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Abstract Gas extraction from the Groningen gas field resulted in significant induced seismicity. We analyze the magnitude‐frequency distribution of these earthquakes in space, time and in view of stress changes calculated based on gas production and reservoir properties. Previous studies suggested variations related to reservoir geometry and stress. While we confirm the spatial variations, we do not detect a clear sensitivity of b‐value to Coulomb stress changes. However, we find that b‐value correlates positively with the rate of Coulomb stress changes. This correlation is statistically significant and robust to uncertainties related to stress change calculation. This study thus points to a possible influence of stress change rate on the probability of the magnitude of induced earthquakes. 

Abstract A variety of geo‐energy operations involve extraction or injections of fluids, including hydrocarbon production or storage, hydrogen storage, CO₂sequestration, and geothermal energy production. The surface deformation resulting from such operations can be a source of information on reservoir geomechanical properties as we show in this study. We analyze the time‐dependent surface deformation in the Groningen region in northeastern Netherlands using a comprehensive geodetic data set, which includes InSAR (Radarsat2, TerraSAR‐X, Sentinel‐1), GNSS, and optical leveling spanning several decades. We resort to an Independent Component Analysis (ICA) to isolate deformation signals of various origins. The signals related to gas production from the Groningen gas field and from seasonal storage at Norg Underground Gas Storage are clearly revealed. Surface deformation associated to the Groningen reservoir show decadal subsidence, with spatially variable subsidence rates dictated by local compressibility. The ICA reveals distinct seasonal fluctuations at Norg, closely mirroring the variations of gas storage. By comparing the observed long‐term subsidence within the Groningen reservoir and seasonal oscillations at Norg from a linear poroelastic compaction model, we quantify the fraction of inelastic deformation of the reservoir in space and time and constrain the reservoir compressibility. In Groningen, increased compressibility indicates inelastic compaction that has built over time and might account for as much as 20% of the total compaction cumulated until 2021, while Norg shows no signs of inelastic deformation and a constant compressibility. This study provides a methodology to monitor and calibrate models of the subsurface deformation induced by geo‐energy operations or aquifer management. 

Abstract Gas extraction from the Groningen gas reservoir, located in the northeastern Netherlands, has led to a drop in pressure and drove compaction and induced seismicity. Stress-based models have shown success in forecasting induced seismicity in this particular context and elsewhere, but they generally assume that earthquake clustering is negligible. To assess earthquake clustering at Groningen, we generate an enhanced seismicity catalog using a deep-learning-based workflow. We identify and locate 1369 events between 2015 and 2022, including 660 newly detected events not previously identified by the standard catalog from the Royal Netherlands Meteorological Institute. Using the nearest-neighbor distance approach, we find that 72% of events are background independent events, whereas the remaining 28% belong to clusters. The 55% of the clustered events are swarm-like, whereas the rest are aftershock-like. Among the swarms include five newly identified sequences propagating at high velocities between 3 and 50 km/day along directions that do not follow mapped faults or existing structures and frequently exhibit a sharp turn in the middle of the sequence. The swarms occurred around the time of the maximum compaction rate between November 2016 and May 2017 in the Zechstein layer, above the anhydrite caprock, and well-above the directly induced earthquakes that occur within the reservoir and caprock. We suggest that these swarms are related to the aseismic deformation within the salt formation rather than fluids. This study suggests that the propagating swarms do not always signify fluid migration. 

ABSTRACT We present an earthquake simulator, Quake-DFN, which allows simulating sequences of earthquakes in a 3D discrete fault network governed by rate and state friction. The simulator is quasi-dynamic, with inertial effects being approximated by radiation damping and a lumped mass. The lumped mass term allows for accounting for inertial overshoot and, in addition, makes the computation more effective. Quake-DFN is compared against three publicly available simulation results: (1) the rupture of a planar fault with uniform prestress (SEAS BP5-QD), (2) the propagation of a rupture across a stepover separating two parallel planar faults (RSQSim and FaultMod), and (3) a branch fault system with a secondary fault splaying from a main fault (FaultMod). Examples of injection-induced earthquake simulations are shown for three different fault geometries: (1) a planar fault with a wide range of initial stresses, (2) a branching fault system with varying fault angles and principal stress orientations, and (3) a fault network similar to the one that was activated during the 2011 Prague, Oklahoma, earthquake sequence. The simulations produce realistic earthquake sequences. The time and magnitude of the induced earthquakes observed in these simulations depend on the difference between the initial friction and the residual friction μi−μf, the value of which quantifies the potential for runaway ruptures (ruptures that can extend beyond the zone of stress perturbation due to the injection). The discrete fault simulations show that our simulator correctly accounts for the effect of fault geometry and regional stress tensor orientation and shape. These examples show that Quake-DFN can be used to simulate earthquake sequences and, most importantly, magnitudes, possibly induced or triggered by a fluid injection near a known fault system. 

