Data-driven slow earthquake dynamics

Friction is a complex phenomenon. This can be seen, for example, in laboratory experiments where stick-slip motion of various kind (i.e., slow and fast instabilities) can be produced when adapting the normal stress applied to the system. Similarly, natural earthquakes also produce
complex stick-slip behaviour. A first challenge in the description of friction comes from the potentially high number of degrees of freedom (dofs) involved in the description of the dynamics of the sliding surfaces. Nonetheless, it was shown that friction can be described with a reduced number of dofs or variables of the dynamics. These may include the shear stress, the relative sliding slip rate, and one or more variables that describe the state of the contact of the sliding surfaces. We investigate the possibility to extract directly from the data the governing equations of friction starting from a simplified synthetic example. We further study the laboratory data with the Hankel Alternative View Of Koopman (HAVOK) theory, a method rooted in dynamical system theory that leverages data driven techniques and produces a Reduced Order Model (ROM) to reconstruct a shadow of the attractor of a system from observational data. We finally compare the results obtained for the laboratory experiments with Cascadia slow earthquakes.