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Complexity and Statistical Physics Approaches to Earthquakes

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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 (17 September 2023) | Viewed by 21112

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Dr. Georgios Michas

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Guest Editor

Department of Geology and Geoenvironment, National and Kapodistrian University of Athens, 15784 Athens, Greece
Interests: seismology; geophysics; tectonics; earthquake physics; complexity; statistical seismology; nonlinear dynamics; statistical physics

Special Issue Information

Dear Colleagues,

In an ever-growing world, there is an increasing and urgent demand to estimate natural hazards more efficiently. A crucial concern to this challenging task is the mitigation of earthquake risk. Earthquake occurrence is inherently a complex phenomenon manifested in the nonlinear dynamics that form the earthquake generation process. Earthquakes interact over a wide range of spatial and temporal scales to generate new events, while the coupling of stress interactions with other aseismic processes, such as fluid flow, poroelastic effects, and aseismic slip, may further reduce the frictional strength of faults, triggering more earthquakes. As such, earthquakes are considered a critical-point phenomenon, exhibiting nonlinearity, self-organized criticality, scaling, clustering, fractal/multifractal structures, and long-range interactions. The analysis of the earthquake phenomenon in the light of complexity theory is thus ubiquitous, and mathematical tools arising from statistical physics offer a consistent theoretical framework to better understand earthquake occurrence. With the significant increase in the number of new data in recent years, these modern tools may provide novel and substantial insights into the physics of earthquakes, with an ultimate goal of mitigating earthquake risk more effectively.

This Special Issue welcomes new contributions and reviews arising from, but not limited to, the fields of complexity theory and statistical physics approaches to earthquakes, random walks, nonlinear analysis, pattern recognition, stochastic models and statistical properties of seismicity, and earthquake forecasting.

Dr. Georgios Michas
Guest Editor

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Keywords

earthquake physics
complexity
statistical physics
nonlinear dynamics
stochastic models
time series analysis
random walks
earthquake triggering
statistical properties
fractal/multifractal structures
earthquake forecasting

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Published Papers (12 papers)

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Editorial

Jump to: Research

3 pages, 165 KiB

Open AccessEditorial

Complexity and Statistical Physics Approaches to Earthquakes

by Georgios Michas

Entropy 2024, 26(1), 59; https://doi.org/10.3390/e26010059 - 10 Jan 2024

Viewed by 1547

Abstract

This Special Issue of Entropy, “Complexity and Statistical Physics Approaches to Earthquakes”, sees the successful publication of 11 original scientific articles [...] Full article

(This article belongs to the Special Issue Complexity and Statistical Physics Approaches to Earthquakes)

Research

Jump to: Editorial

15 pages, 3770 KiB

Open AccessFeature PaperArticle

Spatiotemporal Variations of the Frequency–Magnitude Distribution in the 2019 M_w 7.1 Ridgecrest, California, Earthquake Sequence

by Eirini Sardeli, Georgios Michas, Kyriaki Pavlou and Filippos Vallianatos

Entropy 2023, 25(12), 1612; https://doi.org/10.3390/e25121612 - 1 Dec 2023

Viewed by 1289

Abstract

Significant seismic activity has been witnessed in the area of Ridgecrest (Southern California) over the past 40 years, with the largest being the M_w 5.8 event on 20 September 1995. In July 2019, a strong earthquake of M_w 7.1, preceded by a M_w 6.4 foreshock, impacted Ridgecrest. The mainshock triggered thousands of aftershocks that were thoroughly documented along the activated faults. In this study, we analyzed the spatiotemporal variations of the frequency–magnitude distribution in the area of Ridgecrest using the fragment–asperity model derived within the framework of non-extensive statistical physics (NESP), which is well-suited for investigating complex dynamic systems with scale-invariant properties, multi-fractality, and long-range interactions. Analysis was performed for the entire duration, as well as within various time windows during 1981–2022, in order to estimate the q_M parameter and to investigate how these variations are related to the dynamic evolution of seismic activity. In addition, we analyzed the spatiotemporal q_M value distributions along the activated fault zone during 1981–2019 and during each month after the occurrence of the M_w 7.1 Ridgecrest earthquake. The results indicate a significant increase in the q_M parameter when large-magnitude earthquakes occur, suggesting the system’s transition in an out-of-equilibrium phase and its preparation for seismic energy release. Full article

