Probability of a given-magnitude earthquake induced by a fluid injection

[1] Fluid injections in geothermic and hydrocarbon reservoirs induce small earthquakes (−3 < M < 2). Occasionally, however, earthquakes with larger magnitudes (M ∼ 4) occur. We investigate magnitude distributions and show that for a constant injection pressure the probability to induce an earthquake with a magnitude larger than a given value increases with injection time corresponding to a bi-logarithmical law with a proportionality coefficient close to one. We find that the process of pressure diffusion in a poroelastic medium with randomly distributed sub-critical cracks obeying a Gutenberg-Richter relation well explains our observations. The magnitude distribution is mainly inherited from the statistics of pre-existing fracture systems. The number of earthquakes greater than a given magnitude also increases with the strength of the injection source and the tectonic activity of the injection site. Our formulation provides a way to estimate expected magnitudes of induced earthquakes. It can be used to avoid significant earthquakes by correspondingly planning fluid injections.