Fisher-Shannon Investigation of the Effect of Nonlinearity of Discrete Langevin Model on Behavior of Extremes in Generated Time Series.

Diverse forms of nonlinearity within stochastic equations give rise to varying dynamics in processes, which may influence the behavior of extreme values. This study focuses on two nonlinear models of the discrete Langevin equation: one with a fixed diffusion function (M1) and the other with a fixed marginal distribution (M2), both characterized by a nonlinearity parameter. Extremes are defined according to the run theory with thresholds based on percentiles. The behavior of inter-extreme times and run lengths is examined by employing Fisher's Information Measure and the Shannon Entropy. Our findings reveal a clear relationship between the entropic and informational measures and the nonlinearity of model M1-these measures decrease as the nonlinearity parameter increases. Similar relationships are evident for the M2 model, albeit to a lesser extent, even though the background data's marginal distribution remains unaffected by this parameter. As thresholds increase, both the values of Fisher's Information Measure and the Shannon Entropy also increase.

Clustering Analysis of Seismicity in the Anatolian Region with Implications for Seismic Hazard.

The Anatolian region is one of the most seismically active tectonic settings in the world. Here, we perform a clustering analysis of Turkish seismicity using an updated version of the Turkish Homogenized Earthquake Catalogue (TURHEC), which contains the recent developments of the still ongoing Kahramanmaras seismic sequence. We show that some statistical properties of seismic activity are related to the regional seismogenic potential. Mapping the local and global coefficients of variation of inter-event times of crustal seismicity which occurred during the last three decades, we find that territories prone to major seismic events during the last century usually host globally clustered and locally Poissonian seismic activity. We suggest that regions with seismicity associated with higher values of the global coefficient of variation of inter-event times, CV, are likely to be more prone to hosting large earthquakes in the near future than other regions characterized by lower values, if their largest seismic events have the same magnitude. If our hypothesis is confirmed, clustering properties should be considered as a possible additional information source for the assessment of seismic hazard. We also find positive correlations between global clustering properties, the maximum magnitude and the seismic rate, while the b-value of the Gutenberg-Richter law is weakly correlated with them. Finally, we identify possible changes in such parameters before and during the 2023 Kahramanmaras seismic sequence.

Multifractal Analysis of MODIS Aqua and Terra Satellite Time Series of Normalized Difference Vegetation Index and Enhanced Vegetation Index of Sites Affected by Wildfires.

The MODIS Aqua and Terra Normalized Difference Vegetation Index (NDVI) and Enhanced Vegetation Index (EVI) time series acquired during nearly two decades (2000 to 2020) covering the area burned by the Camp Fire (California) in 2018 is investigated in this study by using the multifractal detrended fluctuation analysis in relation to the recovery process of vegetation after fire. In 2008, the same area was partially burned by two wildfires, the BTU Lightning Complex Fire and the Humboldt Fire. Our results indicate that all vegetation index time series are featured by six- and twelve-month modulating periodicities, with a larger spectral content at longer periods for two-fire-affected sites. Furthermore, two fires cause an increase of the persistence of the NDVI and EVI time series and an increase of the complexity, suggesting that the recovery process of vegetation dynamics of fire-affected sites is characterized by positive feedback mechanisms, driving the growth-generating phenomena, which become even more effective in those sites affected by two fires.

Exploring Long-Term Anomalies in the Vegetation Cover of Peri-Urban Parks Using the Fisher-Shannon Method.

The main goal of this study was to evaluate the potential of the Fisher-Shannon statistical method applied to the MODIS satellite time series to search for and explore any small multiyear trends and changes (herein also denoted as inner anomalies) in vegetation cover. For the purpose of our investigation, we focused on the vegetation cover of three peri-urban parks close to Rome and Naples (Italy). For each of these three areas, we analyzed the 2000-2020 time variation of four MODIS-based vegetation indices: evapotranspiration (ET), normalized difference vegetation index (NDVI), leaf area index (LAI), and enhanced vegetation index (EVI). These data sets are available in the Google Earth Engine (GEE) and were selected because they are related to the interactions between soil, water, atmosphere, and plants. To account for the great variability exhibited by the seasonal variations while identifying small multiyear trends and changes, we devised a procedure composed of two steps: (i) application of the Singular Spectrum Analysis (SSA) to each satellite-based time series to detect and remove the annual cycle including the seasonality and then (ii) analysis of the detrended signals using the Fisher-Shannon method, which combines the Shannon entropy and the Fisher Information Measure (FIM). Our results indicate that among all the three pilot test areas, Castel Volturno is characterized by the highest Shannon entropy and the lowest FIM that indicate a low level of order and organization of vegetation time series. This behaviour can be linked to the degradation phenomena induced by the parasite (Toumeyella parvicornis) that has affected dramatically the area in recent years. Our results were nicely confirmed by the comparison with in situ analyzed and independent data sets revealing the existence of subtle, small multiyear trends and changes in MODIS-based vegetation indices.

