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.

Complexity and Statistical Physics Approaches to Earthquakes.

This Special Issue of Entropy, "Complexity and Statistical Physics Approaches to Earthquakes", sees the successful publication of 11 original scientific 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.

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.

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.

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.

Author Correction: High-resolution record reveals climate-driven environmental and sedimentary changes in an active rift.

A correction to this article has been published and is linked from the HTML and PDF versions of this paper. The error has not been fixed in the paper.

High-resolution record reveals climate-driven environmental and sedimentary changes in an active rift.

Young rifts are shaped by combined tectonic and surface processes and climate, yet few records exist to evaluate the interplay of these processes over an extended period of early rift-basin development. Here, we present the longest and highest resolution record of sediment flux and paleoenvironmental changes when a young rift connects to the global oceans. New results from International Ocean Discovery Program (IODP) Expedition 381 in the Corinth Rift show 10s-100s of kyr cyclic variations in basin paleoenvironment as eustatic sea level fluctuated with respect to sills bounding this semi-isolated basin, and reveal substantial corresponding changes in the volume and character of sediment delivered into the rift. During interglacials, when the basin was marine, sedimentation rates were lower (excepting the Holocene), and bioturbation and organic carbon concentration higher. During glacials, the basin was isolated from the ocean, and sedimentation rates were higher (~2-7 times those in interglacials). We infer that reduced vegetation cover during glacials drove higher sediment flux from the rift flanks. These orbital-timescale changes in rate and type of basin infill will likely influence early rift sedimentary and faulting processes, potentially including syn-rift stratigraphy, sediment burial rates, and organic carbon flux and preservation on deep continental margins worldwide.

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.

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.

Processing of meats and cardiovascular risk: time to focus on preservatives.

Dietary guidelines emphasize selecting lean (low-fat) meats to reduce saturated fat and cholesterol, but growing evidence suggests that health effects may relate to other ingredients, such as sodium, heme iron, or L-carnitine. Understanding how meats influence health, and on which nutrients this relationship depends, is essential to advise consumer choices, set guidelines, and inform food reformulations. A recent study published in BMC Medicine involving 448,568 participants in 10 European countries, provides important evidence in this regard. After multivariate adjustment, intake of unprocessed red meat was not significantly associated with total or cause-specific mortality; conversely, intake of processed meat was associated with a 30% higher rate of cardiovascular disease (CVD) (per 50 g/day, relative risk 1.30, 95% confidence interval 1.17 to 1.45) and also higher cancer mortality. These findings are consistent with our previous meta-analysis, based on smaller studies, showing strong associations of processed meats, but not unprocessed meats, with CVD. Preservatives are the notable difference; the calculated blood-pressure effects of sodium differences (around 400% higher in processed meats) explain most of the observed higher risk. Although unprocessed red meats seem to be relatively neutral for CVD, healthier choices are available, including fish, nuts, legumes, fruits, and vegetables. Public-health guidance should prioritize avoidance of processed meats, including the low-fat deli meats currently marketed as healthy choices, and the food industry should substantially reduce sodium and other preservatives in processed meats.See related research article here http://www.biomedcentral.com/1741-7015/11/63.

Unprocessed red and processed meats and risk of coronary artery disease and type 2 diabetes--an updated review of the evidence.

Growing evidence suggests that effects of red meat consumption on coronary heart disease (CHD) and type 2 diabetes could vary depending on processing. We reviewed the evidence for effects of unprocessed (fresh/frozen) red and processed (using sodium/other preservatives) meat consumption on CHD and diabetes. In meta-analyses of prospective cohorts, higher risk of CHD is seen with processed meat consumption (RR per 50 g: 1.42, 95 %CI = 1.07-1.89), but a smaller increase or no risk is seen with unprocessed meat consumption. Differences in sodium content (~400 % higher in processed meat) appear to account for about two-thirds of this risk difference. In similar analyses, both unprocessed red and processed meat consumption are associated with incident diabetes, with higher risk per g of processed (RR per 50 g: 1.51, 95 %CI = 1.25-1.83) versus unprocessed (RR per 100 g: 1.19, 95 % CI = 1.04-1.37) meats. Contents of heme iron and dietary cholesterol may partly account for these associations. The overall findings suggest that neither unprocessed red nor processed meat consumption is beneficial for cardiometabolic health, and that clinical and public health guidance should especially prioritize reducing processed meat consumption.

Assessment of musculoskeletal system in women with jumping mechanography.

The purpose of this study was to investigate and add reference data about the musculoskeletal system in women. The mechanography system of the Leonardo™ platform (Novotec, Germany) was used to measure parameters of movement (velocity, force, power) in 176 healthy Greek women aged 20-79 years, separated according to age decade in six groups: group 1 (n = 12), 20-29 years; group 2 (n = 14), 30-39 years; group 3 (n = 33), 40-49 years; group 4 (n = 59), 50-59 years including 21 postmenopausal; group 5 (n = 31), 60-69 years including 12 postmenopausal; and group 6 (n = 27), 70-79 years all postmenopausal. This system measures forces applied to the plate over time, calculates through acceleration the vertical velocity of center of gravity and using force and velocity it calculates power of vertical movements. All women performed a counter-movement jump (brief squat before the jump) with freely moving arms. Weight was recorded on the platform before the jump and height was measured with a wall-mounted ruler. Body weight and body mass index were gradually increased; on the contrary height and all movement parameters except force (velocity, power) were statistically decreased during aging and after menopause.