Scaling instability in self-potential earthquake-related signals

Scaling behavior of the temporal variability in self-potential data recorded in the frequency range during 1995 at Acapulco station (Mexico) was identified and analyzed. In this period, a strong earthquake (Ms=7.4) struck the monitored area on September 14, 1995. Using the detrended fluctuation analysis (DFA), which is a powerful method to detect scaling in nonstationary time series, deviations from stable power-law scaling were quantified. Our findings point to an evident unstable scaling behavior in self-potential data before the occurrence of the seismic event. These first results could be useful in the framework of earthquake prediction studies.     

Space-magnitude dependent scaling behaviour in seismic interevent series revealed by detrended fluctuation analysis

The scaling behaviour of the 1981-2007 seismicity data in central Italy, which is one of the most seismically active areas in Italy is investigated. In particular we examined the earthquakes located in a circular area centred on the epicentre of the strongest event, occurred in September 26, 1997 (duration magnitude M_D=5.8). On the base of the detrended fluctuation analysis (DFA), we found that in the magnitude range between 2.5 and 2.9 the scaling exponents fall into disjoint sets for events relatively close and far from the epicentre of the strongest event.     

Cycles,scaling and crossover phenomenon in length of the day (LOD) time series

The dynamics of the temporal fluctuations of the length of the day (LOD) time series from January 1, 1962 to November 2, 2006 were investigated. The power spectrum of the whole time series has revealed annual, semi-annual, decadal and daily oscillatory behaviors, correlated with oceanic–atmospheric processes and interactions. The scaling behavior was analyzed by using the detrended fluctuation analysis (DFA), which has revealed two different scaling regimes, separated by a crossover timescale at approximately 23 days. Flicker-noise process can describe the dynamics of the LOD time regime involving intermediate and long timescales, while Brownian dynamics characterizes the LOD time series for small timescales.     

Different scaling behaviors in daily temperature records over China

Long-range correlations of five kinds of daily temperature records (i.e. daily average temperature records, daily maximum temperature records, daily minimum temperature records, diurnal temperature range and the sum of daily maximum and minimum temperature records) from 164 weather stations over China during 1951-2004 are analyzed by means of detrended fluctuation analysis (DFA). These five kinds of fluctuation series are found to be power-law correlated with scaling exponents larger than 0.5. Local changes of scaling exponents are examined and the spatial distributions of these different kinds of temperature records are similar except the diurnal temperature range (DTR for short) records. Furthermore, the differences of the scaling behavior among diurnal temperature records and other kinds of temperature records are discussed.     

Temporal variations of long-term correlations in seismic activity fluctuations

The scaling behavior of the 1998-2009 seismicity in Guerrero, southern Mexico, was studied by means of the detrended fluctuation analysis (DFA). We found that inter-seismic periods are correlated with a transition in the scaling behavior at about 200 seismic events. Correlations are relatively weak for small time scales. However, for large time scales, correlations are associated with a 1/f fractional process, indicating that the seismicity pattern emerges from a self-organized critical state. Temporal variations of the scaling exponent along years computed from the DFA indicate the presence of a quasi-biennial cycle in the seismicity correlations. This cyclic behavior was apparently triggered by the large 2001-2002 slow slip event in the Guerrero seismic gap. Besides, the significant seismic events (M_w>5) originate, on the average, at deeper regions in each cycle.     

Investigation of scaling properties in monthly streamflow and Standardized Streamflow Index (SSI) time series in the Ebro basin (Spain)

Scaling behaviors in monthly streamflow and Standardized Streamflow Index (SSI) of 11 gauging stations in Ebro basin (Spain) were analyzed: four located in the mainstream and seven in tributaries. The time span is from 1950 to 2005. The methods used are the power spectrum and the detrended fluctuation analysis. All the streamflows are signaled by the presence of the yearly oscillation, which also plays the role of crossover between two regions: for frequencies smaller than the yearly cycle (or timescales higher than 1 year) the dynamics is approximately random, while for frequencies higher than the yearly frequency (or timescales smaller than 1 year) the dynamics is persistently correlated. The SSI shows approximately similar characteristics, although the annual oscillation is not evidenced. Except for a few peculiar features, the power spectrum and the detrended fluctuation analysis (DFA) have shown similar results for all the streamflow and SSI time series, indicating a universal scaling behavior over the Ebro basin.     

Long-range correlations in two-dimensional spatio-temporal seismic fluctuations

We analysed the scaling behaviour of the two-dimensional (2-D) sequence (Δs, Δt) of the 1981–1998 southern California seismicity, where Δs is the distance between two consecutive earthquakes (jump) and Δt is their interevent interval. The 2-D seismic spatio-temporal fluctuations were investigated by means of the detrended fluctuation analysis (DFA), well-known methodology used to detect scaling behaviour in observational time series possibly affected by nonstationarities. The estimated scaling exponents α_DFA, larger than 0.5, indicate the presence of persistent long-range correlations in the 2-D sequence analysed. The variation of the scaling exponent with the increase of threshold magnitude shows a two-fold behaviour: in the range between 1.5 (the completeness magnitude of the catalog) and 3.0, the scaling exponent is quite constant and denoting a flicker-noise dynamics; while for magnitudes larger than 3.0 it decreases with the increase of magnitude, indicating a tendency toward a 2-D space–time Poissonian process for large events.     