Visibility Graph Analysis of Reservoir-Triggered Seismicity: The Case of Song Tranh 2 Hydropower, Vietnam.

In this study, the visibility graph analysis of seismicity triggered by Song Tranh 2 hydropower (Vietnam) is performed. The relationship between the seismic (the Gutenberg-Richter b-value) and topological (the k-M slope) parameters of seismicity is analysed. Our findings indicate that the relationship between the Gutenberg-Richter b-value and the k-M slope of the investigated seismicity is in agreement with that characterising the tectonic seismicity. The results obtained from analysing the reservoir-triggered seismicity of Song Tranh 2 area could contribute to better characterisation of the relationship between the seismological and topological parameters of seismicity, strengthening the universal character of the relationship between the b-value and the k-M slope.

Correlation between seismic activity and tidal stress perturbations highlights growing instability within the brittle crust.

Faults become more and more responsive to stress perturbations as instability mounts. We utilize this property in order to identify the different phases of the seismic cycle. Our analysis provides new insights about the features of impending mainshocks, which are proposed to emerge from a large-scale crustal-weakening preparation process whose duration depends on their seismic moments, according to the power-law T [Formula: see text] M[Formula: see text] for M[Formula: see text] [Formula: see text] 10[Formula: see text] N m. Moreover, further studies are performed about the impact of tidal stress perturbation on seismicity; in particular, the relationship between frequency-magnitude scaling and perturbations is discussed, showing that the sensitivity of earthquakes to solid Earth tides decreases as their magnitudes increase.

Spectral and Informational Analysis of Temperature and Chemical Composition of Solfatara Fumaroles (Campi Flegrei, Italy).

Temperature and composition at fumaroles are controlled by several volcanic and exogenous processes that operate on various time-space scales. Here, we analyze fluctuations of temperature and chemical composition recorded at fumarolic vents in Solfatara (Campi Flegrei caldera, Italy) from December 1997 to December 2015, in order to better understand source(s) and driving processes. Applying the singular spectral analysis, we found that the trends explain the great part of the variance of the geochemical series but not of the temperature series. On the other hand, a common source, also shared by other geo-indicators (ground deformation, seismicity, hydrogeological and meteorological data), seems to be linked with the oscillatory structure of the investigated signals. The informational characteristics of temperature and geochemical compositions, analyzed by using the Fisher-Shannon method, appear to be a sort of fingerprint of the different periodic structure. In fact, the oscillatory components were characterized by a wide range of significant periodicities nearly equally powerful that show a higher degree of entropy, indicating that changes are influenced by overlapped processes occurring at different scales with a rather similar intensity. The present study represents an advancement in the understanding of the dominant driving mechanisms of volcanic signals at fumaroles that might be also valid for other volcanic areas.

Unveiling Informational Properties of the Chen-Ouillon-Sornette Seismo-Electrical Model.

The seismo-electrical coupling is critical to understand the mechanism of geoelectrical precursors to earthquakes. A novel seismo-electrical model, called Chen-Ouillon-Sornette (COS) model, has been developed by combining the Burridge-Knopoff spring-block system with the mechanisms of stress-activated charge carriers (i.e., electrons and holes) and pressure-stimulated currents. Such a model, thus, can simulate fracture-induced electrical signals at a laboratory scale or earthquake-related geoelectrical signals at a geological scale. In this study, by using information measures of time series analysis, we attempt to understand the influence of diverse electrical conditions on the characteristics of the simulated electrical signals with the COS model. We employ the Fisher-Shannon method to investigate the temporal dynamics of the COS model. The result showed that the electrical parameters of the COS model, particularly for the capacitance and inductance, affect the levels of the order/disorder in the electrical time series. Compared to the field observations, we infer that the underground electrical condition has become larger capacitance or smaller inductance in seismogenic processes. Accordingly, this study may provide a better understanding of the mechanical-electrical coupling of the earth's crust.

