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SUMMARY A number of recent modelling studies of induced seismicity have used the 1994 rate-and-state 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 rate-and-state 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 rate-and-state 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 time-varying 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 Chi-squared 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 Oscillatory stresses are ubiquitous on Earth and other solid‐surface bodies. Tides and seasonal signals perpetually stress faults in the crust. Relating seismicity to these stresses offers fundamental insight into earthquake triggering. We present a simple model that describes seismicity rate due to perpetual oscillatory stresses. The model applies to large‐amplitude, nonharmonic, and quasiperiodic stressing. However, it is not valid for periods similar to the characteristic timet_a. We show that seismicity rate from short‐period stressing scales with the stress amplitude, but for long periods with the stressing rate. Further, that background seismicity rateris equal to the average seismicity rate during short‐period stressing. We suggest thatAσ₀may be underestimated if stresses are approximated by a single harmonic function. We revisit Manga et al. (2019,https://doi.org/10.1029/2019GL082892), which analyzed the tidal triggering of marsquakes and provide a rescaling of their seismicity rate response that offers a self‐consistent comparison of different hydraulic conditions. 

Abstract Dike propagation is an intrinsically multiphase problem, where deformation and fluid flow are intricately coupled in a fracture process. Here we perform the first fully coupled simulations of dike propagation in two dimensions, accounting for depressurization of a circular magma chamber, dynamic fluid flow, fracture formation, and elastic deformation. Despite the complexity of the governing equations, we observe that the lengthening is well explained by a simple model, whereis the dike length,is time, andandare constants. We compare the model to seismic data from eight dikes in Iceland and Ethiopia, and, in spite of the assumption of plane strain, we find good agreement between the data and the model. In addition, we derive an approximate model for the depressurization of the chamber with the dike length. These models may help forecast the growth of lateral dikes and magma chamber depressurization.