Local Distributions and Rate Fluctuations in a Unified Scaling Law for Earthquakes

TL;DR

This paper analyzes a unified scaling law for earthquake interoccurrence times, revealing how local rate fluctuations influence the overall distribution, with theoretical insights and empirical data from Southern California.

Contribution

It introduces a decomposition of the earthquake interoccurrence time distribution into local distributions scaled by occurrence rate, highlighting the role of rate fluctuations in the scaling law.

Findings

Rate fluctuations follow a doubly power-law distribution.

Overall interoccurrence times also exhibit a double power-law behavior.

Theoretical and empirical analysis confirms the significance of rate variability.

Abstract

A recently proposed unified scaling law for interoccurrence times of earthquakes [P. Bak et al., Phys. Rev. Lett. {\bf 88}, 178501 (2002)] is analyzed, both theoretically and with data from Southern California. We decompose the corresponding probability density into local-instantaneous distributions, which scale with the rate of earthquake occurrence. The fluctuations of the rate, characterizing the non-stationarity of the process, show a doubly power-law distribution and are fundamental to determine the overall behavior, described by a double power law as well.