Bifurcation of the earthquake source at the end of the Omori epoch

TL;DR

This paper models the earthquake aftershock process using differential equations, identifies a constant phase called the Omori epoch, and hypothesizes that its end signifies a bifurcation indicating a change in the earthquake source state.

Contribution

It introduces an inverse problem approach to determine the source deactivation coefficient and proposes that the end of the Omori epoch corresponds to a bifurcation point in the earthquake source.

Findings

Existence of a constant deactivation coefficient during the Omori epoch

Identification of complex variations at the end of the Omori epoch

Hypothesis that the epoch's end indicates a bifurcation in source state

Abstract

The earthquake source after the main shock can theoretically be represented as a black box without an entrance. At the output, there is a signal in the form of aftershocks, the frequency of which decreases on average with time according to the Omori law. The task of the researcher is to evaluate the structure, state and mechanism of functioning of a dynamic system simulating the earthquake source based on the output signal. In this paper, we outline an approach to a partial solution of this general problem. Omori's law is presented as a differential equation of aftershock evolution. An inverse problem has been posed and solved, the essence of which is to determine the source deactivation coefficient from the observed frequency of aftershocks. The existence of the so-called Omori epoch, during which the deactivation coefficient remains constant, has been discovered. At the end of the Omori epoch, the deactivation coefficient experiences complex variations. A hypothesis has been put forward that the end of the Omori epoch indicates a bifurcation, i.e. about the transition of the source from one state to a qualitatively different state. Our paper is written for the 100th anniversary of the death of Fusakichi Omori. Keywords: aftershocks, Omori law, evolution equation, deactivation coefficient, inverse problem, Omori epoch, bifurcation point.