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Complexity and Nonlinear Dynamics in the Geosciences: Methods and Applications

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A special issue of Entropy (ISSN 1099-4300). This special issue belongs to the section "Multidisciplinary Applications".

Deadline for manuscript submissions: closed (28 February 2023) | Viewed by 19331

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Special Issue Editor

Dr. Luciano Telesca

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Guest Editor

Institute of Methodologies for Environmental Analysis, National Research Council, 85050 Tito, PZ, Italy
Interests: geophysical time series analysis; statistical methods for the investigation of geophysical processes; point processes; fractals and multifractals; graphs and networks; complexity; information theory
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Natural processes are complex, and thus suited methodologies are required to investigate their inner time dynamics. Statistical physics and mechanics have been applied to better our understanding of geosciences and natural hazards, contributing to a better comprehension of Earth processes. Fractal, informational, and topological methods represent just a few of the existing approaches that can elucidate the dynamical and statistical features of natural phenomena. Seismic, hydrologic, atmospheric, vegetational, land surface processes, etc., are all characterized by complexity, and generally feature nonlinearity, nonstationarity, and heterogeneity that could be revealed and interpreted with proper statistical methodologies.

This Special Issue aims to collect papers considering the diverse aspects of complexity in geosciences and natural hazards. Original research and reviews focused on the application of standard and advanced statistical methodologies for the understanding of complex geophysical systems and natural phenomena will be considered for this Special Issue.

Dr. Luciano Telesca
Guest Editor

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Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

complexity
fractals and multifractals
time series analysis
networks and graphs
information theory
chaos
signal and image processing
statistics
remote sensing

Published Papers (13 papers)

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Research

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13 pages, 1435 KiB

Open AccessArticle

Modeling Exact Frequency-Energy Distribution for Quakes by a Probabilistic Cellular Automaton

by Mariusz Białecki, Mateusz Gałka, Arpan Bagchi and Jacek Gulgowski

Entropy 2023, 25(5), 819; https://doi.org/10.3390/e25050819 - 19 May 2023

Cited by 1 | Viewed by 866

Abstract

We develop the notion of Random Domino Automaton, a simple probabilistic cellular automaton model for earthquake statistics, in order to provide a mechanistic basis for the interrelation of Gutenberg–Richter law and Omori law with the waiting time distribution for earthquakes. In this work, we provide a general algebraic solution to the inverse problem for the model and apply the proposed procedure to seismic data recorded in the Legnica-Głogów Copper District in Poland, which demonstrate the adequacy of the method. The solution of the inverse problem enables adjustment of the model to localization-dependent seismic properties manifested by deviations from Gutenberg–Richter law. Full article

(This article belongs to the Special Issue Complexity and Nonlinear Dynamics in the Geosciences: Methods and Applications)

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16 pages, 2953 KiB

Open AccessArticle

On the Possibility of Reproducing Utsu’s Law for Earthquakes with a Spring-Block SOC Model

by Alfredo Salinas-Martínez, Jennifer Perez-Oregon, Ana María Aguilar-Molina, Alejandro Muñoz-Diosdado and Fernando Angulo-Brown

Entropy 2023, 25(5), 816; https://doi.org/10.3390/e25050816 - 18 May 2023

Cited by 1 | Viewed by 957

Abstract

The Olami, Feder and Christensen (OFC) spring-block model has proven to be a powerful tool for analyzing and comparing synthetic and real earthquakes. This work proposes the possible reproduction of Utsu’s law for earthquakes in the OFC model. Based on our previous works, several simulations characterizing real seismic regions were performed. We located the maximum earthquake in these regions and applied Utsu’s formulae to identify a possible aftershock area and made comparisons between synthetic and real earthquakes. The research compares several equations to calculate the aftershock area and proposes a new one with the available data. Subsequently, the team performed new simulations and chose a mainshock to analyze the behavior of the surrounding events, so as to identify whether they could be catalogued as aftershocks and relate them to the aftershock area previously determined using the formula proposed. Additionally, the spatial location of those events was considered in order to classify them as aftershocks. Finally, we plot the epicenters of the mainshock, and the possible aftershocks comprised in the calculated area resembling the original work of Utsu. Having analyzed the results, it is likely to say that Utsu’s law is reproducible using a spring-block model with a self-organized criticality (SOC) model. Full article

(This article belongs to the Special Issue Complexity and Nonlinear Dynamics in the Geosciences: Methods and Applications)

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19 pages, 8870 KiB

Open AccessArticle

Multifractal Properties of Time Series of Synthetic Earthquakes Obtained from a Spring-Block Model

by Ana M. Aguilar-Molina, Alejandro Muñoz-Diosdado, Alfredo Salinas Martínez and Fernando Angulo-Brown

Entropy 2023, 25(5), 773; https://doi.org/10.3390/e25050773 - 09 May 2023

Viewed by 928

Abstract

With the spring-block model proposed by Olami, Feder, and Christensen (OFC), we obtained a time series of synthetic earthquakes with different values of the conservation level (

β

), which measures the fraction of the energy that a relaxing block passes to its [...] Read more.

