Non-extensive Statistical Physics Research Articles

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.

Fracture network organization with continuation of injections in the Habanero field (Cooper Basin, Australia) disclosed by coda wave fluctuations

Hydraulic stimulation of a geothermal reservoir aims to increase the permeability of the rock formations by creating/enhancing a fracture network, to take advantage of the geothermal energy hosted by deep hot formations. A common side effect of the fracturing process is the small-in-magnitude but abundant induced seismicity. In this work, we study the seismicity induced during the hydraulic stimulation of the Habanero 4 well, in the Cooper Basin (Australia), where an extensive network of sensors has been deployed to monitor the stimulation process. The detailed monitoring of the induced seismic events enabled the study of the dynamic characteristics of the enhanced fracture network by making use of the seismic coda waves scattering properties. Since the Earth’s crust has inhomogeneities with fractal properties, manifested in the seismic coda waves, we address the fracture network as a complex, non-equilibrium system. In this line, the framework of Non-Extensive Statistical Physics (NESP) and the maximum entropy principle were used to study the fluctuations of the seismic coda waves and their possible variations during the hydraulic stimulation. The analysis shows that the probability density functions of the normalized increments of S-coda waves present heavy tails with asymptotic power-law behavior, enhancing the probabilities of large fluctuations. The results further indicate that as the stimulation progresses, this enhancement becomes even more pronounced. The observed scaling behavior can exactly be approximated with the q-Gaussian distribution, derived in the framework of NESP, showing a modest uprising trend of the entropic index (q-value) with continuation of injections. These results suggest that the system of fractures progressively becomes more organized, with stronger memory effects and long-range interactions, as the hydraulic stimulation progresses.

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.

A Non-Extensive Statistical Physics View of the Temporal Properties of the Recent Aftershock Sequences of Strong Earthquakes in Greece

Greece is one of Europe’s most seismically active areas. Seismic activity in Greece has been characterized by a series of strong earthquakes with magnitudes up to Mw = 7.0 over the last five years. In this article we focus on these strong events, namely the Mw6.0 Arkalochori (27 September 2021), the Mw6.3 Elassona (3 March 2021), the Mw7.0 Samos (30 October 2020), the Mw5.1 Parnitha (19 July 2019), the Mw6.6 Zakynthos (25 October 2018), the Mw6.5 Kos (20 July 2017) and the Mw6.1 Mytilene (12 June 2017) earthquakes. Based on the probability distributions of interevent times between the successive aftershock events, we investigate the temporal evolution of their aftershock sequences. We use a statistical mechanics model developed in the framework of Non-Extensive Statistical Physics (NESP) to approach the observed distributions. NESP provides a strictly necessary generalization of Boltzmann–Gibbs statistical mechanics for complex systems with memory effects, (multi)fractal geometries, and long-range interactions. We show how the NESP applicable to the temporal evolution of recent aftershock sequences in Greece, as well as the existence of a crossover behavior from power-law (q ≠ 1) to exponential (q = 1) scaling for longer interevent times. The observed behavior is further discussed in terms of superstatistics. In this way a stochastic mechanism with memory effects that can produce the observed scaling behavior is demonstrated. To conclude, seismic activity in Greece presents a series of significant earthquakes over the last five years. We focus on strong earthquakes, and we study the temporal evolution of aftershock sequences of them using a statistical mechanics model. The non-extensive parameter q related with the interevent times distribution varies between 1.62 and 1.71, which suggests a system with about one degree of freedom.

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.