Investigating the temporal variation of the scaling behavior in rainfall data measured in central Argentina by means of detrended fluctuation analysis

Investigation of the time variant scaling behavior of six monthly rainfall series recorded in central Argentina from 1860 to 2006 by using detrending fluctuation analysis (DFA) was performed. Changes in precipitation extremes are analyzed for several regions of Argentina using long-term monthly rainfall data (back to 1860) recorded by rain gauges extended for more than 10 latitude-degrees, from subtropical regions until 39^° S. A moving window was employed in order to analyze statistical changes. Three different types of time patterns can be distinguished: (i) eastern stations show visible crossovers between persistent and random behavior; (ii) north-western stations are characterized by random behavior approximately at any time and do not present visible crossovers between different types of scaling behaviors; (iii) one station (i.e. Corrientes) shows a peculiar pattern, since it is characterized by several crossovers from persistent to random behavior, indicating a more fluctuating time dynamics without a well defined trend. The obtained results can be interpreted in the context of the climatological conditions of Central Argentina, which is characterized by the continental heat low in the northwest region, by the subtropical rainforest in the eastern provinces and by a transition zone (from maritime to continental regime) fluctuating with the South Atlantic high-pressure cell.     

The scaling behavior of hand motions reveals self-organization during an executive function task

Recent approaches to cognition explain cognitive phenomena in terms of interaction-dominant dynamics. In the current experiment, we extend this approach to executive function, a construct used to describe flexible, goal-oriented behavior. Participants were asked to perform a widely used executive function task, card sorting, under two conditions. In one condition, participants were given a rule with which to sort the cards. In the other condition, participants had to induce the rule from experimenter feedback. The motion of each participant’s hand was tracked during the sorting task. Detrended fluctuation analysis was performed on the inter-point time series using a windowing strategy to capture changes over each trial. For participants in the induction condition, the Hurst exponent sharply increased and then decreased. The Hurst exponents for the explicit condition did not show this pattern. Our results suggest that executive function may be understood in terms of changes in stability that arise from interaction-dominant dynamics.     

Phases of scaling and cross-correlation behavior in traffic

While many microscopic models of traffic flow describe transitions between different traffic phases, such transitions are difficult to quantify in measured traffic data. Here we study long-term traffic recordings consisting of ≈2900$\approx 2900$ days of flow, density, and velocity time series with minute resolution from a Spanish motorway. We calculate fluctuations, cross-correlations, and long-term persistence properties of these quantities in the flow–density diagram. This leads to a data-driven definition of (local) traffic states based on the dynamical properties of the data, which differ from those given in standard guidelines. We find that detrending techniques must be used for persistence analysis because of non-stationary daily and weekly traffic flow patterns. We compare our results for the measured data with analysis results for a microscopic traffic model, finding good agreement in most quantities. However, the simulations cannot easily reproduce the congested traffic states observed in the data. We show how fluctuations and cross-correlations in traffic data may be used for prediction, i.e., as indications of increasing or decreasing velocities.     

On the scaling ranges of detrended fluctuation analysis for long-term memory correlated short series of data

We examine the scaling regime for the detrended fluctuation analysis (DFA)—the most popular method used to detect the presence of long-term memory in data and the fractal structure of time series. First, the scaling range for DFA is studied for uncorrelated data as a function of time series length L$L$ and the correlation coefficient of the linear regression R²$R^2$ at various confidence levels. Next, a similar analysis for artificial short series of data with long-term memory is performed. In both cases the scaling range λ$\lambda$ is found to change linearly—both with L$L$ and R²$R^2$. We show how this dependence can be generalized to a simple unified model describing the relation λ=λ(L,R²,H)$\lambda =\lambda (L,R^2,H)$ where H$H$ (1/2≤H≤1$1/2\le H\le 1$) stands for the Hurst exponent of the long range autocorrelated signal. Our findings should be useful in all applications of DFA technique, particularly for instantaneous (local) DFA where a huge number of short time series has to be analyzed at the same time, without possibility of checking the scaling range in each of them separately.     

Strong anticipation: Sensitivity to long-range correlations in synchronization behavior

Strong anticipation has emerged as a new framework for studying prospective control. According to earlier theories of prediction, anticipatory behavior rests on temporally local predictions from internal models. Strong anticipation eschews internal models and draws on the embedding of an organism in its environment. In this formulation, behavior is sensitive to the non-local temporal structure of the environment. We present initial evidence for strong anticipation in a synchronization task with tapping as the behavior. Participants were instructed to synchronize, to the best of their abilities, with a (unpredictable) chaotic signal. Our data suggest a close relationship between the long-range correlations of the chaotic signal and the long-range correlations of the synchronization behavior.     