Abstract Reservoir operations for gas extraction, fluid disposal, carbon dioxide storage, or geothermal energy production are capable of inducing seismicity. Modeling tools exist for seismicity forecasting using operational data, but the computational costs and uncertainty quantification (UQ) pose challenges. We address this issue in the context of seismicity induced by gas production from the Groningen gas field using an integrated modeling framework, which combines reservoir modeling, geomechanical modeling, and stress-based earthquake forecasting. The framework is computationally efficient thanks to a 2D finite-element reservoir model, which assumes vertical flow equilibrium, and the use of semianalytical solutions to calculate poroelastic stress changes and predict seismicity rate. The earthquake nucleation model is based on rate-and-state friction and allows for an initial strength excess so that the faults are not assumed initially critically stressed. We estimate uncertainties in the predicted number of earthquakes and magnitudes. To reduce the computational costs, we assume that the stress model is true, but our UQ algorithm is general enough that the uncertainties in reservoir and stress models could be incorporated. We explore how the selection of either a Poisson or a Gaussian likelihood influences the forecast. We also use a synthetic catalog to estimate the improved forecasting performance that would have resulted from a better seismicity detection threshold. Finally, we use tapered and nontapered Gutenberg–Richter distributions to evaluate the most probable maximum magnitude over time and account for uncertainties in its estimation. Although we did not formally account for uncertainties in the stress model, we tested several alternative stress models, and found negligible impact on the predicted temporal evolution of seismicity and forecast uncertainties. Our study shows that the proposed approach yields realistic estimates of the uncertainties of temporal seismicity and is applicable for operational forecasting or induced seismicity monitoring. It can also be used in probabilistic traffic light systems. 

Abstract Deterministic earthquake prediction remains elusive, but time‐dependent probabilistic seismicity forecasting seems within reach thanks to the development of physics‐based models relating seismicity to stress changes. Difficulties include constraining the earthquake nucleation model and fault initial stress state. Here, we analyze induced earthquakes from the Groningen gas field, where production is strongly seasonal, and seismicity began 3 decades after production started. We use the seismicity response to stress variations to constrain the earthquake nucleation process and calibrate models for time‐dependent forecasting of induced earthquakes. Remarkable agreements of modeled and observed seismicity are obtained when we consider (a) the initial strength excess, (b) the finite duration of earthquake nucleation, and (c) the seasonal variations of gas production. We propose a novel metric to quantify the nucleation model's ability to capture the damped amplitude and the phase of the seismicity response to short‐timescale (seasonal) stress variations which allows further tightening the model's parameters. 

Abstract Induced seismicity observed during Enhanced Geothermal Stimulation at Otaniemi, Finland is modeled using both statistical and physical approaches. The physical model produces simulations closest to the observations when assuming rate‐and‐state friction for shear failure with diffusivity matching the pressure build‐up at the well‐head at onset of injections. Rate‐and‐state friction implies a time‐dependent earthquake nucleation process which is found to be essential in reproducing the spatial pattern of seismicity. This implies that permeability inferred from the expansion of the seismicity triggering front (Shapiro et al., 1997,https://doi.org/10.1111/j.1365-246x.1997.tb01215.x) can be biased. We suggest a heuristic method to account for this bias that is independent of the earthquake magnitude detection threshold. Our modeling suggests that the Omori law decay during injection shut‐ins results mainly from stress relaxation by pore pressure diffusion. During successive stimulations, seismicity should only be induced where the previous maximum of Coulomb stress changes is exceeded. This effect, commonly referred to as the Kaiser effect, is not clearly visible in the data from Otaniemi. The different injection locations at the various stimulation stages may have resulted in sufficiently different effective stress distributions that the effect was muted. We describe a statistical model whereby seismicity rate is estimated from convolution of the injection history with a kernel which approximates earthquake triggering by fluid diffusion. The statistical method has superior computational efficiency to the physical model and fits the observations as well as the physical model. This approach is applicable provided the Kaiser effect is not strong, as was the case in Otaniemi. 

