On the elementary theory of earthquake aftershocks

TL;DR

This paper discusses a simple mathematical theory of earthquake aftershocks, introduces a two-stage relaxation model, and proposes a new concept of source proper time to improve seismic data analysis.

Contribution

It presents a novel two-stage relaxation mode and introduces the concept of source proper time within the elementary theory of aftershocks.

Findings

Discovered a two-stage relaxation mode of earthquake sources.

Established the usefulness of source proper time in seismic studies.

Validated the effectiveness of elementary theory in data analysis.

Abstract

The elementary theory of aftershocks, being relatively simple mathematically, belongs to the basics of earthquake physics. The paper briefly outlines the concepts and ideas of the theory, provides equations for the relaxation of the source after the main shock, and emphasizes the effectiveness of the theory in the search for new approaches to the processing and analysis of aftershock observation data. The main attention is paid to the discussion of two new results obtained on the basis of elementary theory. Firstly, a two-stage relaxation mode of the earthquake source was discovered. In the first stage, called the Omori epoch, the Omori law is strictly observed. The first stage ends with a bifurcation of the source, and the second stage of relaxation begins, during which the evolution of aftershocks proceeds chaotically. Secondly, within the framework of the elementary theory of aftershocks, a fundamentally new concept of the proper time of the source was introduced. Keywords: earthquake source, deactivation coefficient, Omori law, dynamic system, inverse problem, relaxation, proper time. The source proper time has proven useful in experimental studies of seismic activity.