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Our ability to forecast earthquakes and slow slip events is hampered by limited information on the current state of stress on faults. Ensemble data assimilation methods permit estimating the state by combining physics-based models and observations, while considering their uncertainties. We use an ensemble Kalman filter (EnKF) to estimate shear stresses, slip rates and the state θ acting on a fault point governed by rate-and-state friction embedded in a 1-D elastic medium. We test the effectiveness of data assimilation by conducting perfect model experiments. We assimilate noised shear-stress and velocity synthetic values acquired at a small distance to the fault. The assimilation of uncertain shear stress observations improves in particular the estimates of shear stress on fault segments hosting slow slip events, while assimilating observations of velocity improves their slip-rate estimation. Both types of observations help equally well to better estimate the state θ. For earthquakes, the shear stress observations improve the estimation of shear stress, slip rates and the state θ , whereas the velocity observations improve in particular the slip-rate estimation. Data assimilation significantly improves the estimates of the temporal occurrence of slow slip events and to a large extent also of earthquakes. Rapid and abrupt changes in velocity and shear stress during earthquakes lead to non-Gaussian priors for subsequent assimilation steps, which breaks the assumption of Gaussian priors of the EnKF. In spite of this, the EnKF still provides estimates that are unexpectedly close to the true evolution. In fact, the forecastability for earthquakes for the same alarm duration is very similar to slow slip events, having a very low miss rate with an alarm duration of just 10 per cent of the recurrence interval of the events. These results confirm that data assimilation is a promising approach for the combination of uncertain physics and indirect, noisy observations for the forecasting of both slow slip events and earthquakes. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The relative contribution of tectonic and kinematic processes to seismic behaviour of mountain belts is still controversial. To understand the partitioning between these processes we developed a model that simulates both tectonic and seismic processes in a continental collision setting. These 2D seismo-thermo-mechanical (STM) models obtain a Gutenberg–Richter frequency–magnitude distribution due to spontaneous events occurring throughout the orogen. Our simulations suggest that both the corresponding slope ( b value) and maximum earthquake magnitude ( M W m a x ) correlate linearly with plate convergence rate. By analyzing 1D rheological profiles and isotherm depths we demonstrate that plate convergence rate controls the brittle strength through a rheological feedback with temperature and strain rate. Faster convergence leads to cooler temperatures and also results in more larger seismogenic domains, thereby increasing both M W m a x and the relative number of large earthquakes (decreasing b value). This mechanism also predicts a more seismogenic lower crust, which is confirmed by a transition from uni- to bi-modal hypocentre depth distributions in our models. This transition and a linear relation between convergence rate and b value and M W m a x is supported by our comparison of earthquakes recorded across the Alps, Apennines, Zagros and Himalaya. These results imply that deformation in the Alps occurs in a more ductile manner compared to the Himalayas, thereby reducing its seismic hazard. Furthermore, a second set of experiments with higher temperature and different orogenic architecture shows the same linear relation with convergence rate, suggesting that large-scale tectonic structure plays a subordinate role. We thus propose that plate convergence rate, which also controls the average differential stress of the orogen and its linear relation to the b value, is the first-order parameter controlling seismic hazard of mountain belts. [ABSTRACT FROM AUTHOR]