Estimation and Forecasting of Seismic Cycles using a Fault-Slip Model with Uncertain Parameters - Implications for Data Assimilation

The feasibility of forecasting future earthquakes will directly depend on how well we can calibrate models to represent real earthquake scenarios given the uncertainties in both models and data. In this study, we investigate the problem of inferring posterior probabilities of fault state estimates which includes the slip, slip velocity and shear stress in faults, when dealing with parameter uncertainties in data assimilation. The model chosen for this study represents a generalization of the Burridge-Knopoff spring-block model with Dieterich-Ruina's nonlinear rate and state-dependent friction law. An important feature of these nonlinear models is that seemingly minor changes in parameters can lead to different fault behaviour. Therefore, it is crucial to use appropriate parameter values in such models and to incorporate their uncertainties. To account for this, we perform simulations to demonstrate the feasibility and benefits of parameter updates in data assimilation. In particular, we update the uncertain parameters along with the state variables using a particle filter and compare it to the case where we only update state variables. Our results suggests that updating the parameters can improve the state estimates and forecasts considerably.