Abstract
Fracturing processes within solid Earth materials are inherently a complex phenomenon so that the underlying physics that control fracture initiation and evolution still remain elusive. However, universal scaling relations seem to apply to the collective properties of fracturing phenomena. In this article we present a statistical physics approach to fracturing based on the framework of non-extensive statistical physics (NESP). Fracturing phenomena typically present intermittency, multifractality, long-range correlations and extreme fluctuations, properties that motivate the NESP approach. Initially we provide a brief review of the NESP approach to fracturing and earthquakes and then we analyze stress and stress direction time series within Arctic sea ice. We show that such time series present large fluctuations and probability distributions with “fat” tails, which can exactly be described with the q-Gaussian distribution derived in the framework of NESP. Overall, NESP provide a consistent theoretical framework, based on the principle of entropy, for deriving the collective properties of fracturing phenomena and earthquakes.
Highlights
Stress increase within solid Earth materials and the buildup of a proportional amount of strain eventually culminates in the deformation and fracture of the material
In the present work we present a brief review and new results regarding the application of non-extensive statistical physics (NESP) to fracturing processes and earthquakes
Abe and Suzuki [25,50] showed that the cumulative distribution functions (CDFs) of inter-event distances P (>r) and inter-event times P (>T) between successive earthquakes in California and Japan scale according to the q-exponential distribution (Equation (8)), for q-values of qr < 1 and qT > 1, respectively
Summary
Stress increase within solid Earth materials and the buildup of a proportional amount of strain eventually culminates in the deformation and fracture of the material. The temporal evolution of seismicity is characterized by multifractality and correlations at all timescales [8,9,10], while the production rate of aftershocks that follow a mainshock generally decays as a power-law with time according to the modified Omori formula [11]. Such properties have motivated the consideration of statistical physics as a consistent tool for explaining the macroscopic behavior of fracturing phenomena [4,12,13]. Such findings provide further insights in how to model risk of large deformation events that present large ice motion induced stresses, which can impact any given place in the Arctic sea ice pack
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