With the spring-block model proposed by Olami, Feder, and Christensen (OFC), we obtained a time series of synthetic earthquakes with different values of the conservation level (

β

), which measures the fraction of the energy that a relaxing block passes to its neighbors. The time series have multifractal characteristics, and we analyzed them with the Chhabra and Jensen method. We calculated the width, symmetry, and curvature parameters for each spectrum. As the value of conservation level increases, the spectra widen, the symmetric parameter increases, and the curvature around the maximum of the spectra decreases. In a long series of synthetic seismicity, we located earthquakes of the greatest magnitude and built overlapping windows before and after them. For the time series in each window, we performed multifractal analysis to obtain multifractal spectra. We also calculated the width, symmetry, and curvature around the maximum of the multifractal spectrum. We followed the evolution of these parameters before and after large earthquakes. We found that the multifractal spectra had greater widths, were less skewed to the left, and were very pointed around the maximum before rather than after large earthquakes. We studied and calculated the same parameters and found the same results in the analysis of the Southern California seismicity catalog. This suggests that there seems to be a process of preparation for a great earthquake and that its dynamics are different from the one that occurs after this mainshock based on the behavior of the parameters mentioned before. Full article

(This article belongs to the Special Issue Complexity and Nonlinear Dynamics in the Geosciences: Methods and Applications)

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15 pages, 19902 KiB

Open AccessArticle

Acoustic Emissions in Rock Deformation and Failure: New Insights from Q-Statistical Analysis

by Sergio C. Vinciguerra, Annalisa Greco, Alessandro Pluchino, Andrea Rapisarda and Constantino Tsallis

Entropy 2023, 25(4), 701; https://doi.org/10.3390/e25040701 - 21 Apr 2023

Cited by 1 | Viewed by 1216

Abstract

We propose a new statistical analysis of the Acoustic Emissions (AE) produced in a series of triaxial deformation experiments leading to fractures and failure of two different rocks, namely, Darley Dale Sandstone (DDS) and AG Granite (AG). By means of q-statistical formalism, we are able to characterize the pre-failure processes in both types of rocks. In particular, we study AE inter-event time and AE inter-event distance distributions. Both of them can be reproduced with q-exponential curves, showing universal features that are observed here for the first time and could be important in order to understand more in detail the dynamics of rock fractures. Full article

(This article belongs to the Special Issue Complexity and Nonlinear Dynamics in the Geosciences: Methods and Applications)

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22 pages, 7946 KiB

Open AccessArticle

Complexity of Recent Earthquake Swarms in Greece in Terms of Non-Extensive Statistical Physics

by Eirini Sardeli, Georgios Michas, Kyriaki Pavlou, Filippos Vallianatos, Andreas Karakonstantis and Georgios Chatzopoulos

Entropy 2023, 25(4), 667; https://doi.org/10.3390/e25040667 - 16 Apr 2023

Cited by 3 | Viewed by 1374

Abstract

Greece exhibits the highest seismic activity in Europe, manifested in intense seismicity with large magnitude events and frequent earthquake swarms. In the present work, we analyzed the spatiotemporal properties of recent earthquake swarms that occurred in the broader area of Greece using the Non-Extensive Statistical Physics (NESP) framework, which appears suitable for studying complex systems. The behavior of complex systems, where multifractality and strong correlations among the elements of the system exist, as in tectonic and volcanic environments, can adequately be described by Tsallis entropy (S_q), introducing the Q-exponential function and the entropic parameter q that expresses the degree of non-additivity of the system. Herein, we focus the analysis on the 2007 Trichonis Lake, the 2016 Western Crete, the 2021–2022 Nisyros, the 2021–2022 Thiva and the 2022 Pagasetic Gulf earthquake swarms. Using the seismicity catalogs for each swarm, we investigate the inter-event time (T) and distance (D) distributions with the Q-exponential function, providing the q_T and q_D entropic parameters. The results show that q_T varies from 1.44 to 1.58, whereas q_D ranges from 0.46 to 0.75 for the inter-event time and distance distributions, respectively. Furthermore, we describe the frequency–magnitude distributions with the Gutenberg–Richter scaling relation and the fragment–asperity model of earthquake interactions derived within the NESP framework. The results of the analysis indicate that the statistical properties of earthquake swarms can be successfully reproduced by means of NESP and confirm the complexity and non-additivity of the spatiotemporal evolution of seismicity. Finally, the superstatistics approach, which is closely connected to NESP and is based on a superposition of ordinary local equilibrium statistical mechanics, is further used to discuss the temporal patterns of the earthquake evolution during the swarms. Full article

