Pore fluids in rocks and pore-pressure relaxation can induce aftershocks of earthquakes. Sometimes rock stimulations by fluid injections into geothermal boreholes are able to trigger perceptible or even potentially damaging earthquakes. This seems to be not the case by hydraulic fracturing of hydrocarbon reservoirs. Reasons of such a difference and factors defining magnitudes of induced earthquakes (triggered tectonically as well as induced artificially) remain unclear. Here we show that one of the main factors limiting the probability to induce a large-magnitude event is the minimum principal axis of a fluid-stimulated rock volume. This geometrical scale controls the order of a largest possible magnitude. We analyze an impact of the geometry of a stimulated volume on the Gutenberg-Richter-type frequency-magnitude distribution of induced earthquakes. It seems that a rupture is only probable along a surface located mainly inside a stimulated rock volume. Therefore, monitoring of a spatial growth of seismicity in real time can help to constrain a risk of damaging induced earthquakes.


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