依赖关系。
• 解决奥莫里定律与地震能量释放中能量守恒定律之间看似矛盾的问题。
• 提出一种适用于余震序列以外其他地震现象的方法论框架。

提出的方法

• 基于奥莫里经验定律推导描述余震频次时间演化的微分方程。
• 将“源去活化因子”引入为控制余震衰减速率的时变参数。
• 通过理论分析推导去活化因子与主震震级的函数关系。
• 利用地震目录中的实证数据验证理论模型，评估去活化因子随震级增加而单调递减的特性。
• 将能量守恒原理应用于模型，以解决其与奥莫里定律之间的不一致。
• 利用微分模型重新诠释奥莫里时代为源逐步去活化的过程。

实验结果

研究问题

• RQ1 如何将余震衰减的奥莫里定律重新表述为微分方程，以模拟地震源活动的时间演化？
• RQ2 在余震序列背景下，源去活化因子的物理意义与数学形式是什么？
• RQ3 去活化因子如何随主震震级变化，且该关系是否具有单调性？
• RQ4 所提出的模型能否调和奥莫里定律与地震系统中能量守恒原理之间的矛盾？
• RQ5 该方法论方法在建模地震源动力学方面具有哪些更广泛的应用？

主要发现

• 去活化因子（代表源能量损失速率）随主震震级增大而单调递减。
• 理论分析与实证数据均证实，随着主震震级增加，去活化因子呈现一致且单调的下降趋势。
• 微分模型通过考虑源随时间的渐进去活化过程，成功调和了奥莫里定律与能量守恒之间的矛盾。
• 该模型为奥莫里时代提供了一种物理解释，即地震源的指数去活化阶段。
• 该方法为分析传统经验定律之外的地震源动力学提供了新框架。
• 结果表明，更大的主震导致更慢的去活化，意味着由于源活动持续时间更长，余震序列也更持久。