We investigate the magnitudes of earthquakes stimulated by fluid injections in boreholes. A model is developed which provides a theoretical basis for observed magnitude distributions. We assume that the process of pore pressure diffusion is responsable for the induced seismicity. Both injection-related parameters as well as the statistics of the pre-existing fracture systems influence the number of earthquakes. This increases with injection pressure and injection time and also with the hydraulic diffusivity and the tectonic activity of the injection site. We test our model with well-documented real datasets and find a good agreement between the observations and the predictions from the model. The presented concept should be helpful for the future design of fluid injection experiment, e.g. in hydrocarbon and geothermic reservoirs, in such a way that the probability of stimulating larger earthquakes is minimized.


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