Stochastic modeling of injection induced seismicity based on the continuous time random walk model.

The spatiotemporal evolution of earthquakes induced by fluid injections into the subsurface can be erratic owing to the complexity of the physical process. To effectively mitigate the associated hazard and to draft appropriate regulatory strategies, a detailed understanding of how induced seismicity may evolve is needed. In this work, we build on the well-established continuous-time random walk (CTRW) theory to develop a purely stochastic framework that can delineate the essential characteristics of this process. We use data from the 2003 and 2012 hydraulic stimulations in the Cooper Basin geothermal field that induced thousands of microearthquakes to test and demonstrate the applicability of the model. Induced seismicity in the Cooper Basin shows all the characteristics of subdiffusion, as indicated by the fractional order power-law growth of the mean square displacement with time and broad waiting-time distributions with algebraic tails. We further use an appropriate master equation and the time-fractional diffusion equation to map the spatiotemporal evolution of seismicity. The results show good agreement between the model and the data regarding the peak earthquake concentration close to the two injection wells and the stretched exponential relaxation of seismicity with distance, suggesting that the CTRW model can be efficiently incorporated into induced seismicity forecasting.

Spatiotemporal Variations of the Frequency-Magnitude Distribution in the 2019 Mw 7.1 Ridgecrest, California, Earthquake Sequence.

Significant seismic activity has been witnessed in the area of Ridgecrest (Southern California) over the past 40 years, with the largest being the Mw 5.8 event on 20 September 1995. In July 2019, a strong earthquake of Mw 7.1, preceded by a Mw 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 qM parameter and to investigate how these variations are related to the dynamic evolution of seismic activity. In addition, we analyzed the spatiotemporal qM value distributions along the activated fault zone during 1981-2019 and during each month after the occurrence of the Mw 7.1 Ridgecrest earthquake. The results indicate a significant increase in the qM parameter when large-magnitude earthquakes occur, suggesting the system's transition in an out-of-equilibrium phase and its preparation for seismic energy release.

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

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 (Sq), 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 qT and qD entropic parameters. The results show that qT varies from 1.44 to 1.58, whereas qD 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.

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

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.

Cluster Analysis of Seismicity in the Eastern Gulf of Corinth Based on a Waveform Template Matching Catalog.

The Corinth Rift, in Central Greece, is one of the most seismically active areas in Europe. In the eastern part of the Gulf of Corinth, which has been the site of numerous large and destructive earthquakes in both historic and modern times, a pronounced earthquake swarm occurred in 2020-2021 at the Perachora peninsula. Herein, we present an in-depth analysis of this sequence, employing a high-resolution relocated earthquake catalog, further enhanced by the application of a multi-channel template matching technique, producing additional detections of over 7600 events between January 2020 and June 2021. Single-station template matching enriches the original catalog thirty-fold, providing origin times and magnitudes for over 24,000 events. We explore the variable levels of spatial and temporal resolution in the catalogs of different completeness magnitudes and also of variable location uncertainties. We characterize the frequency-magnitude distributions using the Gutenberg-Richter scaling relation and discuss possible b-value temporal variations that appear during the swarm and their implications for the stress levels in the area. The evolution of the swarm is further analyzed through spatiotemporal clustering methods, while the temporal properties of multiplet families indicate that short-lived seismic bursts, associated with the swarm, dominate the catalogs. Multiplet families present clustering effects at all time scales, suggesting triggering by aseismic factors, such as fluid diffusion, rather than constant stress loading, in accordance with the spatiotemporal migration patterns of seismicity.

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

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.

Estimation of Earthquake Early Warning Parameters for Eastern Gulf of Corinth and Western Attica Region (Greece). First Results.

The main goal of an Earthquake Early Warning System (EEWS) is to alert before the arrival of damaging waves using the first seismic arrival as a proxy, thus becoming an important operational tool for real-time seismic risk management on a short timescale. EEWSs are based on the use of scaling relations between parameters measured on the initial portion of the seismic signal after the arrival of the first wave. To explore the plausibility of EEWSs around the Eastern Gulf of Corinth and Western Attica, amplitude and frequency-based parameters, such as peak displacement (Pd), the integral of squared velocity (IV 2) and the characteristic period (τc), were analyzed. All parameters were estimated directly from the initial 3 s, 4 s, and 5 s signal windows (tw) after the P arrival. While further study is required on the behavior of the proxy quantities, we propose that the IV 2 parameter and the peak amplitudes of the first seconds of the P waves present significant stability and introduce the possibility of a future on-site EEWS for areas affected by earthquakes located in the Eastern Gulf of Corinth and Western Attica. Parameters related to regional-based EEWS need to be further evaluated.

Strong Ground Motion Sensor Network for Civil Protection Rapid Decision Support Systems.

