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 earthq uakes in terms of coarse-grained properties of the mechanical plate. A statistical physics model, which simulates anti-plane shear deformati on of a thin plate with inhomogeneous elastic properties, is thus anal yzed theoretically and numerically in order to study the spatio-tempor al evolution of rupture patterns in response to a constant applied str ain rate at its borders, mimicking the effect of neighboring plates. R upture occurs when the local stress reaches a threshold value. Broken elements are instantaneously healed and retain the original material p roperties, enabling the occurrence of recurrent earthquakes. Extending previous works (COWIE et al., 1993; MILTENBERGER et al., 1993), we pr esent a study of the most startling feature of this model which is tha t ruptures become strongly correlated in space and time leading to the spontaneous development of multifractal structures and gradually accu mulate large displacements. The formation of the structures and the te mporal variation of rupture activity is due to a complex interplay bet ween the random structure, long-range clastic interactions and the thr eshold nature of rupture physics. The spontaneous formation of fractal fault structures by repeated earthquakes is mirrored at short times b y the spatio-temporal chaotic dynamics of earthquakes, well-described by a Gutenberg-Richter power law. We also show that the fault structur es can be understood as pure geometrical objects, namely minimal manif olds, which in two dimensions correspond to the random directed polyme r (RDP) problem. This mapping allows us to use the results of many stu dies on the RDP in the field of statistical physics, where it is an ex act result that the minimal random manifolds in 2D systems are self-af fine with a roughness exponent 2/3. We also present results pertaining to the influence of the degree beta of stress release per earthquake on the competition between faults. Our results provide a rigorous fram ework from which to initiate rationalization of many reported fractal fault studies.