Quality evaluation of assimilation-based forecast of rate-and-state governed fault analog

During an earthquake, the frictional resistance of a fault suddenly drops to release the elastic energy that has been accumulating over decades to centuries. In addition to the steady increase of stress on faults due to tectonics, external perturbations have been shown to modulate the fault behavior over a wide range of time scales. The spring block slider model following rate-and-state friction framework with velocity-weakening behavior undergoing periodic perturbations has been known to host complex stick-slip events ranging from fast earthquakes to slow earthquakes, making it a good analog of a simple fault. Accurate characterization of system state and tidal forcing parameters is critical for understanding the triggering mechanisms and ultimately improving seismic hazard assessment. In this work, we employ ensemble-based data assimilation techniques to carry out state and joint state-parameter estimation in a tidal modulated spring slider. We perform twin experiments to estimate the tidal perturbation parameters such as period and amplitude. In this scenario, we compare the iterative ensemble Kalman smoother (I-EnKS) with ensemble Kalman filter (EnKF) variants for joint state-parameter estimation. Using the smoothed estimates, we assess forecast quality by evaluating prediction accuracy over multiple recurrence intervals. To account for model uncertainties, we incorporate additive stochastic forcing to examine its effect on state-parameter estimation and forecast accuracy.