Method for processing and analyzing tectonic earthquake aftershocks: A new look at old problem

TL;DR

This paper introduces a new method for analyzing earthquake aftershocks using a deactivation coefficient, revealing a two-stage relaxation process and challenging existing laws like Hirano-Utsu law.

Contribution

It develops an explicit calculation method for the deactivation factor from observed data and uncovers a two-stage source relaxation process after earthquakes.

Findings

Two-stage relaxation of seismic source identified

Deactivation factor can be computed from aftershock data

Hirano-Utsu law is not applicable for aftershock evolution

Abstract

The deactivation coefficient has been introduced for the source that cools down after the mainshock of the earthquake. The deactivation coefficient satisfies two conditions. First, it can be computed from observed aftershock frequency data (axiom of computability). Second, the deactivation factor is independent of time if and only if Omori law is strictly satisfied (hyperbolicity axiom). From the two axioms follows an explicit expression for calculating the source deactivation factor from observed aftershock data. A simple and efficient method for processing and analyzing aftershocks using the deactivation factor has been developed. A two-stage mode of the source relaxation to a new equilibrium state after the formation of the main rupture of rock continuity in it was discovered. In the first stage, called the Omori epoch, the Omori law is strictly followed. The duration of the first stage is tentatively 10 to 100 days. In the Omori epoch, the average frequency of aftershocks is predictable with high accuracy. At the end of the Omori epoch, a bifurcation occurs. In the second stage, the deactivation factor changes with time in an unpredictable way. The phase portrait of the source allows us to visualize the complex dynamics of seismic activity in the second stage of the source relaxation. The experiment shows that the Hirano-Utsu law is inapplicable for describing the evolution of aftershocks neither at the first nor at the second stage of the source relaxation. Keywords: deactivation factor, evolution equation, phase portrait, Omori law, Hirano-Utsu law.