Analysis of Multifractal and Organization/Order Structure in Suomi-NPP VIIRS Normalized Difference Vegetation Index Series of Wildfire Affected and Unaffected Sites by Using the Multifractal Detrended Fluctuation Analysis and the Fisher-Shannon Analysis.

The analysis of vegetation dynamics affected by wildfires contributes to the understanding of ecological changes under disturbances. The use of the Normalized Difference Vegetation Index (NDVI) of satellite time series can effectively contribute to this investigation. In this paper, we employed the methods of multifractal detrended fluctuation analysis (MFDFA) and Fisher-Shannon (FS) analysis to investigate the NDVI series acquired from the Visible Infrared Imaging Radiometer Suite (VIIRS) of the Suomi National Polar-Orbiting Partnership (Suomi-NPP). Four study sites that were covered by two different types of vegetation were analyzed, among them two sites were affected by a wildfire (the Camp Fire, 2018). Our findings reveal that the wildfire increases the heterogeneity of the NDVI time series along with their organization structure. Furthermore, the fire-affected and fire-unaffected pixels are quite well separated through the range of the generalized Hurst exponents and the FS information plane. The analysis could provide deeper insights on the temporal dynamics of vegetation that are induced by wildfire.

Visibility graph analysis of synthetic earthquakes generated by the Olami-Feder-Christensen spring-block model.

In this study, we investigate the relationship between topological and seismological parameters of earthquake sequences generated by the Olami-Feder-Christensen (OFC) [Olami et al., Phys. Rev. Lett. 68(8), 1244 (1992)] spring-block model and converted in undirected graphs by using the visibility graph method [Lacasa et al., Proc. Natl. Acad. Sci. U.S.A. 105(13), 4972-4975 (2008)]. In particular, we study the relationship between the Gutenberg-Richter b-value and the so-called K-M slope, which describes the relationship between magnitudes and connectivity degrees. This relationship was found to follow a rather universal law in observational earthquake sequences, and, thus, in the present work, we aim at verifying such universality also in earthquake sequences generated by the OFC spring-block model. We found that for ⟨b⟩ between approximately 1 and 2, which is nearly the range of variation for most of the real seismicity cases observed worldwide, the relationship between ⟨b⟩ and ⟨K-M slope⟩ does not depend on the lattice size L. Furthermore, the slope of the regression line between ⟨b⟩ and ⟨K-M slope⟩ in the range of ⟨b⟩ between 1 and 2 changes with the definition of magnitude and the length of the earthquake sequence.

Clustering of extreme events in time series generated by the fractional Ornstein-Uhlenbeck equation.

We analyze the time clustering phenomenon in sequences of extremes of time series generated by the fractional Ornstein-Uhlenbeck (fO-U) equation as the source of long-term correlation. We used the percentile-based definition of extremes based on the crossing theory or run theory, where a run is a sequence of L contiguous values above a given percentile. Thus, a sequence of extremes becomes a point process in time, being the time of occurrence of the extreme the starting time of the run. We investigate the relationship between the Hurst exponent related to the time series generated by the fO-U equation and three measures of time clustering of the corresponding extremes defined on the base of the 95th percentile. Our results suggest that for persistent pure fractional Gaussian noise, the sequence of the extremes is clusterized, while extremes obtained by antipersistent or Markovian pure fractional Gaussian noise seem to behave more regularly or Poissonianly. However, for the fractional Ornstein-Uhlenbeck equation, the clustering of extremes is evident even for antipersistent and Markovian cases. This is a result of short range correlations caused by differential and drift terms. The drift parameter influences the extremes clustering effect-it drops with increasing value of the parameter.

Community detection analysis in wind speed-monitoring systems using mutual information-based complex network.

A mutual information-based weighted network representation of a wide wind speed-monitoring system in Switzerland was analyzed in order to detect communities. Two communities have been revealed, corresponding to two clusters of sensors situated, respectively, on the Alps and on the Jura-Plateau that define the two major climatic zones of Switzerland. The silhouette measure is used to evaluate the obtained communities and confirm the membership of each sensor to its cluster.

Fisher-Shannon Complexity Analysis of High-Frequency Urban Wind Speed Time Series.

One-hertz wind time series recorded at different levels (from 1.5-25.5 m) in an urban area are investigated by using the Fisher-Shannon (FS) analysis. FS analysis is a well-known method to gain insight into the complex behavior of nonlinear systems, by quantifying the order/disorder properties of time series. Our findings reveal that the FS complexity, defined as the product between the Fisher information measure and the Shannon entropy power, decreases with the height of the anemometer from the ground, suggesting a height-dependent variability in the order/disorder features of the high-frequency wind speed measured in urban layouts. Furthermore, the correlation between the FS complexity of wind speed and the daily variance of the ambient temperature shows a similar decrease with the height of the wind sensor. Such correlation is larger for the lower anemometers, indicating that ambient temperature is an important forcing of the wind speed variability in the vicinity of the ground.

