Detrended fluctuation analysis of earthquake data

TL;DR

This paper applies detrended fluctuation analysis to earthquake data and models, revealing crossover phenomena indicative of non-stationarity and characteristic time scales in seismic activity.

Contribution

It demonstrates the effectiveness of DFA in detecting non-stationarity and characteristic scales in earthquake-related point processes, both synthetic and real.

Findings

Crossover phenomena indicate non-stationarity in earthquake data

DFA can extract characteristic time scales of seismic activity

Real earthquake data shows similar crossover behavior as synthetic models

Abstract

The detrended fluctuation analysis (DFA) is extensively useful in stochastic processes to unveil the long-term correlation. Here, we apply the DFA to point processes that mimick earthquake data. The point processes are synthesized by a model similar to the Epidemic-Type Aftershock Sequence model, and we apply the DFA to time series $N(t)$ of the point processes, where $N(t)$ is the cumulative number of events up to time $t$. Crossover phenomena are found in the DFA for these time series, and extensive numerical simulations suggest that the crossover phenomena are signatures of non-stationarity in the time series. We also find that the crossover time represents a characteristic time scale of the non-stationary process embedded in the time series. Therefore, the DFA for point processes is especially useful in extracting information of non-stationary processes when time series are superpositions of stationary and non-stationary signals. Furthermore, we apply the DFA to the cumulative number $N(t)$ of real earthquakes in Japan, and we find a crossover phenomenon similar to that found for the synthesized data.