(This article belongs to the Special Issue Complexity and Statistical Physics Approaches to Earthquakes)

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14 pages, 1077 KiB

Open AccessArticle

Solar Flare 1/f Fluctuations from Amplitude-Modulated Five-Minute Oscillation

by Masahiro Morikawa and Akika Nakamichi

Entropy 2023, 25(12), 1593; https://doi.org/10.3390/e25121593 - 28 Nov 2023

Cited by 1 | Viewed by 1308

Abstract

We first report that the solar flare time sequence exhibits a fluctuation characterized by its power spectral density being inversely proportional to the signal frequency. This is the 1/f fluctuation, or pink noise, observed ubiquitously in nature. Using GOES16 data, we found that [...] Read more.

E \leq E_{m e a n}

) display 1/f fluctuations, whereas high-energy flares (

E > E_{m e a n}

) show a flat spectrum. Furthermore, we found that the timing sequence of the flares reveals clearer 1/f fluctuations. These observations suggest that the solar flare 1/f fluctuations are associated with low-energy phenomena. We investigated the origin of these 1/f fluctuations based on our recent hypothesis: 1/f fluctuations arise from amplitude modulation and demodulation. We propose that this amplitude modulation is encoded by the resonance with the solar five-minute oscillation (SFO) and demodulated by magnetic reconnections. We partially demonstrate this scenario by analyzing the SFO eigenmodes resolving the frequency degeneration in the azimuthal order number m using the solar rotation and resonance. Given the robust nature of 1/f fluctuations, we speculated that the solar flare 1/f fluctuations may be inherited by the various phenomena around the Sun, such as the sunspot numbers and cosmic rays. In addition, we draw parallels between solar flares and earthquakes, both exhibiting 1/f fluctuations. Interestingly, the analysis applied to solar flares can also be adapted to earthquakes if we read the SFO as Earth’s free oscillation and magnetic reconnections as fault ruptures. Moreover, we point out the possibility that the same analysis also applies to the activity of a black hole/disk system if we read the SFO as the quasi-periodic oscillation of a black hole. Full article

(This article belongs to the Special Issue Complexity and Statistical Physics Approaches to Earthquakes)

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16 pages, 1181 KiB

Open AccessFeature PaperArticle

Connection between Variations of the Probability Distribution of the Recurrence Time and Phases of the Seismic Activity

by Elisa Varini and Renata Rotondi

Entropy 2023, 25(10), 1441; https://doi.org/10.3390/e25101441 - 12 Oct 2023

Cited by 1 | Viewed by 1716

Abstract

The probability distribution of the interevent time between two successive earthquakes has been the subject of numerous studies for its key role in seismic hazard assessment. In recent decades, many distributions have been considered, and there has been a long debate about the possible universality of the shape of this distribution when the interevent times are properly rescaled. In this work, we aim to discover if there is a link between the different phases of a seismic cycle and the variations in the distribution that best fits the interevent times. To do this, we consider the seismic activity related to the

M_{w}

6.1 L’Aquila earthquake that occurred on 6 April 2009 in central Italy by analyzing the sequence of events recorded from April 2005 to July 2009, and then the seismic activity linked to the sequence of the Amatrice-Norcia earthquakes of

M_{w}

6 and 6.5, respectively, and recorded in the period from January 2009 to June 2018. We take into account some of the most studied distributions in the literature: q-exponential, q-generalized gamma, gamma and exponential distributions and, according to the Bayesian paradigm, we compare the value of their posterior marginal likelihood in shifting time windows with a fixed number of data. The results suggest that the distribution providing the best performance changes over time and its variations may be associated with different phases of the seismic crisis. Full article

