Statistical physics model for the spatiotemporal evolution of faults

A statistical physics model is used to simulate antiplane shear deformation and rupture of a tectonic plate with heterogeneous material properties. Rupture occurs when the chosen state variable reaches a threshold value. After rupture, broken elements are instantaneously healed and retain the original material properties. We document the spatiotemporal evolution of the rupture pattern in response to a constant velocity boundary condition. A fundamental feature of this model is that ruptures become strongly correlated in space and time, leading to the development of complex fractal structures. These structures, or “faults,” are simply defined by the loci where deformation accumulates. Repeated rupture of a fault occurs in events (“earthquakes”) which themselves exhibit both spatial and temporal clustering. Furthermore, we observe that a fault may be active for long periods of time until the locus of activity spontaneously switches to a different fault. The formation of the faults and the temporal variation of rupture activity is due to a complex interplay between the random small-scale structure, long-range elastic interactions, and the threshold nature of rupture physics. The characteristics of this scalar model suggest that spontaneous self-organization of active tectonics does not result solely from the tensorial nature of crustal deformation; that is, kinematic compatibility is not required for complex fault pattern formation. Furthermore, the localization of the deformation is a dynamical effect rather than a consequence of preexisting structure or preferential weakening of faults compared to the surrounding medium. We present an analysis of scaling relationships exhibited by the fault pattern and the earthquakes in this model.

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