SOME CHARACTERISTICS OF THE EARTHQUAKE CATALOG AND THE SEISMIC PROCESS ACCORDING TO THE KNET NETWORK

Some characteristics of the earthquake catalog and seismic process are considered. The catalog is obtained according to the KNET network (KN-code in FSDN, International Federation of Digital Seismograph Networks, that is operated by Research Station of RAS, RS RAS) and contains more than 10000 earthquake parameters from 1994 to 2020. The catalog and seismicity characteristics were determined the whole catalog as well as the catalog that is limited by the coordinates of the Bishkek geodynamic polygon (BGP). Statistical analysis of arrival times of direct P- and S-waves registered at KNET network stations was carried out. The maximum P- and S-waves were registered at AAK station, the minimum – at ULHL station. The territory of the BGP is covered by great P-traces density. We analyzed earthquake localization errors, i.e. the difference between the observed and calculated arrival times of P-and S-wave fronts (RMS), horizontal error (ERH, epicenter) and vertical error (ERZ, depth). Occurred on the BGP territory earthquakes have minimum values of the considered errors. The representative sample is defined: for the whole catalog it includes K≥7.2 earthquakes and for the limited by BGP coordinates catalog – K≥6.7. Statistical characteristics of the representative part of the catalog in terms of time and depth are determined. The temporal distribution of earthquakes by energy classes is constructed and the absence of positive or negative trends in the number of events is noted. Spatial distribution of earthquakes by depth – 0–5, 5–10, 10–15 and more than 15 km is constructed. The smallest errors of earthquake depth determination have the events that occurred on the BGP territory. During the study 46 moderate earthquakes with K≥12 occurred. The most part of these events happened in the North Tien Shan seismgenic zone. 22 events were determined with K≥10 followed by aftershock sequences and give some aftershock characteristics. The most events with aftershocks occurred in the eastern part of the Kyrgyz ridge. The distribution of earthquake numbers and STD intensity is constructed. Zones of seismic activity and maximum intense Earth’s crust deformation are identified. The Gutenberg – Richter law and provisions of nonextensive statistical physics were used to describe the energy distribution function of earthquakes.

On the Patterns and Scaling Properties of the 2021–2022 Arkalochori Earthquake Sequence (Central Crete, Greece) Based on Seismological, Geophysical and Satellite Observations

The 27 September 2021 damaging mainshock (Mw6.0) close to Arkalochori village is the strongest earthquake that was recorded during the instrumental period of seismicity in Central Crete (Greece). The mainshock was preceded by a significant number of foreshocks that lasted nearly four months. Maximum ground subsidence of about 18 cm was estimated from InSAR processing. The aftershock sequence is located in an almost NE-SW direction and divided into two main clusters, the southern and the northern ones. The foreshock activity, the deformation area, and the strongest aftershocks are located within the southern cluster. Based on body-wave travel times, a 3-D velocity model was developed, while using combined space and ground-based geodetic techniques, the co-seismic ground deformation is presented. Moreover, we examined the co-seismic static stress changes with respect to the aftershocks’ spatial distribution during the major events of the foreshocks, the Mw = 6.0 main event as well as the largest aftershock. Both the foreshock and the aftershock sequences obey the scaling law for the frequency-magnitude distribution as derived from the framework of non-extensive statistical physics (NESP). The aftershock production rate decays according to the modified Omori scaling law, exhibiting various Omori regimes due to the generation of secondary aftershock sequences. The analysis of the inter-event time distribution, based on NESP, further indicates asymptotic power-law scaling and long-range correlations among the events. The spatiotemporal evolution of the aftershock sequence indicates triggering by co-seismic stress transfer, while its slow migration towards the outer edges of the area of the aftershocks, related to the logarithm of time, further indicates a possible afterslip.

Analysis of temporal variations of seismicity through non-extensive statistical physics

SUMMARYIn recent years, there has been increasing interest in theoretical descriptions of seismicity in terms of statistical physics. Most aspects of these studies are encompassed by the concept of ‘intermittent criticality’, in which a region alternately approaches and retreats from a critical point. In this study, we analyse a descriptor of seismic activity that acts as a measure of the criticality of a system, such that its variations can be associated with changes in the state of the system. As some classical methods of analysis are not suitable for dealing with some of the features of complex systems such as the Earth’s crust, we derive the probability distribution of the magnitude by maximizing a non-extensive generalization of the Boltzmann–Gibbs entropy given by the Tsallis entropy. In particular, the shape parameter q of this distribution, called the entropic index, characterizes the subadditive q > 1 and superadditive q < 1 regimes. Following the Bayesian approach for parameter estimation, we examine the seismic activity that has affected two seismogenic areas in central Italy that were hit recently by destructive earthquakes: L’Aquila in 2009, and Amatrice–Norcia in 2016. To analyse in detail the variations of the q index and the entropy, we estimate these for time windows of a fixed number of events that shift at each new event. Both the q index and the Tsallis entropy show significant and lasting decreases before the first strong earthquake in the sequences, and sudden increases after them. This indicates that these quantities can be considered as indicators of the level of concentration of energy, and hence of the activation state of the systems. More reliable results need to come from further studies of different cases in different seismotectonic settings.