A multifractal detrended fluctuation analysis (MDFA) of the Chinese growth enterprise market (GEM)

A multifractal, detrended fluctuation approach is used to analyze the growth enterprise market (GEM) in China involving a range of correlations in fluctuations of share prices (fat tail), persistent and anti-persistent states. Our analysis exhibits company-specific multifractal characteristics, which vary among the companies listed in the same industry, e.g., the power-law cross-correlations between computer and electronics sectors. These results may help reduce the risk in complex financial markets.     

Assessment of long-range correlation in animal behavior time series: The temporal pattern of locomotor activity of Japanese quail (Coturnix coturnix) and mosquito larva (Culex quinquefasciatus)

Detrended Fluctuation Analysis (DFA) is a method that has been frequently used to determine the presence of long-range correlations in human and animal behaviors. However, according to previous authors using statistical model systems, in order to correctly use DFA different aspects should be taken into account such as: (1) the establishment by hypothesis testing of the absence of short term correlation, (2) an accurate estimation of a straight line in the log–log plot of the fluctuation function, (3) the elimination of artificial crossovers in the fluctuation function, and (4) the length of the time series. Taking into consideration these factors, herein we evaluated the presence of long-range correlation in the temporal pattern of locomotor activity of Japanese quail (Coturnix coturnix) and mosquito larva (Culex quinquefasciatus  ). In our study, modeling the data with the general autoregressive integrated moving average (ARFIMA) model, we rejected the hypothesis of short-range correlations (d=0)$(d=0)$ in all cases. We also observed that DFA was able to distinguish between the artificial crossover observed in the temporal pattern of locomotion of Japanese quail and the crossovers in the correlation behavior observed in mosquito larvae locomotion. Although the test duration can slightly influence the parameter estimation, no qualitative differences were observed between different test durations.     

Long correlations and Levy models applied to the study of memory effects in high frequency (tick) data

This work is devoted to the study of long correlations, memory effects and other statistical properties of high frequency (tick) data. We use a sample of 25 stocks for this purpose.We verify that the behavior of the return is compatible with that of continuous time Levy processes. We also study the presence of memory effects and long-range correlations in the values of the return.     

Statistical and Criticality Analysis of the Lower Ionosphere Prior to the 30 October 2020 Samos (Greece) Earthquake (M6.9), Based on VLF Electromagnetic Propagation Data as Recorded by a New VLF/LF Receiver Installed in Athens (Greece)

In this work we present the statistical and criticality analysis of the very low frequency (VLF) sub-ionospheric propagation data recorded by a VLF/LF radio receiver which has recently been established at the University of West Attica in Athens (Greece). We investigate a very recent, strong (M6.9), and shallow earthquake (EQ) that occurred on 30 October 2020, very close to the northern coast of the island of Samos (Greece). We focus on the reception data from two VLF transmitters, located in Turkey and Israel, on the basis that the EQ’s epicenter was located within or very close to the 5th Fresnel zone, respectively, of the corresponding sub-ionospheric propagation path. Firstly, we employed in our study the conventional analyses known as the nighttime fluctuation method (NFM) and the terminator time method (TTM), aiming to reveal any statistical anomalies prior to the EQ’s occurrence. These analyses revealed statistical anomalies in the studied sub-ionospheric propagation paths within ~2 weeks and a few days before the EQ’s occurrence. Secondly, we performed criticality analysis using two well-established complex systems’ time series analysis methods—the natural time (NT) analysis method, and the method of critical fluctuations (MCF). The NT analysis method was applied to the VLF propagation quantities of the NFM, revealing criticality indications over a period of ~2 weeks prior to the Samos EQ, whereas MCF was applied to the raw receiver amplitude data, uncovering the time excerpts of the analyzed time series that present criticality which were closest before the Samos EQ. Interestingly, power-law indications were also found shortly after the EQ’s occurrence. However, it is shown that these do not correspond to criticality related to EQ preparation processes. Finally, it is noted that no other complex space-sourced or geophysical phenomenon that could disturb the lower ionosphere did occur during the studied time period or close after, corroborating the view that our results prior to the Samos EQ are likely related to this mainshock.     

Sub-coercive field dynamic hysteresis in morphotropic phase boundary composition of Pb(Zr1/2Ti1/2)O3-Pb(Zn1/3Nb2/3)O3 ceramic and its scaling behavior

Sub-coercive field dynamic ferroelectric hysteresis of a morphotropic phase boundary composition of the PZT-PZN ceramic was investigated under influence of the compressive stress. The scaling relation of hysteresis area 〈A〉 against frequency f, field amplitude E₀, and stress σ took a form of , which is not different significantly to that of other PZT-PZN compositions with pure tetragonal or rhombohedral structure, as well as to that of soft and hard PZT bulk ceramics. This study suggested that the domain structures, not ceramic compositions, played a key role in controlling dynamic hysteresis behavior of ferroelectric materials.