Stochastic Chaos in Laboratory Earthquakes

Earthquakes are a complex natural phenomenon. They typically are the result of frictional instabilities along preexisting weakness zones called faults. The strain slowly builds up in the fragile Earth crust because of the presence of an external loading counterbalanced by friction forces at the faults’ interface. When the load cannot be balanced by the friction any further, the fault slips releasing the accumulated strain. Friction is a nonlinear phenomenon, and as such frictionally controlled systems may be subject to chaotic behavior. Seismic cycle analogs can be reproduced with rock friction experiments in the laboratory with a double direct shear apparatus. We show that laboratory earthquakes follow a low-dimensional random attractor. We explain the observations with a model of stochastic differential equations based on the rate- and state-friction framework. We show that small perturbations (less than 1‰) on the shear and normal stress can induce laboratory earthquakes aperiodic behavior with coefficient of variations of the order of some percent. The nonlinear nature of friction amplifies small scale perturbations, making mid-long term predictions of the system possible only statistically even for stick-slip events in a well controlled environment like the laboratory.