Stelios M. Potirakis

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

This review provides a summary of methods originated in (non-equilibrium) statistical mechanics and information theory, which have recently found successful applications to quantitatively studying complexity in various components of the complex system Earth. Specifically, we discuss two classes of methods: (i) entropies of different kinds (e.g., on the one hand classical Shannon and R´enyi entropies, as well as non-extensive Tsallis entropy based on symbolic dynamics techniques and, on the other hand, approximate entropy, sample entropy and fuzzy entropy); and (ii) measures of statistical interdependence and causality (e.g., mutual information and generalizations thereof, transfer entropy, momentary information transfer). We review a number of applications and case studies utilizing the above-mentioned methodological approaches for studying contemporary problems in some exemplary fields of the Earth sciences, highlighting the potentials of different techniques.

Current challenges for pre-earthquake electromagnetic emissions: shedding light from micro-scale plastic flow, granular packings, phase transitions and self-affinity notion of fracture process

Abstract. Are there credible electromagnetic (EM) potential earthquake (EQ) precursors? This a question debated in the scientific community and there may be legitimate reasons for the critical views. The negative view concerning the existence of EM potential precursors is enhanced by features that accompany their observation which are considered as paradox ones, namely, these signals: (i) are not observed at the time of EQs occurrence and during the aftershock period, (ii) are not accompanied by large precursory strain changes, (iii) are not accompanied by simultaneous geodetic or seismological precursors and (iv) their traceability is considered problematic. In this work, the detected candidate EM potential precursors are studied through a shift in thinking towards the basic science findings relative to granular packings, micron-scale plastic flow, interface depinning, fracture size effects, concepts drawn from phase transitions, self-affine notion of fracture and faulting process, universal features of fracture surfaces, recent high quality laboratory studies, theoretical models and numerical simulations. We try to contribute to the establishment of strict criteria for the definition of an emerged EM anomaly as a possibly EQ-related one, and to the explanation of potential precursory EM features which have been considered as paradoxes. A three-stage model for EQ generation by means of pre-EQ fracture-induced EM emissions is proposed. The claim that the observed EM potential precursors may permit a real-time and step-by-step monitoring of the EQ generation is tested.

Natural time analysis of critical phenomena: The case of pre-fracture electromagnetic emissions

Criticality of complex systems reveals itself in various ways. One way to monitor a system at critical state is to analyze its observable manifestations using the recently introduced method of natural time. Pre-fracture electromagnetic (EM) emissions, in agreement to laboratory experiments, have been consistently detected in the MHz band prior to significant earthquakes. It has been proposed that these emissions stem from the fracture of the heterogeneous materials surrounding the strong entities (asperities) distributed along the fault, preventing the relative slipping. It has also been proposed that the fracture of heterogeneous material could be described in analogy to the critical phase transitions in statistical physics. In this work, the natural time analysis is for the first time applied to the pre-fracture MHz EM signals revealing their critical nature. Seismicity and pre-fracture EM emissions should be two sides of the same coin concerning the earthquake generation process. Therefore, we also examine the corresponding foreshock seismic activity, as another manifestation of the same complex system at critical state. We conclude that the foreshock seismicity data present criticality features as well.

Criticality features in ULF magnetic fields prior to the 2011 Tohoku earthquake

The criticality of ULF (Ultra-low-frequency) magnetic variations is investigated for the 2011 March 11 Tohoku earthquake (EQ) by natural time analysis. For this attempt, some ULF parameters were considered: (1) Fh (horizontal magnetic field), (2) Fz (vertical magnetic field), and (3) Dh (inverse of horizontal magnetic field). The first two parameters refer to the ULF radiation, while the last parameter refers to another ULF effect of ionospheric signature. Nighttime (L.T. = 3 am ± 2 hours) data at Kakioka (KAK) were used, and the power of each quantity at a particular frequency band of 0.03–0.05 Hz was averaged for nighttime hours. The analysis results indicate that Fh fulfilled all criticality conditions on March 3–5, 2011, and that the additional parameter, Dh reached also a criticality on March 6 or 7. In conclusion, criticality has reached in the pre-EQ fracture region a few days to one week before the main shock of the Tohoku EQ.

Relation between seismicity and pre-earthquake electromagnetic emissions in terms of energy, information and entropy content

Abstract. In this paper we show, in terms of Fisher information and approximate entropy, that the two strong impulsive kHz electromagnetic (EM) bursts recorded prior to the Athens earthquake (EQ) (7 September 1999, magnitude 5.9) present compatibility with the radar interferometry data and the seismic data analysis, which indicates that two fault segments were activated during Athens EQ. The calculated Fisher information and approximate entropy content ratios closely follow the radar interferometry result that the main fault segment was responsible for 80 % of the total energy released, while the secondary fault segment for the remaining 20 %. This experimental finding, which appears for the first time in the literature, further enhances the hypothesis for the seismogenic origin of the analyzed kHz EM bursts.