SUMMARY Earthquakes come in clusters formed of mostly aftershock sequences, swarms and occasional foreshock sequences. This clustering is thought to result either from stress transfer among faults, a process referred to as cascading, or from transient loading by aseismic slip (pre-slip, afterslip or slow slip events). The ETAS statistical model is often used to quantify the fraction of clustering due to stress transfer and to assess the eventual need for aseismic slip to explain foreshocks or swarms. Another popular model of clustering relies on the earthquake nucleation model derived from experimental rate-and-state friction. According to this model, earthquakes cluster because they are time-advanced by the stress change imparted by the mainshock. This model ignores stress interactions among aftershocks and cannot explain foreshocks or swarms in the absence of transient loading. Here, we analyse foreshock, swarm and aftershock sequences resulting from cascades in a Discrete Fault Network model governed by rate-and-state friction. We show that the model produces realistic swarms, foreshocks and aftershocks. The Omori law, characterizing the temporal decay of aftershocks, emerges in all simulations independently of the assumed initial condition. In our simulations, the Omori law results from the earthquake nucleation process due to rate and state friction and from the heterogeneous stress changes due to the coseismic stress transfers. By contrast, the inverse Omori law, which characterizes the accelerating rate of foreshocks, emerges only in the simulations with a dense enough fault system. A high-density complex fault zone favours fault interactions and the emergence of an accelerating sequence of foreshocks. Seismicity catalogues generated with our discrete fault network model can generally be fitted with the ETAS model but with some material differences. In the discrete fault network simulations, fault interactions are weaker in aftershock sequences because they occur in a broader zone of lower fault density and because of the depletion of critically stressed faults. The productivity of the cascading process is, therefore, significantly higher in foreshocks than in aftershocks if fault zone complexity is high. This effect is not captured by the ETAS model of fault interactions. It follows that a foreshock acceleration stronger than expected from ETAS statistics does not necessarily require aseismic slip preceding the mainshock (pre-slip). It can be a manifestation of a cascading process enhanced by the topological properties of the fault network. Similarly, earthquake swarms might not always imply transient loading by aseismic slip, as they can emerge from stress interactions. 

Abstract Induced seismicity and surface deformation are common observable manifestations of the geomechanical effect of reservoir operations whether related to geothermal energy production, gas extraction or the storage of carbon dioxide, gas, air or hydrogen. Modelling tools to quantitatively predict surface deformation and seismicity based on operation data could thus help manage such reservoirs. To that effect, we present an integrated and modular modelling framework which combines reservoir modelling, geomechanical modelling and earthquake forecasting. To allow effective computational cost, we assume vertical flow equilibrium, semi-analytical Green's functions to calculate surface deformation and poroelastic stresses and a simple earthquake nucleation model based on Coulomb stress changes. We use the test case of the Groningen gas field in the Netherlands to validate the modelling framework and assess its usefulness for reservoir management. For this application, given the relative simplicity of this sandstone reservoir, we assume homogeneous porosity and permeability and single-phase flow. The model fits the measured pressure well, yielding a root mean square error (RMSE) of 0.95 MPa, and the seismicity observations as well. The pressure residuals show, however, a systematic increase with time that probably reflects groundwater ingression into the depleted reservoir. The interaction with groundwater could be accounted for by implementing a multiphase-flow vertical flow equilibrium (VFE) model. This is probably the major factor that limits the general applicability of the modelling framework. Nevertheless, he modelled subsidence and seismicity fit very well the historical observations in the case of the Groningen gas field. 

SUMMARY We introduce a scheme for probabilistic hypocentre inversion with Stein variational inference. Our approach uses a differentiable forward model in the form of a physics informed neural network, which we train to solve the Eikonal equation. This allows for rapid approximation of the posterior by iteratively optimizing a collection of particles against a kernelized Stein discrepancy. We show that the method is well-equipped to handle highly multimodal posterior distributions, which are common in hypocentral inverse problems. A suite of experiments is performed to examine the influence of the various hyperparameters. Once trained, the method is valid for any seismic network geometry within the study area without the need to build traveltime tables. We show that the computational demands scale efficiently with the number of differential times, making it ideal for large-N sensing technologies like Distributed Acoustic Sensing. The techniques outlined in this manuscript have considerable implications beyond just ray tracing procedures, with the work flow applicable to other fields with computationally expensive inversion procedures such as full waveform inversion.