We present an earthquake simulator, QuakeDFN, which allows simulating sequences of earthquakes in a 3D discrete fault network governed by rate and state friction. The simulator is quasidynamic, 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. QuakeDFN is compared against three publicly available simulation results: (1) the rupture of a planar fault with uniform prestress (SEAS BP5QD), (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 injectioninduced 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 QuakeDFN can be used to simulate earthquake sequences and, most importantly, magnitudes, possibly induced or triggered by a fluid injection near a known fault system.
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ABSTRACT Free, publiclyaccessible full text available May 31, 2025 
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 stressbased earthquake forecasting. The framework is computationally efficient thanks to a 2D finiteelement 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 rateandstate 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.
Free, publiclyaccessible full text available December 15, 2024 
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.1365246x.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 (preslip, 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 rateandstate friction. According to this model, earthquakes cluster because they are timeadvanced 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 rateandstate 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 highdensity 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 (preslip). 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, semianalytical 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 singlephase 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 multiphaseflow 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 wellequipped 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 largeN 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.

Abstract We investigate the relative importance of injection and production on the spatial‐temporal distribution of induced seismicity at the Raft River geothermal field. We use time‐series of InSAR measurements to document surface deformation and calibrate a hydro‐mechanical model to estimate effective stress changes imparted by injection and production. Seismicity, located predominantly in the basement, is induced primarily by poroelastic stresses from cold water reinjection into a shallower reservoir. The poroelastic effect of production from a deeper reservoir is minimal and inconsistent with observed seismicity, as is pore‐pressure‐diffusion in the basement and along reactivated faults. We estimate an initial strength excess of ∼20 kPa in the basement and sedimentary cover, but the seismicity rate in the sedimentary cover is four times lower, reflecting lower density of seed‐points for earthquake nucleation. Our modeling workflow could be used to assess the impact of fluid extraction or injection on seismicity and help design or guide operations.

SUMMARY A number of recent modelling studies of induced seismicity have used the 1994 rateandstate friction model of Dieterich 1994 to account for the fact that earthquake nucleation is not instantaneous. Notably, the model assumes a population of seismic sources accelerating towards instability with a distribution of initial slip speeds such that they would produce earthquakes steadily in the absence of any perturbation to the system. This assumption may not be valid in typical intraplate settings where most examples of induced seismicity occur, since these regions have low stressing rates and initially low seismic activity. The goal of this paper is twofold. First, to derive a revised Coulomb rateandstate model, which takes into account that seismic sources can be initially far from instability. Second, to apply and test this new model, called the Threshold rateandstate model, on the induced seismicity of the Groningen gas field in the Netherlands. Stress changes are calculated based on a model of reservoir compaction since the onset of gas production. We next compare the seismicity predicted by our threshold model and Dieterich’s model with the observations. The two models yields comparable spatial distributions of earthquakes in good agreement with the observations. We find however that the Threshold model provides a better fit to the observed timevarying seismicity rate than Dieterich’s model, and reproduces better the onset, peak and decline of the observed seismicity rate. We compute the maximum magnitude expected for each model given the Gutenberg–Richter distribution and compare to the observations. We find that the Threshold model both shows better agreement with the observed maximum magnitude and provides result consistent with lack of observed seismicity prior to 1993. We carry out analysis of the model fit using a Chisquared reduced statistics and find that the model fit is dramatically improved by smoothing the seismicity rate. We interpret this finding as possibly suggesting an influence of source interactions, or clustering, on a long timescale of about 3–5 yr.

Abstract While the notion that injecting fluids into the subsurface can reactivate faults by reducing frictional resistance is well established, the ensuing evolution of the slip is still poorly understood. What controls whether the induced slip remains stable and confined to the fluid‐affected zone or accelerates into a runaway earthquake? Are there observable indicators of the propensity to earthquakes before they happen? Here, we investigate these questions by modeling a unique fluid‐injection experiment on a natural fault with laboratory‐derived friction laws. We show that a range of fault models with diverging stability with sustained injection reproduce the slip measured during pressurization. Upon depressurization, however, the most unstable scenario departs from the observations, suggesting that the fault is relatively stable. The models could be further distinguished with optimized depressurization tests or spatially distributed monitoring. Our findings indicate that avoiding injection near low‐residual‐friction faults and depressurizing during slip acceleration could help prevent large‐scale earthquakes.