Fracture and electric current in the crust: a q-statistical approach

We have conducted room-temperature, triaxial compression experiments on samples of Carrara marble, recording concurrently acoustic and electric current signals emitted during deformation as well as mechanical loading information and ultrasonic wave velocities. Our results reveal that, in a non-piezoelectric rock under simulated crustal conditions, a measurable and increasing electric current (nA) is generated within the stressed sample in the region beyond (quasi-)linear elastic deformation; i.e. in the region of permanent deformation beyond the yield point of the material and in the presence of microcracking. This has implications for the earthquake preparation process. Our results extend to shallow crustal conditions previous observations of electric current signals in quartz-free rocks undergoing uniaxial deformation, supporting the idea of a universal electrification mechanism related to deformation; a number of which have been proposed. Confining pressure conditions of our slow strain rate experiments range from the purely brittle regime to the semi-brittle transition where cataclastic flow is the dominant deformation mechanism. Electric current evolution under these two confining pressures shows some markedly different features, implying the existence of a current-producing mechanism during both microfracture and frictional sliding, possibly related to crack localisation. In order to analyse these 'pressure-stimulated' electric currents, we adopt an entropy-based non-extensive statistical physics approach that is particularly suited to the study of fracture-related phenomena. In the presence of a long timescale (hours) external driving force (i.e. loading), the measured electric current exhibits transient, nonstationary behaviour with strong fluctuations over short timescales (seconds); calmer periods punctuated by bursts of strong activity. We find that the probability distribution of normalised electric current fluctuations over short time intervals (0.5s) can be well-described by a 'superstatistical' q-Gaussian distribution of a form similar to that which describes turbulent flows. We interpret this to mean that the measured electric current is driven to varying, temporary, local equilibria during deformation. This behaviour is analogous to the self-organising avalanche-like behaviour of fracture events and suggests that the observed behaviour of measured electric current is in direct response to the microcracking events themselves, their localisation within the sample and their increasing number. We also apply a similar non-extensive approach to analyse the magnitudes and interevent-times of the acoustic emissions and find that these are well-described by q-exponential distributions. We interpret the q-parameter for both electric and acoustic emissions as a physical one describing the stability of the system, with changes in stability being reflected in the evolution of the q-parameter during deformation. Our results have positive implications for the application of non-extensive statistical physics to seismic hazard and electric earthquake precursors.