Strong motion sensor networks deployed in metropolitan areas are able to provide valuable information for civil protection Decision Support Systems (DSSs) aiming to mitigate seismic risk and earthquake social-economic impact. To this direction, such a network is installed and real-time operated in Chania (Crete Island, Greece), city located in the vicinity of the seismically active south front of the Hellenic Subduction Zone. A blend of both traditional and advanced analysis techniques and interpretation methods of strong ground motion data are presented, studying indicative cases of Chania shaking due to earthquakes in the last couple years. The orientation independent spectral acceleration as well as the spatial distribution of the strong ground motion parameters such as the Peak Ground Acceleration (PGA), Peak Ground Velocity (PGV), Peak Ground Displacement (PGD) and Arias Ιntensity observed at the urban area of Chania are presented with the use of a Geographic Information System (GIS) environment. The results point to the importance of the strong ground motion networks as they can provide valuable information on earthquake hazards prior to and after detrimental seismic events to feed rapid systems supporting civil protection decisions for prevention and emergency response.

Complexity of Fracturing in Terms of Non-Extensive Statistical Physics: From Earthquake Faults to Arctic Sea Ice Fracturing.

Fracturing processes within solid Earth materials are inherently a complex phenomenon so that the underlying physics that control fracture initiation and evolution still remain elusive. However, universal scaling relations seem to apply to the collective properties of fracturing phenomena. In this article we present a statistical physics approach to fracturing based on the framework of non-extensive statistical physics (NESP). Fracturing phenomena typically present intermittency, multifractality, long-range correlations and extreme fluctuations, properties that motivate the NESP approach. Initially we provide a brief review of the NESP approach to fracturing and earthquakes and then we analyze stress and stress direction time series within Arctic sea ice. We show that such time series present large fluctuations and probability distributions with "fat" tails, which can exactly be described with the q-Gaussian distribution derived in the framework of NESP. Overall, NESP provide a consistent theoretical framework, based on the principle of entropy, for deriving the collective properties of fracturing phenomena and earthquakes.

Complex Electrical Conductivity of Biotite and Muscovite Micas at Elevated Temperatures: A Comparative Study.

The unique physicochemical, electrical, mechanical, and thermal properties of micas make them suitable for a wide range of industrial applications, and thus, the interest for these kind of hydrous aluminosilicate minerals is still persistent, not only from a practical but also from a scientific point of view. In the present work, complex impedance spectroscopy measurements were carried out in muscovite and biotite micas, perpendicular to their cleavage planes, over a broad range of frequencies (10-2 Hz to 106 Hz) and temperatures (473-1173 K) that have not been measured so far. Different formalisms of data representation were used, namely, Cole-Cole plots of complex impedance, complex electrical conductivity and electric modulus to analyze the electrical behavior of micas and the electrical signatures of the dehydration/dehydroxylation processes. Our results suggest that ac-conductivity is affected by the structural hydroxyls and the different concentrations of transition metals (Fe, Ti and Mg) in biotite and muscovite micas. The estimated activation energies, i.e., 0.33-0.83 eV for biotite and 0.69-1.92 eV for muscovite, were attributed to proton and small polaron conduction, due to the bound water and different oxidation states of Fe.

An Overview of the Experimental Studies on the Electrical Conductivity of Major Minerals in the Upper Mantle and Transition Zone.

In this paper, we present the recent progress in the experimental studies of the electrical conductivity of dominant nominally anhydrous minerals in the upper mantle and mantle transition zone of Earth, namely, olivine, pyroxene, garnet, wadsleyite and ringwoodite. The main influence factors, such as temperature, pressure, water content, oxygen fugacity, and anisotropy are discussed in detail. The dominant conduction mechanisms of Fe-bearing silicate minerals involve the iron-related small polaron with a relatively large activation enthalpy and the hydrogen-related defect with lower activation enthalpy. Specifically, we mainly focus on the variation of oxygen fugacity on the electrical conductivity of anhydrous and hydrous mantle minerals, which exhibit clearly different charge transport processes. In representative temperature and pressure environments, the hydrogen of nominally anhydrous minerals can tremendously enhance the electrical conductivity of the upper mantle and transition zone, and the influence of trace structural water (or hydrogen) is substantial. In combination with the geophysical data of magnetotelluric surveys, the laboratory-based electrical conductivity measurements can provide significant constraints to the water distribution in Earth's interior.

Complexity of the Yellowstone Park Volcanic Field Seismicity in Terms of Tsallis Entropy.