Accelerating deformation seismicity patterns before the March 3, 2021 Thessaly strong earthquake. First results

A widely felt strong shallow earthquake with Mw 6.3 magnitude occurred in Thessaly (Central Greece) on March 3, 2021. This recent strong event attracted our interest to apply and evaluate the capabilities of the Accelerating Deformation method. Based on the recently proposed generalized Benioff strain idea which could be justified by the terms of Non-Extensive Statistical Physics (NESP), the common critical exponent was calculated in order to define the critical stage before a strong event. The present analysis comprised a complex spatiotemporal iterative procedure to examine the possible seismicity patterns at a broad region and identify the best one associated with the preparation process before the strong event. The starting time of the accelerating period, the size and location of the critical area are unknown parameters to be determined. Furthermore, although, the time of failure is already known, in the present research it was not set as a fixed value in the algorithm to define the other unknown parameters but instead different catalogue ending dates have been tried out to be with an objective way. The broad region to be investigated was divided with a square mesh and the search of events around a point has been carried on with different size circular and elliptical shapes. Among the obtained results, the solution which exhibits the most dominant scaling law behavior as well as the one which exhibits the smallest spatial area and yet the more dominant scaling law behavior are presented.

Scaling properties of the Mw7.0 Samos (Greece), 2020 aftershock sequence

On October 30, 2020, a strong and shallow earthquake (Mw = 7.0) hit Samos, an island on the eastern edge of the Aegean Sea (Greece). The epicenter was located on the north offshore of the Greek island of Samos. The goal of our work is to provide a first analysis of the scaling properties observed in the aftershock sequence as reported until December 31, 2020, as numerous seismic clusters activated. Our analysis is focused on the main of the clusters observed in the East area of the activated fault zone and strongly related with the mainshock’s fault. The aftershock sequence follows the Omori law with a value of p ≈ 1.01 for the main cluster which is remarkably close to a logarithmic evolution. The analysis of interevent times distribution, based on non-extensive statistical physics indicates a system in an anomalous equilibrium with a crossover from anomalous (q > 1) to normal (q = 1) statistical mechanics, as great interevent times approached. A discussion of the crossover observed, is given in terms of superstatistics. In addition, the obtained value q ≈ 1.67 suggests a system with one degree of freedom. Furthermore, a scaling of the migration of aftershock zone as a function of the logarithm of time is discussed in terms of rate strengthening rheology that govern the evolution of afterslip process.

A generalized q growth model based on nonadditive entropy

We present a general growth model based on nonextensive statistical physics. We show that the most common unidimensional growth laws such as power law, exponential, logistic, Richards, Von Bertalanffy, Gompertz can be obtained. This model belongs to a particular case reported in (Physica A 369, 645 (2006)). The new evolution equation resembles the “universality” revealed by West for ontogenetic growth (Nature 413, 628 (2001)). We show that for early times the model follows a power law growth as [Formula: see text], where the exponent [Formula: see text] classifies different types of growth. Several examples are given and discussed.

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.

Fermi energy in the q-deformed quantum mechanics

In this paper, we use the q-derivative emerging in the non-extensive statistical physics to formulate the q-deformed quantum mechanics. We find the algebraic structure related to this deformed theory and investigate some properties of the q-deformed elementary functions. Using this mathematical background, we formulate the q-deformed Heisenberg algebra and q-deformed time-dependent Schrödinger equation. As an example, we deal with the infinite potential well and compute the Fermi energy in the q-deformed theory.

