Evolution of the Tohoku earthquake aftershocks in the framework of the phenomenological theory of aftershocks

TL;DR

This paper analyzes the aftershocks of the Tohoku earthquake using a phenomenological theory that models the earthquake source as a dynamic system with a deactivation coefficient, revealing three distinct relaxation phases.

Contribution

It introduces a novel application of a phenomenological model with a proper time concept to describe aftershock dynamics and phase transitions in earthquake sources.

Findings

Identified three phases of source relaxation post-earthquake

Discovered sharp phase transitions resembling bifurcations

Showed the effectiveness of a relativity of time framework in seismology

Abstract

The aftershocks of the Tohoku earthquake are analyzed in light of the phenomenological theory of aftershocks. The theory is based on the concept of an earthquake source as a dynamic system, the state of which is described by a deactivation coefficient. The concept of the proper time of the source is used, which in general differs from world time. The "underground clock" and the clock showing world time have been synchronized. For an observer using the underground impacts as time markers, the flow of world time will be uneven. The admissibility and effectiveness of the idea of this specific relativity of time is shown. Three phases of relaxation of the source after the main shock were discovered. In the initial phase, the deactivation coefficient is zero. In the main phase, the deactivation coefficient has a finite value and does not change over time. In the recovery phase, the deactivation coefficient changes randomly over time. The sharp transitions between phases resemble the phenomenon of bifurcation.