Detrended fluctuation analysis of earthquake data

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 mimic 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 of the point processes, where is the cumulative number of events up to time . Crossover phenomena are found in the DFA for these time series, and extensive numerical simulations suggest that the crossover phenomena are signatures of nonstationarity in the time series. We also find that the crossover time represents a characteristic time scale of the nonstationary process embedded in the time series. Therefore, the DFA for point processes is especially useful in extracting information of nonstationary processes when time series are superpositions of stationary and nonstationary signals. Furthermore, we apply the DFA to the cumulative number of real earthquakes in Japan, and we find a crossover phenomenon similar to that found for the synthesized data.