The Yellowstone Park volcanic field is one of the most active volcanic systems in the world, presenting intense seismic activity that is characterized by several earthquake swarms over the last decades. In the present work, we focused on the spatiotemporal properties of the recent earthquake swarms that occurred on December-January 2008-2009 and the 2010 Madison Plateau swarm, using the approach of Non Extensive Statistical Physics (NESP). Our approach is based on Tsallis entropy, and is used in order to describe the behavior of complex systems where fracturing and strong correlations exist, such as in tectonic and volcanic environments. This framework is based on the maximization of the non-additive Tsallis entropy Sq, introducing the q-exponential function and the entropic parameter q that expresses the degree of non-extentivity of the system. The estimation of the q-parameters could be used as a correlation degree among the events in the spatiotemporal evolution of seismicity. Using the seismic data provided by University of Utah Seismological Stations (UUSS), we analyzed the inter-event time (T) and distance (r) distribution of successive earthquakes that occurred during the two swarms, fitting the observed data with the q-exponential function, resulting in the estimation of the Tsallis entropic parameters qT, qr for the inter-event time and distance distributions, respectively. Furthermore, we studied the magnitude-frequency distribution of the released earthquake energies E as formulated in the frame of NESP, which results in the estimation of the qE parameter. Our analysis provides the triplet (qE, qT, qr) that describes the magnitude-frequency distribution and the spatiotemporal scaling properties of each of the studied earthquake swarms. In addition, the spatial variability of qE throughout the Yellowstone park volcanic area is presented and correlated with the existence of the regional hydrothermal features.

A Complexity View into the Physics of the Accelerating Seismic Release Hypothesis: Theoretical Principles.

Observational indications support the hypothesis that many large earthquakes are preceded by accelerating-decelerating seismic release rates which are described by a power law time to failure relation. In the present work, a unified theoretical framework is discussed based on the ideas of non-extensive statistical physics along with fundamental principles of physics such as the energy conservation in a faulted crustal volume undergoing stress loading. We define a generalized Benioff strain function Ω ξ ( t ) = ∑ i = 1 n ( t ) E i ξ ( t ) , where Ei is the earthquake energy, 0 ≤ ξ ≤ 1 . and a time-to-failure power-law of Ω ξ ( t ) derived for a fault system that obeys a hierarchical distribution law extracted from Tsallis entropy. In the time-to-failure power-law followed by Ω ξ ( t ) the existence of a common exponent mξ which is a function of the non-extensive entropic parameter q is demonstrated. An analytic expression that connects mξ with the Tsallis entropic parameter q and the b value of Gutenberg-Richter law is derived. In addition the range of q and b values that could drive the system into an accelerating stage and to failure is discussed, along with precursory variations of mξ resulting from the precursory b-value anomaly. Finally our calculations based on Tsallis entropy and the energy conservation give a new view on the empirical laws derived in the literature, the associated average generalized Benioff strain rate during accelerating period with the background rate and connecting model parameters with the expected magnitude of the main shock.

Composition and temperature dependence of self-diffusion in Si1-x Ge x alloys.

The knowledge of diffusion processes in semiconducting alloys is very important both technologically and from a theoretical point of view. Here we show that, self-diffusion in Si1-x Ge x alloys as a function of temperature and Ge concentration can be described by the cBΩ thermodynamic model. This model connects the activation Gibbs free energy of point defects formation and migration with the elastic and expansion properties of the bulk material. The approach allows the systematic investigation of point defect thermodynamic parameters such as activation enthalpy, activation entropy and activation volume, based on the thermo-elastic properties (bulk modulus and its derivatives, mean atomic volume and thermal expansion coefficient) of the two end-members of the Si1-x Ge x alloy. Considerable deviations from Vegard's law are observed, due to the diversification of the bulk properties of Si and Ge, in complete agreement with the available experimental data.

Generalized statistical mechanics approaches to earthquakes and tectonics.

Despite the extreme complexity that characterizes the mechanism of the earthquake generation process, simple empirical scaling relations apply to the collective properties of earthquakes and faults in a variety of tectonic environments and scales. The physical characterization of those properties and the scaling relations that describe them attract a wide scientific interest and are incorporated in the probabilistic forecasting of seismicity in local, regional and planetary scales. Considerable progress has been made in the analysis of the statistical mechanics of earthquakes, which, based on the principle of entropy, can provide a physical rationale to the macroscopic properties frequently observed. The scale-invariant properties, the (multi) fractal structures and the long-range interactions that have been found to characterize fault and earthquake populations have recently led to the consideration of non-extensive statistical mechanics (NESM) as a consistent statistical mechanics framework for the description of seismicity. The consistency between NESM and observations has been demonstrated in a series of publications on seismicity, faulting, rock physics and other fields of geosciences. The aim of this review is to present in a concise manner the fundamental macroscopic properties of earthquakes and faulting and how these can be derived by using the notions of statistical mechanics and NESM, providing further insights into earthquake physics and fault growth processes.