An experimental approach to non - extensive statistical physics and Epidemic Type Aftershock Sequence (ETAS) modeling. The case of triaxially deformed sandstones using acoustic emissions.

Abstract:

Fracturing is the most prevalent deformation mechanism in rocks deformed in the laboratory under simulated upper crustal conditions. Fracturing produces acoustic emissions (AE) at the laboratory scale and earthquakes on a crustal scale. The AE technique provides a means to analyse microcracking activity inside the rock volume and since experiments can be performed under confining pressure to simulate depth of burial, AE can be used as a proxy for natural processes such as earthquakes.

Experimental rock deformation provides us with several ways to investigate time-dependent brittle deformation. Two main types of experiments can be distinguished: (1) “constant strain rate” experiments in which stress varies as a result of deformation, and (2) “creep” experiments in which deformation and deformation rate vary over time as a result of an imposed constant stress.

We conducted constant strain rate experiments on air-dried Darley Dale sandstone samples in a variety of confining pressures (30MPa, 50MPa, 80MPa) and in water saturated samples with 20 MPa initial pore fluid pressure. The results from these experiments used to determine the initial loading in the creep experiments.

Non-extensive statistical physics approach was applied to the AE data in order to investigate the spatio-temporal pattern of cracks close to failure. A more detailed study was performed for the data from the creep experiments. When axial stress is plotted against time we obtain the trimodal creep curve. Calculation of Tsallis entropic index q is performed to each stage of the curve and the results are compared with the ones from the constant strain rate experiments.

The Epidemic Type Aftershock Sequence model (ETAS) is also applied to each stage of the creep curve and the ETAS parameters are calculated. We investigate whether these parameters are constant across all stages of the curve, or whether there are interesting patterns of variation.

This research has been co-funded by the European Union (European Social Fund) and Greek national resources under the framework of the “THALES Program: SEISMO FEAR HELLARC” project of the “Education & Lifelong Learning” Operational Programme.