(This article belongs to the Special Issue Complexity and Nonlinear Dynamics in the Geosciences: Methods and Applications)

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18 pages, 1179 KiB

Open AccessArticle

Decision-Making Teaching Practice Based on the Maximum Entropy Method in a Water Engineering Economics Course

by Runjuan Zhou, Yingke Sun, Shuai Shao, Kuo Zhang and Ming Zhang

Entropy 2023, 25(3), 441; https://doi.org/10.3390/e25030441 - 02 Mar 2023

Viewed by 1246

Abstract

The purpose of this paper is to put forward a decision model with wide applicability and differentiated decision scheme scores so as to improve the ability of students to learn during a water engineering economics course. The main novelty and contributions of this paper are that the multi-attribute decision-making method proposed is more objective and does not require rich subjective experience from decision-makers in the application process, which is particularly suitable for beginners who are learning in a water engineering economics course. The method involves standardizing each index value of the decision scheme first, constructing the objective function of maximum entropy distribution, calculating the weight of each index by the genetic algorithm, and finally ranking the pros and cons of the scheme according to the score of each scheme. The example results of three water engineering scheme decisions show that the maximum entropy model proposed in this paper can achieve reasonable decision results, and there is a large degree of differentiation between the decision schemes. The proposed scheme, a decision maximum entropy model, has wide applicability, can improve the rationality of the decisions made regarding water engineering schemes, and can be popularized and applied when teaching decision-making in water engineering economics courses. Full article

(This article belongs to the Special Issue Complexity and Nonlinear Dynamics in the Geosciences: Methods and Applications)

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17 pages, 1597 KiB

Open AccessArticle

Characterizing the Solar Activity Using the Visibility Graph Method

by Tomás Zurita-Valencia and Víctor Muñoz

Entropy 2023, 25(2), 342; https://doi.org/10.3390/e25020342 - 13 Feb 2023

Cited by 1 | Viewed by 1437

Abstract

In this paper, the Sun and its behavior are studied by means of complex networks. The complex network was built using the Visibility Graph algorithm. This method maps time series into graphs in which every element of the time series is considered as a node and a visibility criterion is defined in order to connect them. Using this method, we construct complex networks for magnetic field and sunspots time series encompassing four solar cycles, and various measures such as degree, clustering coefficient, mean path length, betweenness centrality, eigenvector centrality and decay exponents were calculated. In order to study the system in several time scales, we perform both a global, where the network contains information on the four solar cycles, and a local analysis, involving moving windows. Some metrics correlate with solar activity, while others do not. Interestingly, those metric which seem to respond to varying levels of solar activity in the global analysis, also do in the moving windows analysis. Our results suggest that complex networks can provide a useful way to follow solar activity, and reveal new features on solar cycles. Full article

(This article belongs to the Special Issue Complexity and Nonlinear Dynamics in the Geosciences: Methods and Applications)

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18 pages, 6720 KiB

Open AccessArticle

Wavelet Entropy: A New Tool for Edge Detection of Potential Field Data

by Divyanshu Dwivedi, Ashutosh Chamoli and Sandip Kumar Rana

Entropy 2023, 25(2), 240; https://doi.org/10.3390/e25020240 - 28 Jan 2023

Cited by 4 | Viewed by 1593

Abstract

Subsurface source boundary identification is a major step in the interpretation of potential field anomalies in geophysical exploration. We investigated the behavior of wavelet space entropy over the boundaries of 2D potential field source edges. We tested the robustness of the method for complex source geometries with distinct source parameters of prismatic bodies. We further validated the behavior with two datasets by delineating the edges of (i) the magnetic anomalies due to the popular Bishop model and (ii) the gravity anomalies of the Delhi fold belt region, India. The results showed prominent signatures for the geological boundaries. Our findings indicate sharp changes in the wavelet space entropy values corresponding to the source edges. The effectiveness of wavelet space entropy was compared with the established edge detection techniques. The findings can help with a variety of geophysical source characterization problems. Full article

(This article belongs to the Special Issue Complexity and Nonlinear Dynamics in the Geosciences: Methods and Applications)