Recent Field Observations Indicating an Earth System in Critical Condition Before the Occurrence of a Significant Earthquake

In this letter, we show, in terms of the fractureinduced electromagnetic emissions (EME) recorded prior to the earthquake of Chania, Greece [(35.50° N, 23.28° E); October 12, 2013; Mw = 6.4] and the seismicity of the area, that there were different evidence indicating the advent of the main shock a few days before its occurrence. Specifically, both the megahertz (MHz) EME and the foreshock seismicity activity came to critical condition a few days before the main shock occurrence. The analysis was performed by means of two independent methods, namely, the method of critical fluctuations and the natural time method, both revealing critical features.

Sudden drop of fractal dimension of electromagnetic emissions recorded prior to significant earthquake

The variation of fractal dimension and entropy during a damage evolution process, especially approaching critical failure, has been recently investigated. A sudden drop of fractal dimension has been proposed as a quantitative indicator of damage localization or a likely precursor of an impending catastrophic failure. In this contribution, electromagnetic emissions recorded prior to significant earthquake are analysed to investigate whether they also present such sudden fractal dimension and entropy drops as the main catastrophic event is approaching. The pre-earthquake electromagnetic time series analysis results reveal a good agreement to the theoretically expected ones indicating that the critical fracture is approaching.

The Earth as a living planet: human-type diseases in the earthquake preparation process

Abstract. The new field of complex systems supports the view that a number of systems arising from disciplines as diverse as physics, biology, engineering, and economics may have certain quantitative features that are intriguingly similar. The Earth is a living planet where many complex systems run perfectly without stopping at all. The earthquake generation is a fundamental sign that the Earth is a living planet. Recently, analyses have shown that human-brain-type disease appears during the earthquake generation process. Herein, we show that human-heart-type disease appears during the earthquake preparation of the earthquake process. The investigation is mainly attempted by means of critical phenomena, which have been proposed as the likely paradigm to explain the origins of both heart electric fluctuations and fracture-induced electromagnetic fluctuations. We show that a time window of the damage evolution within the heterogeneous Earths crust and the healthy hearts electrical action present the characteristic features of the critical point of a thermal second-order phase transition. A dramatic breakdown of critical characteristics appears in the tail of the fracture process of heterogeneous system and the injured hearts electrical action. Analyses by means of Hurst exponent and wavelet decomposition further support the hypothesis that a dynamical analogy exists between the geological and biological systems under study.

Dynamical analogy between epileptic seizures and seismogenic electromagnetic emissions by means of nonextensive statistical mechanics

The field of study of complex systems considers that the dynamics of complex systems are founded on universal principles that may be used to describe a great variety of scientific and technological approaches of different types of natural, artificial, and social systems. Several authors have suggested that earthquake dynamics and neurodynamics can be analyzed within similar mathematical frameworks. Recently, authors have shown that a dynamical analogy supported by scale-free statistics exists between seizures and earthquakes, analyzing populations of different seizures and earthquakes, respectively. The purpose of this paper is to suggest a shift in emphasis from the large to the small scale: our analyses focus on a single epileptic seizure generation and the activation of a single fault (earthquake) and not on the statistics of sequences of different seizures and earthquakes. We apply the concepts of the nonextensive statistical physics to support the suggestion that a dynamical analogy exists between the two different extreme events, seizures and earthquakes. We also investigate the existence of such an analogy by means of scale-free statistics (the Gutenberg–Richter distribution of event sizes and the distribution of the waiting time until the next event). The performed analysis confirms the existence of a dynamic analogy between earthquakes and seizures, which moreover follow the dynamics of magnetic storms and solar flares.

Wireless sensor network-based communication for cooperative simultaneous localization and mapping

This paper presents a novel approach of using a Wireless Sensor Network (WSN) as the communication means for Multi-Robot, Cooperative, Simultaneous Localization and Mapping (CSLAM) applications investigating the associated design challenges and suggesting corresponding solutions. Although the proposed approach brings several benefits including an increased coverage and communication range, self-organization capabilities, quick deployment, and flexible architecture, the realization is interrelated with performance in terms of energy efficiency and reliability. In this respect, the applicability of the WSNs for the presented approach is investigated. Centralized and distributed map merging methods in WSN-based CSLAM are evaluated in detail and the impacts of packet delays and losses on the performance of CSLAM algorithms are shown. Additionally, the involved network congestion and contention dynamics are presented, while the effects of observation range, speed, time intervals between observations, and odometry readings on the SLAM accuracy are shown based on an extensive set of simulation studies.