Induced seismicity observed during Enhanced Geothermal Stimulation (EGS) at Otaniemi, Finland is modelled 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, 1997) can be biased. We suggest a heuristic method to account for this bias that is independent of the earthquake magnitude detection threshold. Our modelling 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.  

Numerical simulations of Sequences of Earthquakes and Aseismic Slip (SEAS) have rapidly progressed to address fundamental problems in fault mechanics and provide self-consistent, physics-based frameworks to interpret and predict geophysical observations across spatial and temporal scales. To advance SEAS simulations with rigor and reproducibility, we pursue community efforts to verify numerical codes in an expanding suite of benchmarks. Here we present code comparison results from a new set of benchmark problems BP6-QD-A/S/C that consider a single aseismic slip transient induced by changes in pore fluid pressure consistent with fluid injection and diffusion in fault models with different treatments of fault friction. Ten modeling groups participated in problems BP6-QD-A and BP6-QD-S considering rate-and-state fault models using the aging and slip law formulations for frictional state evolution, respectively, allowing us to explore these ingredients across multiple codes and better understand how various computational factors affect the simulated evolution of pore pressure and aseismic slip. Comparisons of problems using the aging versus slip law illustrate how models of aseismic slip can differ in the timing and amount of slip achieved with different treatments of fault friction given the same perturbations in pore fluid pressure. We achieve excellent quantitative agreement across participating codes, with further agreement being found by ensuring sufficiently fine time-stepping and consistent treatment of remote boundary conditions. Our benchmark efforts offer a community-based example to reveal sensitivities of numerical modeling results, which is essential for advancing multi-physics SEAS models to better understand and construct reliable predictive models of fault dynamics.