The induced seismicity in the Groningen gas field, The Netherlands, presents contrasted spatio-temporal patterns between the central area and the south west area. Understanding the origin of this contrast requires a thorough assessment of two factors: (1) the stress development on the Groningen faults and (2) the frictional response of the faults to induced stresses. Both factors have large uncertainties that must be honoured and then reduced with the observational constraints. Ensembles of induced stress realizations are built by varying the Poisson's ratio in a poro-elastic model incorporating the 3-D complexities of the geometries of the Groningen gas reservoir and its faults, and the historical pore pressure distribution. The a priori uncertainties in the frictional response are mapped by varying the parameters of a seismicity model based on rate-and-state friction. The uncertainties of each component of this complex physics-based model are honoured through an efficient data assimilation algorithm. By assimilating the seismicity data with an Ensemble-Smoother, the prior uncertainties of each model parameter are effectively reduced, and the posterior seismicity rate predictions are consistent with the observations. Our integrated workflow allows us to disentangle the contributions of the main two factors controlling the induced seismicity at Groningen, induced stress development and fault frictional response. Posterior distributions of the model parameters of each modelling component are contrasted between the central and south west area at Groningen. We find that, even after honouring the spatial heterogeneity in stress development across the Groningen gas field, the spatial variability of the observed induced seismicity rate still requires spatial heterogeneity in the fault frictional response. This work is enabled by the unprecedented deployment of an Ensemble-Smoother combined with physics-based modelling over a complex case of reservoir induced seismicity.

We implement a Coulomb rate-and-state approach to explore the nonlinear relation between stressing rate and seismicity rate in the Groningen gas field. Coulomb stress rates are calculated, taking into account the 3-D structural complexity of the field and including the poroelastic effect of the differential compaction due to fault offsets. The spatiotemporal evolution of the Groningen seismicity must be attributed to a combination of both (i) spatial variability in the induced stressing rate history and (ii) spatial heterogeneities in the rate-and-state model parameters. Focusing on two subareas of the Groningen field where the observed event rates are very contrasted even though the modeled seismicity rates are of similar magnitudes, we show that the rate-and-state model parameters are spatially heterogeneous. For these two subareas, the very low background seismicity rate of the Groningen gas field can explain the long delay in the seismicity response relative to the onset of reservoir depletion. The characteristic periods of stress perturbations, due to gas production fluctuations, are much shorter than the inferred intrinsic time delay of the earthquake nucleation process. In this regime the modeled seismicity rate is in phase with the stress changes. However, since the start of production and for two subareas of our analysis, the Groningen fault system is unsteady and it is gradually becoming more sensitive to the stressing rate.