Experimental and theoretical results of stress relaxations in a model of earthquake dynamics

– We report on experimental and theoretical results on the dynamical behavior of propagating solitary relaxations in a model system for earthquake-like dynamics. In the experiments, a continuous elastic medium is sheared at very slow rate in between two coaxial cylinders. Solitary propagating relaxations travel at speeds that are proportional to the driving speed, though ∼ 10 times faster, and inversely proportional to the number of solitary relaxations in the system. We show that this behavior appears due to the existence of a characteristic length scale which is the typical displacement of a surface element in a relaxation. Stick-slip behavior is an interesting case of complex spatiotemporal dynamics that may appear in extended systems. A particularly relevant phenomenon that may be associated with this type of dynamics is earthquake generation [1]. Once a fault has been formed its further motion is controlled by friction, and can proceed in either a continuous manner at tectonic velocities (fault creep) or through dynamic instabilities (earthquakes) followed by periods of no motion. This common frictional behavior is usually referred to as regular stick-slip. Deterministic spring-block models with different friction laws [2–5] have been used both for describing stick-slip observed in the laboratory and for modeling earthquakes [1]. The physical ingredients of these models are a couple of plates in relative motion, and a chain of blocks that are elastically coupled among themselves and to one of the plates, and sliding on top of the other plate with a given force of friction. The blocks mimic the points of contact between two tectonic plates, the springs represent the elastic response of the contact region to normal and shear stress, and the friction force is the non-linear element of the models. Numerical studies of these models, with velocity weakening friction have shown that several types of complex spatiotemporal dynamics may appear depending on the different length and velocity scales of the system. For instance, disordered regimes [3, 5, 6] and nearly periodic global relaxations [7] may appear. Propagating solutions exist also in systems with periodic boundary conditions, depending on both the size of the system and the pulling rate [8–10].