Ensemble data assimilation for earthquake sequences: Probabilistic estimation and forecasting of fault stresses

Our physical understanding of earthquakes, along with our ability to forecast them, is hampered by limited indications on the current and future state of stress on faults. Integrating indirect observations, laboratory experiments and physics-based numerical modelling to quantitatively estimate this evolution is crucial. However, quantitative integrations are tenuous in light of the scarcity and uncertainty of observations and the difficulty of modelling the physics governing earthquakes. We show that observations and prior physical knowledge, along with their errors, can be efficiently integrated through the statistical framework of ensemble data assimilation (EDA), which is adopted from weather forecasting. To evaluate whether fault stress estimation and forecasting is possible, we perform a perfect model test in a subduction zone setup that mimicks a scaled laboratory experiment. Synthetic noised data on velocities and stresses from one point near the surface are assimilated using an Ensemble Kalman Filter. These data update the velocity and stress states throughout 150 ensemble members, whose dynamics is governed by a seismic cycle model. This visco-elasto-plastic forward model forecasts the system’s evolution through solving Navier–Stokes equations with a strongly rate-dependent friction coefficient. The ensemble assimilation of data from a single location provides probabilistic estimates of fault stress and dynamic strength evolution, which capture the true solution 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. In the analysis step, this covariance allows stress and strength distributions to be reconstructed. In the subsequent forecast step the physical equations are solved to propagate the updated states forward in time. This provides probabilistic information on the likelihood of occurrence of the next earthquake in this synthetic laboratory setting. Throughout the ensemble simulations the forecasting ability for large, quasi-periodic events turns out to be significantly better than that of a periodic recurrence model. For example, it only requires an alarm to sound for 17 per cent instead of 68 per cent of the time to forecast 70 per cent of 21 events. We show that combining our prior knowledge of physical laws with observations through a Bayesian framework provides distinct added value with respect to using observations or numerical models independently. This educational test thus shows vast potential for including physics-based information into probabilistic seismic hazard assessment using EDA. To analyze its real world potential assumptions on an exact representation of the physics in a 2-D simplified system remain to be explored.ISSN:0956-540XISSN:1365-246