Sequential Data Assimilation for Estimation and Forecasting of Fault Slip: a Proof of Concept

Our physical understanding and forecasting ability of earthquakes, and other solid Earth dynamic processes, is significantly hampered by limited indications on the evolving state of stress and strength on faults. Integrating observations and physics-based numerical modeling to quantitatively estimate this evolution of a fault's state is crucial. However, systematic attempts are limited and tenuous, especially in light of the scarcity and uncertainty of natural data and the difficulty of modelling the physics governing earthquakes. We adopt the statistical framework of sequential data assimilation - extensively developed for weather forecasting - to efficiently integrate observations and prior knowledge in a forward model, while acknowledging errors in both. 

To prove this concept we perform a perfect model test in a simplified subduction zone setup, where we assimilate synthetic noised data on velocities and stresses from a single location. Using an Ensemble Kalman Filter, these data and their errors are assimilated to update 150 ensemble members from a Partial Differential Equation-driven seismic cycle model.

Probabilistic estimates of fault stress and dynamic strength evolution capture the truth exceptionally well. This is possible, because the sampled error covariance matrix contains prior information from the physics that relates velocities, stresses and pressure at the surface to those at the fault. During the analysis step, stress and strength distributions are thus reconstructed such that fault coupling can be updated to either inhibit or trigger events. In the subsequent forecast step, the physical equations are solved to propagate the updated states forward in time and thus provide probabilistic information on the occurrence of the next event. At subsequent assimilation steps, the system’s forecasting ability turns out to be significantly better than that of a periodic recurrence model (requiring an alarm ~17% vs. ~68% of the time). This thus provides distinct added value with respect to using observations or numerical models separately. Although several challenges for applications to a natural setting remain, these first results indicate the large potential of data assimilation techniques for probabilistic seismic hazard assessment and other challenges in dynamic solid earth systems.