Long-term memory in earthquakes and the distribution of interoccurrence times

Abstract

We study seismic records in regimes of stationary seismic activity in Northern and Southern California. Our analysis suggests that the earthquakes are long-term power law correlated with a correlation exponent γ close to 0.4. We show explicitly that the long-term correlations can explain both the fluctuations of magnitudes and interoccurrence times (between events above a certain magnitude M) and, without any fit parameter, the scaling form of the distribution function of the interoccurrence times in the seismic records, recently obtained by Corral (Phys. Rev. Lett., 92 (2004) 108501).

Identifying the occurrence time of an impending major earthquake: a review

“…Seismicity is a typical example of complex time series, and earthquakes exhibit complex correlations in time, space and magnitude (M) which have been studied by several authors (for example see Huang 2008Huang , 2011Lennartz et al 2008Lennartz et al , 2011Rundle et al 2012Rundle et al , 2016. The observed earthquake scaling laws (e.g., Turcotte 1997) indicate the existence of phenomena closely associated with the proximity of the system to a critical point (e.g., Holliday et al 2006;Varotsos et al 2011c).…”

Multifactor analysis of multiscaling in volatility return intervals

“…The temporal structure in volatilities is complex and still regarded as an open problem. Return interval τ , also called recurrence time or interspike interval, which is the time interval between two consecutive volatilities above a certain threshold q, provides a new approach to analyze long-term correlated time series [13,14,15,16,17,18,19,20,21,22,23,24]. Recent studies on financial markets [17,18,19,20,21] show that, for both daily and intraday data, i) the distribution of scaled interval τ / τ can be approximated by a single scaling function, where τ is the average of τ .…”

Fractional dynamics and MDS visualization of earthquake phenomena

“…Adopting now the methodology established in Section 5.1, a new correlation index based on the Euclidean distance is tested. Mathematically, this index, d e , is defined by expressions (10) and (11): The 2D and 3D locus of the F-E regions resulting from the MDS analysis are represented in Fig. 9, which suggests that: (i) the regions are organized on the MDS map forming two main clusters, one being much larger than the other; (ii) similarly to the results shown before, regions FE25, FE41 and FE39 are located on the border of one cluster; (iii) as also are regions FE4 and FE32.…”

“…Tectonic plate motion and strain accumulation processes interact on a range of scales from thousands of kilometres to millimetres and loading rates are not uniform in time [8,9]. Earthquakes reveal long-range correlations and long-memory characteristics [10], which are typical of fractional-order systems [11]. Complex correlations in space, time and magnitude are characterized by self-similarity and absence of characteristic length-scale, meaning that seismic parameters exhibit power-law (PL) behaviour, as given by the Gutenberg-Richter (GR) and Omori laws [6,12].…”