(This article belongs to the Special Issue Complexity and Statistical Physics Approaches to Earthquakes)

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13 pages, 1531 KiB

Open AccessArticle

Viscoelastic Slider Blocks as a Model for a Seismogenic Fault

by Charlotte A. Motuzas and Robert Shcherbakov

Entropy 2023, 25(10), 1419; https://doi.org/10.3390/e25101419 - 6 Oct 2023

Viewed by 1483

Abstract

In this work, a model is proposed to examine the role of viscoelasticity in the generation of simulated earthquake-like events. This model serves to investigate how nonlinear processes in the Earth’s crust affect the triggering and decay patterns of earthquake sequences. These synthetic earthquake events are numerically simulated using a slider-block model containing viscoelastic standard linear solid (SLS) elements to reproduce the dynamics of an earthquake fault. The simulated system exhibits elements of self-organized criticality, and results in the generation of avalanches that behave similarly to naturally occurring seismic events. The model behavior is analyzed using the Epidemic-Type Aftershock Sequence (ETAS) model, which suitably represents the observed triggering and decay patterns; however, parameter estimates deviate from those resulting from natural aftershock sequences. Simulated aftershock sequences from this model are characterized by slightly larger p-values, indicating a faster-than-normal decay of aftershock rates within the system. The ETAS fit, along with realistic simulated frequency-size distributions, supports the inclusion of viscoelastic rheology to model the seismogenic fault dynamics. Full article

(This article belongs to the Special Issue Complexity and Statistical Physics Approaches to Earthquakes)

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19 pages, 13870 KiB

Open AccessArticle

Defining the Scale to Build Complex Networks with a 40-Year Norwegian Intraplate Seismicity Dataset

by Claudia Pavez-Orrego and Denisse Pastén

Entropy 2023, 25(9), 1284; https://doi.org/10.3390/e25091284 - 31 Aug 2023

Cited by 1 | Viewed by 1123

Abstract

We present a new complex network-based study focused on intraplate earthquakes recorded in southern Norway during the period 1980–2020. One of the most recognized limitations of spatial complex network procedures and analyses concerns the definition of adequate cell size, which is the focus of this approach. In the present study, we analyze the influence of observational errors of hypocentral and epicentral locations of seismic events in the construction of a complex network, looking for the best cell size to build it and to develop a basis for interpreting the results in terms of the structure of the complex network in this seismic region. We focus the analysis on the degree distribution of the complex networks. We observed a strong result of the cell size for the slope of the degree distribution of the nodes, called the critical exponent

γ

. Based on the Abe–Suzuki method, the slope (

γ

) showed a negligible variation between the construction of 3- and 2-dimensional complex networks. The results were also very similar for a complex network built with subsets of seismic events. These results suggest a weak influence of observational errors measured for the coordinates latitude, longitude, and depth in the outcomes obtained with this particular methodology and for this high-quality dataset. These results imply stable behavior of the complex network, which shows a structure of hubs for small values of the cell size and a more homogeneous degree distribution when the cell size increases. In all the analyses, the

γ

parameter showed smaller values of the error bars for greater values of the cell size. To keep the structure of hubs and small error bars, a better range of the side sizes was determined to be between 8 to 16 km. From now on, these values can be used as the most stable cell sizes to perform any kind of study concerning complex network studies in southern Norway. Full article

(This article belongs to the Special Issue Complexity and Statistical Physics Approaches to Earthquakes)

