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Deformation-Induced Electric Currents in Marble Under Simulated Crustal Conditions: Non-Extensivity, Superstatistical Dynamics and Implications for Earthquake Hazard

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Deformation-Induced Electric Currents in Marble Under Simulated Crustal Conditions: Non-Extensivity, Superstatistical Dynamics and Implications for Earthquake Hazard Institute for Risk and Disaster Reduction University College London Deformation-Induced Electric Currents in Marble Under Simulated Crustal Conditions: Non-Extensivity, Superstatistical Dynamics and Implications for Earthquake Hazard Alexis Cartwright-Taylor Submitted in accordance with the requirements for the degree of Doctor of Philosophy at University College London March 2015 2 Declaration I, Alexis Cartwright-Taylor, confirm that the work presented in this thesis is my own. Where information has been derived from other sources, I confirm that this has been indicated in the thesis. Signature: Date: ——————————————————————— —————————— 3 4 Abstract This thesis investigates electric current signals generated spontaneously in specimens of Carrara marble during deformation under crustal conditions. It extends previous work where similar currents were observed during uniaxial deformation of marble. Since marble is a non-piezoelectric material, one of the main questions is how these currents are related to the mechanical processes of deformation. Another question is whether it is possible to extract from these electric currents information about the deformation dynamics. This is particularly important in light of recent claims that geoelectric anomalies observed in the field are related to crustal deformation and can inform us about changes in the organisation of the fault network in a focal region prior to an earthquake. Using an approach that combines rock deformation experiments and statistical modelling, I examine how these electric currents evolve with deformation at the laboratory scale and make several original discoveries regarding their behaviour. To establish how the current signals varied with experimental condition and deformation mechanism across the brittle-ductile transition, I conducted constant strain rate triaxial compression experiments recording differential electric current flow through the rock samples at various confining pressures, strain rates and pore fluid conditions. I acquired mechanical data, ultrasonic velocities and acoustic emissions simultaneously, along with electric current, to constrain the relationship between electric current and deformation. For the statistical modelling, I used a novel entropy-based model, derived from non-extensive statistical mechanics (Tsal- lis, 1988), which has the advantage of including a term to account for interactions in the system. Interactions are effectively modelled by the non-extensive q-parameter. Small (nanoAmpere) electric currents are generated and sustained during deformation under all the conditions tested. Spontaneous electric current flow in the dry samples is seen only in the region of permanent deformation and is due to the presence of localised electric dipoles. This current flow is correlated to the damage induced by microcracking, with a contribution from other intermittent ductile mechanisms. Current and charge densities are consistent with proposed models of crack separation charging and migrating charged edge dislocations. The onset of current flow occurs only after a 10% reduction in P-wave velocity, implying that some degree of crack damage and/or crack connectivity is required before current will flow through the samples. Electric current evolution exhibits three separate time-scales of behaviour, the absolute and fluctuating components of which can be related to the evolution of stress, deformation mechanism, damage and localisation of deformation leading up to sample failure. In the brittle regime, electric current exhibits a precursory change as the stress drop accelerates towards failure, which is particularly distinct at dynamic strain rates. Current and charge production depend strongly on the experimental conditions. Power-law relationships are seen with confining pressure and strain rate, with the first correspond- ing to increased microcrack suppression and the second to time-dependent differences in 5 deformation mechanism across the brittle-ductile transition. In the presence of an ionic pore fluid, electrokinetic effects dominate over solid-state mechanisms but development of the crack network and charge contribution from solid-state deformation processes drive the variation in electrokinetic parameters. Current flow in the dry samples is approximately proportional to stress within 90% of peak stress. In the fluid-saturated samples, proportionality holds from 40% peak stress, with a significant increase in the rate of current production from 90% peak stress, and is associated with fluid flow during dilatancy. This proportionality, together with