An Ensemble Kalman Filter for Estimating Future Slow Slip Events and Earthquakes on 1D, 2D and 3D Synthetic Experiments

Our ability to forecast future earthquakes is hampered by the very limited information on the fault slip that produce them. In particular the current state of stress, strength, and parameters governing the slip of the faults are highly uncertain. Ensemble data-assimilation methods provide a means to estimate these variables by combining physics-based models and observations while considering their uncertainties. Perfect model experiments with an Ensemble Kalman Filter (EnKF), connected with one-dimensional (1D), two-dimensional (2D), and three-dimensional (3D) earthquake cycle models, demonstrate the ability to estimate the state variables of shear stress, slip velocity, and state (θ) of a straight fault governed by rate-and-state friction surrounded by a homogeneous elastic medium. The models represent a direct-shear laboratory setup in one, two and three dimensions, with an array of shear-strain gauges and piezoelectric transducers located at a small distance to the fault. In this research, we compare the recurrence interval and earthquake occurrence of the EnKF across the different models to better understand the challenges associated with a space-time systems with increasing dimensions and increasingly complex earthquake sequences. The assimilation of synthetic shear-stress and slip-rate observations improves in particular the estimates of shear stress and slip rate on the fault, despite the very low accuracy of the observations. We get reasonable estimates when modelling long-duration earthquakes or slow slip events . Interestingly, we also obtain very good estimates when simulating earthquakes with fast slip rates (up to m/s). The large, nonlinear, changes in stress and velocitiy  during the fast transition from the interseismic to the coseismic phase cause the distributions of the state variables to become bi-modal. The EnKF still provides a reasonable estimate of the time of occurrence of the earthquakes in the synthetic experiments, despite the inherent assumption on the Gaussianity of these distributions.