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17 pages, 8138 KiB

Open AccessArticle

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

by Luciano Telesca, Angelo Aromando, Farid Faridani, Michele Lovallo, Gianfranco Cardettini, Nicodemo Abate, Giancarlo Papitto and Rosa Lasaponara

Entropy 2022, 24(12), 1784; https://doi.org/10.3390/e24121784 - 06 Dec 2022

Cited by 7 | Viewed by 1839

Abstract

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. Full article

(This article belongs to the Special Issue Complexity and Nonlinear Dynamics in the Geosciences: Methods and Applications)

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22 pages, 6259 KiB

Open AccessArticle

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

by Rui Ba, Michele Lovallo, Weiguo Song, Hui Zhang and Luciano Telesca

Entropy 2022, 24(12), 1748; https://doi.org/10.3390/e24121748 - 29 Nov 2022

Cited by 1 | Viewed by 2074

Abstract

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. Full article

(This article belongs to the Special Issue Complexity and Nonlinear Dynamics in the Geosciences: Methods and Applications)

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15 pages, 8469 KiB

Open AccessArticle

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

by Luciano Telesca, Anh Tuan Thai, Michele Lovallo and Dinh Trong Cao

Entropy 2022, 24(11), 1620; https://doi.org/10.3390/e24111620 - 07 Nov 2022

Cited by 4 | Viewed by 1215

Abstract

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. Full article

(This article belongs to the Special Issue Complexity and Nonlinear Dynamics in the Geosciences: Methods and Applications)

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22 pages, 1179 KiB

Open AccessArticle

Evaluating Ecohydrological Model Sensitivity to Input Variability with an Information-Theory-Based Approach

by Mozhgan A. Farahani, Alireza Vahid and Allison E. Goodwell

Entropy 2022, 24(7), 994; https://doi.org/10.3390/e24070994 - 18 Jul 2022

Cited by 4 | Viewed by 2086

Abstract

Ecohydrological models vary in their sensitivity to forcing data and use available information to different extents. We focus on the impact of forcing precision on ecohydrological model behavior particularly by quantizing, or binning, time-series forcing variables. We use rate-distortion theory to quantize time-series forcing variables to different precisions. We evaluate the effect of different combinations of quantized shortwave radiation, air temperature, vapor pressure deficit, and wind speed on simulated heat and carbon fluxes for a multi-layer canopy model, which is forced and validated with eddy covariance flux tower observation data. We find that the model is more sensitive to radiation than meteorological forcing input, but model responses also vary with seasonal conditions and different combinations of quantized inputs. While any level of quantization impacts carbon flux similarly, specific levels of quantization influence heat fluxes to different degrees. This study introduces a method to optimally simplify forcing time series, often without significantly decreasing model performance, and could be applied within a sensitivity analysis framework to better understand how models use available information. Full article

(This article belongs to the Special Issue Complexity and Nonlinear Dynamics in the Geosciences: Methods and Applications)

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Review

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19 pages, 6729 KiB

Open AccessReview

Complexity in Geophysical Time Series of Strain/Fracture at Laboratory and Large Dam Scales: Review

by Tamaz Chelidze, Teimuraz Matcharashvili, Ekaterine Mepharidze and Nadezhda Dovgal

Entropy 2023, 25(3), 467; https://doi.org/10.3390/e25030467 - 07 Mar 2023

Cited by 2 | Viewed by 1272

Abstract

One of the interesting directions of complexity theory is the investigation of the synchronization of mechanical behavior of large-scale systems by weak forcing, which is one of manifestations of nonlinearity/complexity of a system. The effect of periodic weak mechanical or electromagnetic forcing leading to synchronization was studied on the laboratory load–spring system as well as on a big dam’s strain data. Due to synchronization, the phase space structure of the forced system strongly depends on the weak forcing intensity–determinism show itself in the recurrence of definite states of the forced system. The nonlinear dynamics of tilts/strains/seismicity near grand dams reflect both the complexity of the mentioned time series, connected with the natural agents (regional and local geodynamics), which were presented even before dam erection, as well as the effects of the water level (WL) variation in the reservoir, which is a quasi-periodic forcing superimposed on the natural geodynamic background. Both these effects are documented by the almost half-century of observations at the large Enguri Dam. The obtained data on the dynamics of strain/seismicity near a large dam can be used for the assessment of the possible risks, connected with the abrupt change of routine dynamics of construction. Full article

(This article belongs to the Special Issue Complexity and Nonlinear Dynamics in the Geosciences: Methods and Applications)

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