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Analysis of Dynamics in Multiphysics Modelling of Active Faults

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  • Sotiris Alevizos

    (School of Petroleum Engineering, University of New South Wales (UNSW), Sydney, NSW 2052, Australia)

  • Thomas Poulet

    (School of Petroleum Engineering, University of New South Wales (UNSW), Sydney, NSW 2052, Australia
    CSIRO Mineral Resources Flagship, North Ryde, NSW 2113, Australia)

  • Manolis Veveakis

    (School of Petroleum Engineering, University of New South Wales (UNSW), Sydney, NSW 2052, Australia
    CSIRO Mineral Resources Flagship, North Ryde, NSW 2113, Australia)

  • Klaus Regenauer-Lieb

    (School of Petroleum Engineering, University of New South Wales (UNSW), Sydney, NSW 2052, Australia)

Abstract

Instabilities in Geomechanics appear on multiple scales involving multiple physical processes. They appear often as planar features of localised deformation (faults), which can be relatively stable creep or display rich dynamics, sometimes culminating in earthquakes. To study those features, we propose a fundamental physics-based approach that overcomes the current limitations of statistical rule-based methods and allows a physical understanding of the nucleation and temporal evolution of such faults. In particular, we formulate the coupling between temperature and pressure evolution in the faults through their multiphysics energetic process(es). We analyse their multiple steady states using numerical continuation methods and characterise their transient dynamics by studying the time-dependent problem near the critical Hopf points. We find that the global system can be characterised by a homoclinic bifurcation that depends on the two main dimensionless groups of the underlying physical system. The Gruntfest number determines the onset of the localisation phenomenon, while the dynamics are mainly controlled by the Lewis number, which is the ratio of energy diffusion over mass diffusion. Here, we show that the Lewis number is the critical parameter for dynamics of the system as it controls the time evolution of the system for a given energy supply (Gruntfest number).

Suggested Citation

  • Sotiris Alevizos & Thomas Poulet & Manolis Veveakis & Klaus Regenauer-Lieb, 2016. "Analysis of Dynamics in Multiphysics Modelling of Active Faults," Mathematics, MDPI, vol. 4(4), pages 1-14, September.
  • Handle: RePEc:gam:jmathe:v:4:y:2016:i:4:p:57-:d:78638
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    References listed on IDEAS

    as
    1. Peter B. Kelemen & Greg Hirth, 2007. "A periodic shear-heating mechanism for intermediate-depth earthquakes in the mantle," Nature, Nature, vol. 446(7137), pages 787-790, April.
    2. Kostić, Srđan & Vasović, Nebojša & Perc, Matjaž & Toljić, Marinko & Nikolić, Dobrica, 2013. "Stochastic nature of earthquake ground motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(18), pages 4134-4145.
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