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It is being increasingly recognized that geological media are inherently rough with persistent, long-range spatial correlations in physical properties, including electrical conductivity, which spans many decades in length scale. In the present study, the ideas of a multi-scaled geological medium and the anomalous diffusion of EM eddy currents applied, in Keritis Basin (Western Crete, Greece), a complex geological system surrounded by normal faults and with the majority of formations to be calcareous and karstified. We present evidence of a multi-scaled hierarchical structure,based on observed q-exponential distributions of the resistivity, supporting our motivation to introduce fractional diffusion ideas and non-extensive statistical physics to describe the geoelectrical structure of karstified Keritis basin. The essential goal of this paper is to test in a real geological complex formation the TEM response in terms of the rough geological medium where the conductivity of the ground has a spatial distribution, which is described by a roughness parameter,and to better understand the geoelectrical properties of complex geological structure introducing the ideas of fractional diffusion and non extensive statistical physics.
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