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 $N\left(t\right)$ of the point processes, where $N\left(t\right)$ 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 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 $N\left(t\right)$ of real earthquakes in Japan, and we find a crossover phenomenon similar to that found for the synthesized data.

中文翻译：

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地震数据去趋势波动分析

去趋势波动分析 (DFA) 在随机过程中广泛用于揭示长期相关性。在这里，我们将 DFA 应用于模拟地震数据的点过程。点过程由类似于流行型余震序列模型的模型合成，我们将 DFA 应用于时间序列$N\left(吨\right)$ 点过程，其中 $N\left(吨\right)$ 是截至时间的累积事件数 $吨$. 在这些时间序列的 DFA 中发现了交叉现象，广泛的数值模拟表明交叉现象是时间序列中非平稳性的标志。我们还发现，交叉时间代表嵌入在时间序列中的非平稳过程的特征时间尺度。因此，当时间序列是平稳信号和非平稳信号的叠加时，点过程的 DFA 在提取非平稳过程的信息时特别有用。此外，我们将 DFA 应用于累积数$N\left(吨\right)$ 在日本的真实地震中，我们发现了与合成数据中发现的交叉现象类似的交叉现象。