Statistical physics of fault patterns self-organized by repeated earthquakes

This work presents at attempt to model brittle ruptures and slips in a continental plate and its spontaneous organization by repeated earthquakes in terms of coarse-grained properties of the mechanical plate. A statistical physics model, which simulates anti-plane shear deformation of a thin plate with inhomogeneous elastic properties, is thus analyzed theoretically and numerically in order to study the spatio-temporal evolution of rupture patterns in response to a constant applied strain rate at its borders, mimicking the effect of neighboring plates. Rupture occurs when the local stress reaches a threshold value. Broken elements are instantaneously healed and retain the original material properties, enabling the occurrence of recurrent earthquakes. Extending previous works (Cowieet al., 1993;Miltenbergeret al., 1993), we present a study of the most startling feature of this model which is that ruptures become strongly correlated in space and time leading to the spontaneous development of multifractal structures and gradually accumulate large displacements. The formation of the structures and the temporal variation of rupture activity is due to a complex interplay between the random structure, long-range elastic interactions and the threshold nature of rupture physics. The spontaneous formation of fractal fault structures by repeated earthquakes is mirrored at short times by the spatio-temporal chaotic dynamics of earthquakes, well-described by a Gutenberg-Richter power law. We also show that the fault structures can be understood as pure geometrical objects, namely minimal manifolds, which in two dimensions correspond to the random directed polymer (RDP) problem. This mapping allows us to use the results of many studies on the RDP in the field of statistical physics, where it is an exact result that the minimal random manifolds in 2D systems are self-affine with a roughness exponent 2/3. We also present results pertaining to the influence of the degree β of stress release per earthquake on the competition between faults. Our results provide a rigorous framework from which to initiate rationalization of many, reported fractal fault studies.

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