the power- law relationship between current and strain rate is reminiscent of power-law creep, where deformation rate varies as a power-law function of stress, and suggests that the electric signals could be used as a proxy for stress. High frequency fluctuations in the electric current signal can be described by ‘fat-tailed’ q- Gaussian statistics, consistent with an origin in non-extensive statistical mechanics. These distributions can be explained as arising from superstatistical dynamics (Beck, 2001; Beck and Cohen, 2003), i.e., the superposition of local mechanical relaxations in the presence of a slowly varying driving force. The macroscopic distribution parameters provide an excellent prediction of the experimentally observed mean energy dissipation rate of the system (as modelled by the superstatistical β-parameter), particularly at slow strain rates. Furthermore, characteristic q-values are obtained for different deformation regimes across the brittle-ductile transition, and the evolution of q during deformation reveals a two-stage precursory anomaly prior to sample failure, consistent with the stress intensity evolution as modelled from fracture mechanics. These findings indicate that the dynamics of rock deformation are reflected in the statistical properties of the recorded electric current. My findings support the notion that electric currents in the crust can be generated purely from deformation processes themselves. Scaling up the laboratory results to large stressed rock volumes at shallow crustal pressures and constant crustal strain rates, deformation induced transient telluric current systems may be as large as 106 A, even accounting for > 99% dissipation, which corresponds to a huge accumulated net charge of 1022 C. This implies that a significant amount of charge from deforming tectonic regions contributes to the Earth’s telluric currents and electric field, although due to conduction away from the stressed rock volume, it is unlikely that accumulated charge of this quantity would ever be measured in the field. Electric current evolution and its precursory characteristics can be related to models for electric earthquake precursors and fault-zone damage organisation, developed from field observations, providing experimental support for them. However, given the oscillatory nature of the current evolution observed during cataclastic flow processes in the labora- tory, there is a high probability of false alarms. Furthermore, the potential for electric anomalies to be useful as earthquake precursors remains contentious due to the difficulties of separating deformation-induced signals from other telluric noise and the wider issue of establishing a statistically significant link with earthquakes. 6 Acknowledgements I would like to thank the many people who have supported and assisted me during the course of this thesis. Very little of the work presented here could have been undertaken if it were not for the many colleagues, friends and family members who have helped and advised me in countless ways. Firstly, I extend my appreciation to my supervisors Peter Sammonds and Filippos Val- lianatos for their guidance and encouragement. Without their invaluable intellectual, pastoral and financial support, this thesis would never have come to fruition. I also acknowledge UCL Impact, the UCL Institute for Risk and Disaster Reduction and the Technological Educational Institute (TEI) of Crete in Chania for my studentship. Additional funding came from the UCL Roberts Fund, the UCL Graduate School, the Reid Trust and ERASMUS, which allowed me to attend several conferences and training courses and enabled me to spend three months working at the TEI in Chania. Experimental studies are, by their nature, difficult and frustrating. I owe huge thanks to Nic Brantut, Neil Hughes, Steve Boon and John Bowles for their advice and assistance in the laboratory. Their expertise, willingness to help and seemingly endless patience ensured the success of my experimental program and helped to maintain my sanity. I also thank Jim Davy for his company during many hours of sample preparation, and Rosie, Jen, Celine, Leisa and Danuta for their administrative and IT support. To all my fellow PhD students, and particularly Nikki, Mike, Marie and Alexandra (ma posse, innit), thank you for being there and sharing with me this interminable trudge through science. Your friendship, hilarious banter, supportive hugs and the many agreeable hours spent with you chatting and drinking (tea and beer) have made it all worthwhile. I would also like to thank the two Georges for our extensive, non-extensive discussions and my friends at the TEI in Greece, Despina and Eleonora, for welcoming me so warmly into their lives and showing such kindness during my stay. Finally, I would like to express my gratitude to my friends outside UCL and to my family for their unwavering love and support through everything. Mum and Dad, thank you especially for taking me
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