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Transient Electromagnetic Method in the Keritis Basin (Crete, Greece): Evidence of Hierarchy in a Complex Geological Structure in View of Tsallis Distribution

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Transient Electromagnetic Method in the Keritis Basin (Crete, Greece): Evidence of Hierarchy in a Complex Geological Structure in View of Tsallis Distribution ANNALS OF GEOPHYSICS, 60, SUPPLEMENT TO 6, GM675, 2017; doi: 10.4401/ag-7551 Transient Electromagnetic Method in the Keritis basin (Crete, Greece): Evidence of hierarchy in a complex geological structure in view of Tsallis distribution Filippos Vallianatos 1, * 1 Laboratory of Geophysics and Seismology, UNESCO Chair on Solid Earth Physics and Geohazards Risk Reduction, Technological Educational Institute of Crete, Chania, Crete, Greece Article history Received October 12, 2017; accepted November 27, 2017. Subject classification: Transient Electromagnetic Method; Tsallis statistics; Karstified basin; Fractional diffusion; Multi-scaled hierarchical geological structure ABSTRACT 2005, Molz and Hyden 2006, Beskardes et al. 2017]. It is being increasingly recognized that geological media are inherently In Earth sciences the conceptsof fractal geometry rough with persistent, long-range spatial correlations in physical prop - and complexity have been introduced to describe pat - erties, including electrical conductivity, which spans many decades in terns in geophysics, seismicity, volcanology, geomor - length scale. In the present study, the ideas of a multi-scaled geological phology and hydrogeology introducing the fractal medium and the anomalous diffusion of electromagnetic eddy currents properties of multiscale heterogeneity [Vallianatos applied, in Keritis Basin (Western Crete, Greece), a complex geological 1996, Turcotte 1997, White et al. 2002, Bahr et al. 2002, system surrounded by normal faults and with the majority of forma - Kiyashchenko et al. 2004, Kouli et al. 2007, Vallianatos tions to be calcareous and karstified. The evidence of a multi-scaled hi - and Telesca 2012]. Everett and Weiss [2002] showed erarchical structure is presented,based on observed q-exponential that observed electromagnetic responses can be repre - distributions of the resistivity, supporting our motivation to introduce sented as fractal signals due to the inherent multi-scaled fractional diffusion ideas and non-extensive statistical physics to de - structure (called roughness) of the geological medium scribe the geoelectrical structure of karstified Keritis basin. The essen - and placed an emphasis on the need for multiscale anal - tial goal of this paper is to test in a real geological complex formation ysis to develop complex geology models that would the Transient Electromagnetic Method (TEM) response in terms of the permit the recognition of its electromagnetic signature. rough geological medium where the conductivity of the ground has a In Ge et al. [2012, 2015] the complexity of geological spatial distribution, which is described by a roughness parameterand medium introduced, leads to electromagnetic frac - to better understand the geoelectrical properties of complex geological tional diffusion equation to assess the electromagnetic structure introducing the ideas of fractional diffusion and non exten - responses due to a multiscale structured subsurface. sive statistical physics. Weiss and Everett [2007] found evidence for the fractional diffusion of electromagnetic eddy currents 1. Introduction using time domain electromagnetic (TEM) data. They Electromagnetic methods are widely applicable to define a roughness parameter, related to the subsurface the solution of environmental and engineering prob - fracture density, to characterize the complexity of the lems, since they are very effective in applications where geoelectric structure. From all the above mentioned the geoelectric structure is simple and the geological works, it is well documented that anomalous diffusion medium is characterized by a piecewise smooth spatial is strongly associated with spatial variations of mate - distribution of electrical conductivity. However, such a rial properties. Although the electromagnetic response description cannot always be justified and recent results of geological media is a complicated function of suggest that most of the physical properties of geolog - grain/fluid interactions, the spatial hierarchy of a geo - ical media, including electrical conductivity, are inher - logical formation also strongly influences the geome - ently rough forming a multiscaled structure [Pilkington try of electric current pathways. The inherent presence and Todoeschuck 1993, Painter 1996,Tennekoon et al. of multiscale network to most of the structures influ - GM675 VALLIANATOS ence their conductivity parameters, resulting in anoma - 2013] and other miscellaneous geophysical topics such lous diffusion. At a microscopic level, classical diffusion as fault population distribution [Vallianatos et al. 2011, is generated by the random motion of individual parti - Vallianatos and Sammonds, 2011, Vilar et al. 2007, cles/charges and is traditionally described as a stochas - Michas et al. 2015, Papadakis et al. 2016], earthquake tic Gaussian process. However, in anomalous diffusion, energy fluctuations [Wang et al. 2015], rockfalls distri - the mean-square variance of the particle displacement bution [Vallianatos 2013] and polarity reversals of grows faster or slower than that of a Gaussian diffusion Earth’s geomagnetic field [Vallianatos 2011]. In addition process. Thus, the application of fractional electro - concepts of universality between different extreme magnetism is a challenge to describe the effects of geo - events in the Solar-Terrestrial system is given in Balasis electromagnetic induction in geological formations. All et al. [ 2011 a, b, c]. An extended review of the applica - the above mentioned studies, support the idea that real tions of non-extensive statistical mechanics in Earth Sci - subsurface geometries could be viewed as the super - ences is given in Vallianatos et al. [2015] and Vallianatos position of geologic rock types spanning multiple et al. [2016]. length scales. Across all scales, the corresponding elec - In this work we study the statistical features of trical conductivities of the spatial-correlated geologic Earth’s resistivity in a karstic basin as extracted from textures in rocks should generate long-range-depen - TEM soundings introducing the idea of electromag - dent, or fractal-like electromagnetic responses. netic fractional diffusion equation to assess the electro - In a more recent work, Weymeret al. [2015] used magnetic responses due to a multiscale structured the electromagnetic method to evaluate short- and subsurface and viewing the statistical properties of re - long-range correlations in a large scale geological struc - sistivity in terms of non-extensive statistical physics. ture demonstrated that electromagnetic responses are Our results support the idea that long-range correla - governed by long-range dependence effects. To de - tions that are present in Earth’s structure could be ex - scribe the long-range interaction we can consider the tracted in terms of non extensive statistical physics and use of statistical physics to understand the collective to described by q-exponential distributions that ob - properties of geostructures. Then a natural question tained using first principles. The scope of this work is arises. What type of statistical physics is appropriate to not to present a physical model of earth’s resistivity describe effects where long-range dependence effects structure but rather to present a phenomenological ap - are important? An answer to the previous question proach that describes fundamental properties that we could be non-extensive statistical physics (NESP), orig - have to take into account in view of complexity theory. inally introduced by Tsallis [1988] and recently sum - marized in Tsallis [2009]. The latter is strongly 2. Geological and Tectonic Settings of Keritis basin supported by the fact that this type of statistical me - The geology of Crete in the Southern Aegean sea is chanics is the appropriate methodological tool to de - considered to be very interesting due to the position of scribe entities with (multi) fractal distributions of their the island (in the central fore arc of the Hellenic Sub - elements and where long-range dependence are im - duction Zone) and the complexity of its tectonic struc - portant as in fracturing phenomena [Vallianatos et al. ture [Angelier 1976]. 2012] and in most patterns appeared in Earth sciences. The study area is represented by the Keritis Basin NESP is based on a generalization of the classic Boltz - which is situated in the northwestern part of Chania mann-Gibbs entropy and has the main advantage that Prefecture, at Crete Island in Greece (Figure 1). The hy - it considers all-length scale correlations among the ele - drological basin of Keritis represents one of the most ments of a system, leading to a very common in Earth important basins in the municipality of Chania [Kanta Sciences asymptotic power-law behavior. A lot of work et al. 2009a, 2009b, 2013, Parisi et al. 2013]. The area is has been recently done in topics concerning earth sci - drained by the main river of the basin, named Keritis ences in terms of non-extensive statistical mechanics. River. In the area, three different morphological zones This work varies from pre-seismic electromagnetic can be distinguished: the mountainous, the semi-moun - emissions [Kalimeri et al. 2008, Potirakis et al. 2012], tainous and the lowland which comprise, respectively, Geoelectromagnetism and Space Physics [Balasis et al. the south, central and north part of the basin. In par - 2008, 2009, 2016], evolution of seismicity [Telesca 2010, ticular: a) the mountainous zone comprises the north- 2011, Ramirez-Rojas and
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