Experimental evidence of a non-extensive statistical physics behaviour of fracture in triaxially deformed Etna basalt using acoustic emissions

¹ Department of Earth Sciences, University College London - Gower Str., London, WC1E 6BT, UK, EU
² Technological Educational Institute of Crete, Laboratory of Geophysics and Seismology - Crete, Greece, EU
³ Geological Institute, Department of Earth Sciences, Swiss Federal Institute of Technology - Zurich, Switzerland

^a f.vallianatos@ucl.ac.uk

Received: 16 September 2011
Accepted: 6 January 2012

Abstract

Using acoustic emission (AE) data, we apply the concepts of non-extensive statistical physics (NESP) to the time intervals and Euclidean distances between two consecutive AE. The application of NESM is appropriate to systems such as fracture where non-linearity, long-range interactions and scaling are important. We find that the AE scalar moment distribution and the inter-event time distribution reflect a sub-additive system with thermodynamic q-values of q_M=1.82 and q_τ=1.34, respectively, while the inter-event distance distribution follows a q-statistics, with q_D=0.65, supporting the conclusion of the so-called “non-extensive spatio-temporal duality”. The results regarding the inter-event time distribution are discussed using the complementary to the NESP approach of superstatistics which is based on a superposition of ordinary local equilibrium statistical mechanics, using a suitable intensive parameter β that fluctuates on a relatively large temporal scale. This analysis leads us to conclude that a low number of degrees of freedom describe the process which generates the distribution of AE.