Hamed Ali Diab-Montero , Meng Li , Ylona van Dinther, Femke C. Vossepoel

Our ability to forecast earthquakes and slow slip events is hampered by limited information on the current state of stress on faults. Ensemble data assimilation methods permit estimating the state by combining physics-based models and observations, while considering their uncertainties. We employ an Ensemble Kalman Filter (EnKF) to estimate shear stresses, slip rates, and the state theta acting on a fault point governed by rate-and-state friction embedded in a 1D elastic medium. We test the effectiveness of data assimilation by conducting perfect model experiments. We assimilate noised shear-stress and velocity synthetic values acquired at a small distance to the fault. The assimilation of uncertain shear stress observations improves in particular the estimates of the shear stress at the fault of slow-slip events, while assimilating observations of velocity improves their slip-rate estimation. Both types of observations help equally well to better estimate the state theta. For earthquakes, the shear stress observations improve the estimation of shear stress, slip rates and the state theta, while the velocity observation improves in particular the slip-rate estimation. Data assimilation significantly improves the estimates of temporal occurrence of slow slip events and to a large extent also for earthquakes. The latter is reduced due to large, abrupt changes in velocity and shear stress during earthquakes, which lead to non-Gaussian priors for subsequent assimilation steps. These challenge, but do not undermine the effectiveness of the EnKF. In fact, the forecastability for earthquakes for the same alarm duration is very similar to slow slip events, having a very low miss rate with an alarm duration of just 10% of the recurrence interval of the events. These results confirm that data assimilation is a promising approach for the combination of uncertain physics and indirect, noisy observations for the forecasting of both slow-slip events and earthquakes.