Natural time and 1/f "noise"

TL;DR

This paper introduces the concept of natural time to analyze complex systems, demonstrating its effectiveness in identifying critical dynamics and $1/f$ noise behavior in seismic electric signals.

Contribution

It proposes a simple model exhibiting $1/f$ noise in natural time and applies this analysis to real seismic electric signals to reveal their critical dynamics.

Findings

Seismic electric signals follow $1/f^a$ behavior with $a$ close to 1.

Natural time analysis reveals critical dynamics in electric signals.

The model reproduces $1/f$ noise observed in real data.

Abstract

Seismic electric signals have been found to obey the ubiquitous $1/f^a$ behavior [{\em Phys. Rev. E} {\bf 66}, 011902(2002)]. The newly introduced concept of natural time enables the study of the dynamic evolution of a complex system and identifies when the system enters the critical stage. On the basis of this concept, a simple model is proposed here which exhibits the $1/f^a$ behavior with $a$ close to unity. Furthermore, we present recent data of electric signals, which when analyzed in the natural time domain are found to exhibit {\em critical} dynamics and hence can be classified as seismic electric signals.