关于余震演化规律的四种表示形式
On four representations of the law of aftershock evolution
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中文总结 AI 辅助
本文针对余震演化规律，分析Omori图像、Hirano-Utsu表示的不足，提出线性与离散两种新表示形式，揭示余震活动随震源本征时间指数衰减的特性。
中文摘要 AI 辅助
基于余震演化数据，已从理论和实验两方面研究主震后震源的弛豫过程。研究表明，Omori提出的余震演化图像并非完整，而Hirano-Utsu表示与观测结果矛盾，本文提出线性和离散两种表示形式，二者均基于震源的失活及本征时间等原创概念。线性与离散表示的差异在于余震实验数据的处理流程：线性表示中，本征时间由余震频率计算，余震频率由最简非线性微分方程描述；离散表示中，震源本征时间由假想的地下钟测量，其速率与通用时间差异显著，余震频率由一阶线性微分方程描述。研究发现，余震活动随震源本征时间呈指数衰减。
英文摘要
The relaxation of the earthquake source following the main shock has been investigated both theoretically and experimentally, based on data regarding the evolution of aftershocks. It is shown that Omori picture of aftershock evolution is not holistic, whereas the Hirano-Utsu representation contradicts observations. Linear and discrete representations are proposed. They are based on original concepts regarding deactivation and the proper time of the source. The difference between the linear and discrete representations lies in the procedure for processing experimental data on aftershocks. In the linear representation, proper time is calculated based on the frequency of aftershocks. In a discrete representation, the source's proper time is measured by an imaginary underground clock, the rate of which differs radically from that of universal time. In the linear representation, the frequency of aftershocks is described by the simplest nonlinear differential equation. In the discrete representation, the aftershock frequency is described by a first-order linear differential equation. It has been found that aftershock activity decays exponentially with the source's proper time. Keywords: earthquake source, foreshocks, mainshock, aftershock theory, Omori law, Utsu's law, proper time, underground clock, deactivation coefficient, source relaxation.
