Aperiodicity in one-way Markov cycles and repeat times of large earthquakes in faults

TL;DR

This paper proves that one-way Markov cycles used to model earthquake recurrence have an aperiodicity less than one, aligning with observed earthquake patterns worldwide.

Contribution

It demonstrates that all one-way Markov cycle models inherently have an aperiodicity below one, providing a theoretical basis consistent with seismic observations.

Findings

Aperiodicity in Markov cycle models is always less than one.

The model aligns with global earthquake recurrence data.

Provides a theoretical proof connecting Markov models and seismic observations.

Abstract

A common use of Markov Chains is the simulation of the seismic cycle in a fault, i.e. as a renewal model for the repetition of its characteristic earthquakes. This representation is consistent with Reid's elastic rebound theory. Here it is proved that in {\it any} one-way Markov cycle, the aperiodicity of the corresponding distribution of cycle lengths is always lower than one. This fact concurs with observations of large earthquakes in faults all over the world.