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11 pages, 295 KiB

Open AccessArticle

Aftershocks and Fluctuating Diffusivity

by Sumiyoshi Abe, Norikazu Suzuki and Dmitrii A. Tayurskii

Entropy 2023, 25(7), 989; https://doi.org/10.3390/e25070989 - 28 Jun 2023

Cited by 1 | Viewed by 1299

Abstract

The Omori-Utsu law shows the temporal power-law-like decrease of the frequency of earthquake aftershocks and, interestingly, is found in a variety of complex systems/phenomena exhibiting catastrophes. Now, it may be interpreted as a characteristic response of such systems to large events. Here, hierarchical dynamics with the fast and slow degrees of freedom is studied on the basis of the Fokker-Planck theory for the load-state distribution to formulate the law as a relaxation process, in which diffusion coefficient in the space of the load state is treated as a fluctuating slow variable. The evolution equation reduced from the full Fokker-Planck equation and its Green’s function are analyzed for the subdynamics governing the load state as the fast degree of freedom. It is shown that the subsystem has the temporal translational invariance in the logarithmic time, not in the conventional time, and consequently the aging phenomenon appears. Full article

(This article belongs to the Special Issue Complexity and Statistical Physics Approaches to Earthquakes)

15 pages, 29919 KiB

Open AccessArticle

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

by Davide Zaccagnino, Luciano Telesca, Onur Tan and Carlo Doglioni

Entropy 2023, 25(6), 835; https://doi.org/10.3390/e25060835 - 23 May 2023

Cited by 5 | Viewed by 2179

Abstract

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 Kahramanmaraş 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, C

_{V}

, 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 Kahramanmaraş seismic sequence. Full article

(This article belongs to the Special Issue Complexity and Statistical Physics Approaches to Earthquakes)

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18 pages, 5709 KiB

Open AccessArticle

Visibility Graph Analysis of the Seismic Activity of Three Areas of the Cocos Plate Mexican Subduction Where the Last Three Large Earthquakes (M > 7) Occurred in 2017 and 2022

by Alejandro Ramírez-Rojas, Elsa Leticia Flores-Márquez and Carlos Alejandro Vargas

Entropy 2023, 25(5), 799; https://doi.org/10.3390/e25050799 - 15 May 2023

Cited by 2 | Viewed by 1875

Abstract

The understanding of the dynamical behavior of seismic phenomena is currently an open problem, mainly because seismic series can be considered to be produced by phenomena exhibiting dynamic phase transitions; that is, with some complexity. For this purpose, the Middle America Trench in central Mexico is considered a natural laboratory for examining subduction because of its heterogenous natural structure. In this study, the Visibility Graph method was applied to study the seismic activity of three regions within the Cocos plate: the Tehuantepec Isthmus, the Flat slab and Michoacan, each one with a different level of seismicity. The method maps time series into graphs, and it is possible to connect the topological properties of the graph with the dynamical features underlying the time series. The seismicity analyzed was monitored in the three areas studied between 2010 and 2022. At the Flat Slab and Tehuantepec Isthmus, two intense earthquakes occurred on 7 and 19 September 2017, respectively, and, on 19 September 2022, another one occurred at Michoacan. The aim of this study was to determine the dynamical features and the possible differences between the three areas by applying the following method. First, the time evolution of the a- and b-values in the Gutenberg–Richter law was analyzed, followed by the relationship between the seismic properties and topological features using the VG method, the k–M slope and the characterization of the temporal correlations from the γ-exponent of the power law distribution, P(k) ∼ k^−γ, and its relationship with the Hurst parameter, which allowed us to identify the correlation and persistence of each zone. Full article

(This article belongs to the Special Issue Complexity and Statistical Physics Approaches to Earthquakes)

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22 pages, 5267 KiB

Open AccessArticle

Forecasting Strong Subsequent Earthquakes in Greece with the Machine Learning Algorithm NESTORE

by Eleni-Apostolia Anyfadi, Stefania Gentili, Piero Brondi and Filippos Vallianatos

