Preventing Instabilities and Inducing Controlled, Slow-Slip in Frictionally Unstable Systems.

Abstract

We propose a theory for preventing instabilities and inducing controlled, slow‐slip in frictionally unstable systems, such as the Generalized‐Burridge‐Knopoff (GBK) model and seismic fault models. We exploit the dependence of friction on pressure and use it as a backdoor for altering the dynamics of the underlying dynamical system. We use the mathematical Theory of Control and, for the first time, we manage to (a) stabilize and restrict chaos in this kind of systems, (b) guarantee slow frictional dissipation and (c) tune the system toward desirable global asymptotic equilibria of lower energy. Our control approach is robust and does not require exact knowledge of the frictional or elastic behavior of the system. Numerical examples of control are given for a Burridge‐Knopoff system and a strike‐slip fault model obeying rate‐and‐state friction. GBK models are known to present Self‐Organized Critical (SOC) behavior. Therefore, the presented methodology shows an additional example of SOC Control. Even though further developments are necessary before any practical application, we expect our methodology to inspire earthquake mitigation strategies regarding anthropogenic and/or natural seismicity.