Non-extensivity of the isothermal depolarization relaxation currents in uniaxial compressed rocks
Earth Sciences Department, University College London - Gower Street, London, WC1E 6BT, UK, EU
2 Technological Educational Institute of Crete, Laboratory of Geophysics and Seismology - Crete, Greece, EU
3 Department of Electronics, Technological Educational Institute of Athens - Athens, Greece, EU
Accepted: 10 May 2011
The isothermal depolarization current relaxation in uniaxial compressed rocks follows a generalized exponential function which explicitly introduces hierarchically constrained dynamics and macroscopic interactions. The interactions are associated with the non-extensive entropy parameter q and exhibits a behavior indicating a scaling with normalized uniaxial stress Σ=σ/σY, where σY is the yield stress where deviation from the elastic region starts in a stress-strain curve. Combining ideas of Levy and Tsallis statistics we argue the remarkable result that a Levy-walk–type mechanism can organize the geometry of the heterogeneous system to criticality. The stress-dependent q-estimation leads to the conclusion that fracturing is a subextensive process with strong interaction.
PACS: 89.75.Da – Systems obeying scaling laws / 91.30.Px – Earthquakes / 89.75.-k – Complex systems
© EPLA, 2011