Entropy 2023, 25(5), 797; https://doi.org/10.3390/e25050797 - 13 May 2023

Cited by 6 | Viewed by 2127

Abstract

Aftershocks of earthquakes can destroy many urban infrastructures and exacerbate the damage already inflicted upon weak structures. Therefore, it is important to have a method to forecast the probability of occurrence of stronger earthquakes in order to mitigate their effects. In this work, we applied the NESTORE machine learning approach to Greek seismicity from 1995 to 2022 to forecast the probability of a strong aftershock. Depending on the magnitude difference between the mainshock and the strongest aftershock, NESTORE classifies clusters into two types, Type A and Type B. Type A clusters are the most dangerous clusters, characterized by a smaller difference. The algorithm requires region-dependent training as input and evaluates performance on an independent test set. In our tests, we obtained the best results 6 h after the mainshock, as we correctly forecasted 92% of clusters corresponding to 100% of Type A clusters and more than 90% of Type B clusters. These results were also obtained thanks to an accurate analysis of cluster detection in a large part of Greece. The successful overall results show that the algorithm can be applied in this area. The approach is particularly attractive for seismic risk mitigation due to the short time required for forecasting. Full article

(This article belongs to the Special Issue Complexity and Statistical Physics Approaches to Earthquakes)

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12 pages, 3748 KiB

Open AccessArticle

Frequency Seismic Response for EEWS Testing on Uniaxial Shaking Table

by Codrin Donciu, Elena Serea and Marinel Costel Temneanu

Entropy 2023, 25(4), 655; https://doi.org/10.3390/e25040655 - 14 Apr 2023

Cited by 1 | Viewed by 1565

Abstract

Earthquake early warning systems are used as important tools in earthquake risk management, providing timely information to residents and both public and private emergency managers. By doing this, the potential impact of large magnitude seismic events is significantly reduced. These systems use seismic sensors in order to acquire real-time data for the weaker but fast moving P wave (usually the first 3–5 s of the earthquake) and specific algorithms to predict the magnitude and the arrival time of the slower but more destructive surface waves. Most of these projection algorithms make use only of the vertical component of the acceleration and need extensive training in earthquake simulators in order to enhance their performance. Therefore, a low-inertial-mass uniaxial shaking table is proposed and analyzed in terms of frequency response in this paper, providing an effective cost/control ratio and high daily duty cycle. Furthermore, with the large variety of prediction algorithms, which use different frequency ranges, a new concept of selective frequency band error is also introduced and discussed in this paper as being a necessary tool for the final assessment of magnitude estimation algorithm error. Full article

(This article belongs to the Special Issue Complexity and Statistical Physics Approaches to Earthquakes)

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14 pages, 3572 KiB

Open AccessArticle

Universal Non-Extensive Statistical Physics Temporal Pattern of Major Subduction Zone Aftershock Sequences

by Eleni-Apostolia Anyfadi, Sophia-Ekaterini Avgerinou, Georgios Michas and Filippos Vallianatos

Entropy 2022, 24(12), 1850; https://doi.org/10.3390/e24121850 - 19 Dec 2022

Cited by 7 | Viewed by 1801

Abstract

Large subduction-zone earthquakes generate long-lasting and wide-spread aftershock sequences. The physical and statistical patterns of these aftershock sequences are of considerable importance for better understanding earthquake dynamics and for seismic hazard assessments and earthquake risk mitigation. In this work, we analyzed the statistical properties of 42 aftershock sequences in terms of their temporal evolution. These aftershock sequences followed recent large subduction-zone earthquakes of M ≥ 7.0 with focal depths less than 70 km that have occurred worldwide since 1976. Their temporal properties were analyzed by investigating the probability distribution of the interevent times between successive aftershocks in terms of non-extensive statistical physics (NESP). We demonstrate the presence of a crossover behavior from power-law (q ≠ 1) to exponential (q = 1) scaling for greater interevent times. The estimated entropic q-values characterizing the observed distributions range from 1.67 to 1.83. The q-exponential behavior, along with the crossover behavior observed for greater interevent times, are further discussed in terms of superstatistics and in view of a stochastic mechanism with memory effects, which could generate the observed scaling patterns of the interevent time evolution in earthquake aftershock sequences. Full article

(This article belongs to the Special Issue Complexity and Statistical Physics Approaches to Earthquakes)

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