Nonlinear Data Assimilation for State and Parameter Estimation in Earthquake Simulation

The highly nonlinear dynamics of earthquake sequences and the limited availability of stress observations near subsurface faults make it very difficult, if not impossible, to forecast earthquakes. Ensemble data-assimilation methods provide a means to estimate state variables and parameters of earthquake sequences that may lead to a better understanding of the associated fault-slip process and contribute to the forecastability of earthquakes. We illustrate the challenges of data assimilation in earthquake simulation with an overview of three studies, each with different objectives and experiments.

In the first study, by reconstructing a laboratory experiment with an advanced numerical simulator we perform synthetic twin experiments to test the performance of an ensemble Kalman Filter (EnKF) and its ability to reconstruct fault slip behaviour in 1D and 3D simulations. The data assimilation estimates and forecasts earthquakes, even when having highly uncertain observations of the stress field. In these experiments, we assume the friction parameters to be perfectly known, which is typically not the case in reality.

A bias in a friction parameter can cause a significant change in earthquake dynamics, which will complicate the application of data assimilation in realistic cases. The second study addresses how well state estimation and state-parameter estimation can account for friction-parameter bias. For this, we use a 0D model for earthquake recurrence with a particle filter with sequential importance resampling. This shows that in case of intermediate to large uncertainty in friction parameters, combined state-and-parameter estimation is critical to correctly estimate earthquake sequences. The study also highlights the advantage of a particle filter over an EnKF for this nonlinear system.

The post- and inter-seismic deformations following an earthquake are rather gradual and do not pose the same challenges for data assimilation as the deformation during an earthquake event. To estimate the model parameters of surface displacements during these phases, a third study illustrates the application of the Ensemble Smoother-Multiple Data Assimilation and the particle filter with actual GPS data of the Tohoku 2011 earthquake.

Based on the comparison of the various experiments, we discuss the choice of data-assimilation method and -approach in earthquake simulation and suggest directions for future research.