A relationship between Hurst exponents of slip and waiting time data of earthquakes

Long-range correlations and trends in Colombian seismic time series

“…In the first order detrended fluctuation analysis DF A 1 , the variance of the profile in each window represents the square of the fluctuations and then the best linear fit is determinated [34]. We consider in this work the time series associated to the following parameters defined between two successive seismic events: (i) interevent interval [17,18,24,37,43]; (ii) separation distance [38,36]; (iii) depth difference; (iv) magnitude difference. We note that the seismic time series of depth differences and magnitude differences are new for this kind of analysis.…”

“…Long-range power-law correlations are traditionally measured by a scaling parameter or fractal dimension (D). If the time series is self-similar and selfaffine, the parameter D is related to the Hurst exponent (H) through the expression D = 2 − H [23,24]. Thus, the Hurst exponent is a measure of the long-range correlation in time series data and allows to distinguish the persistence (correlation), anti-persistence (anti-correlation) or randomness of the data [25].…”

“…The study of long-range power-law correlations in seismic sequences has been focussed on the calculation of the Hurst exponent for time series of interevent intervals by using the CR/S [24] and the DF A [17,18]. The DFA was also used to calculate the Hurst exponent associated to two-dimensional sequences defined in terms of the time series of interevent intervals and separation distances [36].…”

“…In this work we extend the detection of long-range correlations for the case of new time series that can be extracted from the seismic event data. Additionally to the time series of interevent intervals [17,18,24,37,43], we consider also the time series associated to the following parameters defined between two successive seismic events: separation distance [38,36]; depth difference; magnitude difference. We think that if we study simultaneously the existence of long-range correlations for these four seismic time series, then we have a most complete vision of the fractal structure associated to the seismic events [38].…”

Fractional dynamics in the Rayleigh’s piston

“…The fBm is also called 1/ f noise [5], where f denotes frequency, because its spectrum is given by 1/ f α , α > 0. The fBm is interpreted as a signature of complexity [6] and has been observed in many distinct areas [7], namely in economics and finance [8,9], geophysics [10,11,12,13,14,15], music and speech [16,17,18], biology [19,20,21,22,23] and others. During the last years the relation between fBm and FC was studied by some researchers [24,25,26,27].…”