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.

@en

Gas production in the Groningen field in the Netherlands reactivates faults and induces earthquakes, triggering severe societal unrest. Laboratory experiments indicate the relevant lithologies are velocity-strengthening [1], which favors stable creeping rather than instabilities and thus in theory prohibits earthquake nucleation. This makes the observed seismicity hard to explain. However, slide-hold-slide experiments on the same rocks reveal healing: stress drop and energy release of the subsequent slip after reactivation increase as healing time increases [2]. Given that the Groningen region has been tectonically inactive for millions of years, we will show that the healing history is a key factor for the nucleation of induced earthquakes.

We simulate earthquake sequences on a normal fault governed by rate-and-state friction, crosscutting a depleting gas reservoir. We reproduced the healing behavior observed in the laboratory and extended healing time up to millions of years. Our simulations suggest induced seismicity occur after fault reactivation, no matter whether the frictional behavior is velocity-weakening (VW) or -strengthening (VS). Unlike under VW friction where larger earthquakes with longer recurrence intervals occur as production continues, no subsequent earthquakes are expected under VS friction. No theoretically predictable nucleation size is measured: nucleation zone keeps expanding simultaneously when shear stress is dropping. Rupture propagation is mostly restricted to within the reservoir. Its reduced possibility of propagating into the under- and overburden reduces energy release and thus moment magnitude. The more VS the fault is, the lower the maximum slip rate will be, if under the same healing time. In other words, for a larger (a-b), a longer healing time is required before a large earthquake can happen. Therefore, if the healing history is well constrained, we can have an estimate of the seismic hazard of the coming event before it occurs. However, in order to have an accurate hazard estimate, dynamic weakening mechanisms activated at slip rate of cm/s may not be ignored. Adding flash heating shortens the required healing time by at least eight orders of magnitude in one of our representative models. Parameter space is explored systematically to build analytical expressions of earthquake magnitude as a function of healing time and frictional parameters. This study will help to understand in which tectonic histories, induced seismicity can still occur under VS friction. This is important for forecasting induced seismicity and minimizing the hazard in similar lithologies across northwestern Europe and in subsurface production and storage sites worldwide.

@en