Investigating the time-scaling behavior of the 2004–2010 seismicity of Aswan area (Egypt) by means of the Allan factor statistics and the detrended fluctuation analysis

Abstract

Abstract. The time dynamics of seismicity of Aswan area (Egypt) from 2004 to 2010 was investigated by means of the (i) Allan Factor, which is a powerful tool allowing the capture of time-clusterized properties of temporal point processes; and the (ii) detrended fluctuation analysis, which is capable of detecting scaling in nonstationary time series. The analysis was performed varying the depth and the magnitude thresholds. The 2004-2010 Aswan seismicity is characterized by significant three-fold time-clustering behaviors with scaling exponents ∼0.77 for timescales between 10 4.16 s and 10 5.14 s, ∼0.34 for timescales between 10 5.14 s and 10 6.53 s, and ∼1 for higher timescales. The seismic interevent times and distances are characterized by persistent temporal fluctuations for most of the magnitude and depth thresholds. IntroductionA marked temporal stochastic point process describes events occurring randomly in time (Cox and Isham, 1980) marked by the intensity of the events, and is completely defined by the set of the time occurrences. Such representation was used in modelling several and diverse point processes, like earthquakes (Telesca and Lovallo, 2009; Telesca et al., 2009a, b), lightning , starquakes (Telesca, 2005), solar flares (Telesca, 2007), and also some human and social disasters (Telesca and Lovallo, 2006).A fractal point process displays power-law form in several of its relevant statistics with related scaling exponents, indicating that the represented phenomen contains clusters of points over a relatively large set of timescales (Lowen and Teich, 1995). A fractal point process is, then, characterized by time-clustering behavior, contrarily to homogeneous Poissonian processes, whose density of the event occurrences is nearly constant through time. Generally, in order to capture the main characteristics of the time dynamics of a process, the power spectral density (PSD) is the first method to be used because it furnishes information on the frequency distribution of the process power, which is the physical quantity characterizing a process. By using the Fourier transform, the PSD can be calculated by means of the coefficients of the Fourier transform. The PSD allows detection of periodic or scaling behavior. Periodicities can be revealed by spike-like variations in the PSD, while a power-law shape f −α reveals that the process is scaling; the power-law exponent, also called the scaling exponent, conveys qualitative and quantitative information about the type and strength of the temporal fluctuations governing the process. If the scaling exponent is approximately zero for a wide range of frequency bands, the PSD is approximately flat and the process is a realization of a white noise process, characterized by completely random fluctuations, independence and uncorrelation among all its values as well as absence of any kind of memory phenomenon. If the scaling exponent is negative, the PSD behaves as an increasing function of the frequency f ; this indicates that the high-frequency temporal fluctuati...

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