The relaxation processes of Pressure Stimulated Currents under the concept of Non-extensive statistical physics

This study presents the results of Pressure Stimulated Currents (PSC) analysis using non-extensive statistical physics (NESP) approach when marble and amphibolite specimens were subjected to mechanical stress up to fracture. The specimens were subjected to a constant uniaxial stress, interrupted by an abrupt step-wise stress increase (Step-Stress Technique - SST) while concurrently the PSC emission was recorded. The loading protocol involved eight sequential steps of mechanical stress at a gradually higher level until the failure of the specimens. After each step, the stress was maintained constant until the PSC signal was restored to a final low value. After the PSC restoration the next stress step was applied. The recorded PSC temporal relaxation when the stress remained constant, was analyzed under the concept of NESP based on Tsallis’ entropy and the behavior of the entropic index q was studied for various stress levels. Throughout each next loading step at higher level, the entropic index q shows a progressive increase from 1.15 to 1.40 until the stress attains about 85% of the specimens’ total strength where it reaches a maximum value close to 1.4. When the applied stress becomes higher than the 85% of the specimens’ total strength, the entropic index q gradually decreases. It should be noted that this peak along with the subsequent decline of q coexists with the excessive damage development in the specimens’ bulk due to the applied mechanical stress. Taking into consideration the fact that the entropic index q quantifies the self-organization of the system, this behavior of q, for stress levels higher than 85% of the specimens’ ultimate stress strength, clearly corresponds to dynamic processes that dominate the system and guide the upcoming fracture. The above findings advocate the use of the entropic index q as a pre-failure indicator of the upcoming specimen fracture.

Evidence of Hierarchy in the Drainage Basins Size Distribution of Greece Derived from ASTER GDEM-v2 Data

The drainage basins of Greece are analyzed in terms of hierarchy and discussed in view of Tsallis Entropy. This concept has been successfully used in a variety of complex systems, where fractality, memory and long-range interactions are dominant. The analysis indicates that the statistical distribution of drainage basins’ area in Greece, presents a hierarchical pattern that can be viewed within the frame of non-extensive statistical physics. Our work was based on the analysis of the ASTER GDEM v2 Digital Elevation Model of Greece, which offers a 30 m resolution, creating an accurate drainage basins’ database. Analyzing the drainage size (e.g., drainage basin area)-frequency distribution we discuss the connection of the observed power law exponents with the Tsallis entropic parameters, demonstrating the hierarchy observed in drainage areas for the set created for all over Greece and the subsets of drainages in the internal and external Hellenides that are the main tectonic structures in Greece. Furthermore, we discuss in terms of Tsallis entropy, the hierarchical patterns observed when the drainages are classified according to their relief or the Topographic Position Index (TPI). The deviation of distribution from power law for large drainages area is discussed.

Application of Non-Extensive Statistical Physics on the particle size distribution in natural carbonate fault rocks

This contribution focuses on the results of combined generalized statistical mechanics and microstructural analyses of carbonate fault rock samples, which derive from active extensional fault zones cropping out in peninsular Italy. Specifically, this work is aimed at deciphering the role played by both pre-existing structural elements and structural diagenesis on the dimension and distribution of the largest survivor grains. The studied extensional fault zones were exhumed from shallow crustal depths during the Plio-Quaternary downfaulting of the Apennines. They crosscut Mesozoic platform limestones and dolostones. Despite the different host rocks, all carbonate fault rocks exhibit very similar cataclastic textures but dissimilar pore characteristics. In this work, we apply for the first time the principles of the Non-Extensive Statistical Physics to the study of fault rocks. By considering the Tsallis entropy, which is expressed by the Q-value representing the hierarchical organization of the system, we consider the crossover point value, V0, computed for both 1cm2 and 9cm2 representative fault rock images at the transition from Q-exponential to exponential behaviors. As a result, we document that the limestone grain-supported rocks, which mainly localize in the outer fault cores, are always characterized by smaller V0 values with respect to the dolostone ones. These data are interpreted as due to both burial and thrusting-related pressure solution seams, which pervasively formed in the limestone host rocks. Conversely, the amount of V0 variations computed from outer to inner fault cores are associated to the effects of widespread calcite cement precipitation, which mainly occurred in the limestone matrix-supported fault rocks. By considering the weighted, average areas of survivor grains with dimension larger than V0 a as a proxy for sorting, we document an increase from outer to inner fault cores in all the study fault zones. At a close view, all dolomite-rich fault rock samples show very similar median values, whereas the matrix-supported fault rock samples of the inner limestone fault cores are characterized by smaller median values relative to the grain-supported of the limestone outer fault cores. This discrepancy is interpreted as also due to widespread cementation processes, which formed aggregate grains in the fine-grained fault rocks encompassing the main slip surfaces of the limestone fault cores.