Relation between HVG-irreversibility and persistence in the modified Langevin equation.

In this study, we investigate the relationship between persistence/antipersistence and time-irreversibility by using the Kullback-Leibler Divergence (KLD) in the directed Horizontal Visibility Graph applied to a new modified Langevin equation with persistence parameter d. A non-trivial relationship KLD(d) was found, characterized by a non-symmetric shape, which suggests that time-irreversibility increases with the degree of persistence or antipersistence. The analysis is applied to the population growth model, where the level of irreversibility may represent important features of the population dynamics, like its stability and ecosystem health.

Long-range fluctuations and multifractality in connectivity density time series of a wind speed monitoring network.

This paper studies the daily connectivity time series of a wind speed-monitoring network using multifractal detrended fluctuation analysis. It investigates the long-range fluctuation and multifractality in the residuals of the connectivity time series. Our findings reveal that the daily connectivity of the correlation-based network is persistent for any correlation threshold. Further, the multifractality degree is higher for larger absolute values of the correlation threshold.

Detrended fluctuation analysis of the Ornstein-Uhlenbeck process: Stationarity versus nonstationarity.

The stationary/nonstationary regimes of time series generated by the discrete version of the Ornstein-Uhlenbeck equation are studied by using the detrended fluctuation analysis. Our findings point out to the prevalence of the drift parameter in determining the crossover time between the nonstationary and stationary regimes. The fluctuation functions coincide in the nonstationary regime for a constant diffusion parameter, and in the stationary regime for a constant ratio between the drift and diffusion stochastic forces. In the generalized Ornstein-Uhlenbeck equations, the Hurst exponent H influences the crossover time that increases with the decrease of H.

Multifractal analysis of visibility graph-based Ito-related connectivity time series.

In this study, we investigate multifractal properties of connectivity time series resulting from the visibility graph applied to normally distributed time series generated by the Ito equations with multiplicative power-law noise. We show that multifractality of the connectivity time series (i.e., the series of numbers of links outgoing any node) increases with the exponent of the power-law noise. The multifractality of the connectivity time series could be due to the width of connectivity degree distribution that can be related to the exit time of the associated Ito time series. Furthermore, the connectivity time series are characterized by persistence, although the original Ito time series are random; this is due to the procedure of visibility graph that, connecting the values of the time series, generates persistence but destroys most of the nonlinear correlations. Moreover, the visibility graph is sensitive for detecting wide "depressions" in input time series.

Multifractal analysis of time series generated by discrete Ito equations.

In this study, we show that discrete Ito equations with short-tail Gaussian marginal distribution function generate multifractal time series. The multifractality is due to the nonlinear correlations, which are hidden in Markov processes and are generated by the interrelation between the drift and the multiplicative stochastic forces in the Ito equation. A link between the range of the generalized Hurst exponents and the mean of the squares of all averaged net forces is suggested.

Relationship between the frequency magnitude distribution and the visibility graph in the synthetic seismicity generated by a simple stick-slip system with asperities.

By using the method of the visibility graph (VG) the synthetic seismicity generated by a simple stick-slip system with asperities is analysed. The stick-slip system mimics the interaction between tectonic plates, whose asperities are given by sandpapers of different granularity degrees. The VG properties of the seismic sequences have been put in relationship with the typical seismological parameter, the b-value of the Gutenberg-Richter law. Between the b-value of the synthetic seismicity and the slope of the least square line fitting the k-M plot (relationship between the magnitude M of each synthetic event and its connectivity degree k) a close linear relationship is found, also verified by real seismicity.

Scaling and correlations in the dynamics of forest-fire occurrence.

Forest-fire waiting times, defined as the time between successive fires above a certain size in a given region, are obtained for Italy. The probability densities of the waiting times are found to verify a scaling law, despite that fact that the distribution of fire sizes is not a power law. The meaning of such behavior in terms of the possible self-similarity of the process in a nonstationary system is discussed. We find that the scaling law arises as a consequence of the stationarity of fire sizes and the existence of a nontrivial "instantaneous" scaling law, sustained by the correlations of the process; as a consequence, the nonstationary Poisson process model does not account for all the complexity of the structure of fire occurrence.