On Parameter Bias in Earthquake Sequence Models using Data Assimilation

Abstract. The feasibility of physics-based forecasting of earthquakes depends on how well models can be calibrated to represent earthquake scenarios given uncertainties in both models and data. We investigate whether data assimilation can estimate current and future fault states, i.e., slip rate and shear stress, in the presence of a bias in the friction parameter. We perform state estimation as well as combined state-parameter estimation using a sequential importance resampling particle filter in a 0D generalization of the Burridge–Knopoff spring-block model with rate-and-state friction. Minor changes in the friction parameter epsilon can lead to different state trajectories and earthquake characteristics. The performance of data assimilation in estimating the fault state in the presence of a parameter bias in epsilon depends on the magnitude of the bias. A small parameter bias in epsilon (+3 %) can be compensated very well using state estimation (R²= 0.99), whereas an intermediate bias (-14 %) can only be compensated partly (R²= 0.47). When increasing particle spread by accounting for model error and an additional resampling step R² increases to 0.61. However, when there is a large bias (-43 %) in epsilon, only state-parameter estimation can fully account for the parameter bias (R²= 0.97). Simultaneous state- and parameter estimation thus effectively separates error contributions from friction and shear stress to correctly estimate current and future shear stress and slip rate. This illustrates the potential of data assimilation for estimation of earthquake sequences and provides insight into its application in other non-linear processes with uncertain parameters.