The use of acoustic emissions technique in the monitoring of fracturing in concrete using soundless chemical demolition agent

Soundless chemical demolition agents (SCDAs) have been used during the last decades in the demolition of boulders and concrete structures as well as in open-surface and sub-surface rock excavation, as an alternative to the use of explosives posing safety risks. However, the knowledge of the governing fracture mechanisms in brittle materials is rather limited. In the present work, we thoroughly investigate the use of the acoustic emission technique to study the SCDA-induced fracture process in concrete blocks. Energy-related features and waveform parameters of the recorded AE activity are correlated to the fracture mode of the concrete where a quasi-static behavior is observed. Monitoring of the progressive fracture is also achieved by the 3D localization of the AE sources. The distribution of the inter-event times of the recorded hits is further analyzed in the context of non-extensive statistical physics.

Non-extensive statistical analysis of acoustic emissions series recorded during the uniaxial compression of brittle rocks

Non-extensive statistical physics (NESP) provides the theoretical tool to investigate complex systems that appear in different length-scales and violate the classical Boltzmann–Gibbs statistics. In the present study, we apply the concept of NESP to analyze the Acoustic Emissions (AE) series recorded during uniaxial compression of brittle rocks, such as marble and sandstone specimens. In both types of rock samples, the cumulative distribution of inter-event times (interval times between successive AE hits) are well described by the q-exponential function. The variations of the q-index of Tsallis entropy and of the βq parameter with the applied stress follow distinct behavior in each type of rock, indicating in both cases the entrance of the system to the critical stage of fracture. The analysis of the experimental data suggests that NESP is suitable for describing AE activity in rock samples under compression, in a similar way to Earth’s seismic activity.

Evidence of Tsallis entropy signature on medicane induced ambient seismic signals

The link between hurricanes or typhoons and their generated ambient noise has recently become a frontier topic in the field of applied seismology. In the Mediterranean region, infrequent tropical-like cyclones, known as Medicanes or Mediterranean hurricanes, with similar characteristics with hurricanes appear, with the most recent storm occurred on September 27–30, 2018 in South Greece, which characterized by gale winds, severe precipitation, and a low pressure center, accompanied with a spiral pattern of thunderstorms. In this work, we describe the Medicane’s induced ambient seismic noise fluctuations, as recorded in seismological station along to the path of the recent Medicane, in terms of non-extensive statistical physics. We found that the Medicane’s induced ambient seismic noise increments follow the q-Gaussian distribution. This indicates that Medicane induced ambient seismic noise’s fluctuations are not random and present long-term memory effects that could be described in terms of Tsallis entropy. Our results suggest that in the Medicane system that affected the Southwest Peloponnese the q–values of the induced ambient seismic noise’s fluctuations in the Kalamata (KLMT) seismological station located in Southwest Peloponnese are q≈1.67, which corresponds to n=2 degrees of freedom system, indicating that Medicane induced ambient seismic noise fluctuations compose of two independent Gaussian random variables. For stations as that of APE (Apiranthos, Naxos island, Cyclades), where an attenuated Medicane was observed, a q≈1.57 obtained, which is similar with that observed in the KNDR (Koundoura, South West Crete) seismological station, where the Medicane appears before its main organization as intensively observed in the KLMT station. For the CHAN (Chania, West Crete ) station a q≈1.32 was observed which corresponds to about 5 degrees of freedom indicating that Medicane induced ambient seismic noise fluctuations compose of about five independent Gaussian random variables, in agreement with the week intensity of Medicane observed in Chania.

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 , where Ei is the earthquake energy, . and a time-to-failure power-law of derived for a fault system that obeys a hierarchical distribution law extracted from Tsallis entropy. In the time-to-failure power-law followed by 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.