<p>Forecasting earthquake occurrence is a challenging endeavor, which will ultimately require a combination of observations and physics-based models. Data assimilation may help to combine these and their uncertainties in a statistically solid manner. To understand the potential of ensemble data assimilation, we investigate whether the fault stress state can be estimated and forecasted in the presence of a bias in a friction parameter. In a perfect model test, we introduce different degrees of bias in rate-and-state parameter b. b describes the evolution of frictional strength with fault slip velocity and thus impacts earthquake slip and the subsequent recurrence interval. Our forward model is a simplified, zero-dimensional (0D) Burridge-Knopoff spring-block system with a rate- and state-dependent friction formulation using a ‘slip law’. We assimilate synthetic observations of fault shear stress and slip rate variables and corresponding large uncertainties. We compare state estimation with joint state-parameter estimation using a sequential importance resampling particle filter by evaluating the quality of the estimated fault stress probability density functions (pdf’s).</p><p>The results of the study indicate that state estimation works well for systems with low (3%) to intermediate (15%) bias. This performance for the case of intermediate bias can be improved through increasing model error combined with double resampling in the particle filter. For a large friction-parameter bias (42 %), we show that state-parameter estimation is the only way to correct the bias. This is an important result, because it shows that state-parameter estimation is able to identify trade-offs and separate error contributions coming from stress state and friction parameters.  Furthermore, the results of this study can be applied to other data assimilation applications involving models that are particularly vulnerable to parameter biases.</p>

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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.