Magnitudes M of fluid-induced seismicity are usually in the range −3 < M < 2. Nevertheless, especially for long-term injections with durations of months or years, earthquakes with larger magnitudes (M = 4 or even larger) have been observed (Ake et al., 2005; Majer et al., 2007). Fluid-induced earthquakes with M from 3 to 4 occurred at several Enhanced Geothermal Systems (EGS) like those of Basel, Cooper Basin, The Geysers Field and Soultz (Giardini, 2009; Majer et al., 2007; Häring et al., 2008; Dyer et al., 2008; Baisch et al., 2009). Smaller but still perceptible events can be also observed by hydraulic fracturing of hydrocarbon reservoirs.

Induced seismic hazard is a topic of significance in the shale-gas industry (National Research Council, 2013). Its understanding is of a considerable importance for mining of deep geothermic energy. It is of significance for CO2 underground storage (see Zoback and Gorelick, 2012) and possibly also for other types of geo-technological activities (see Avouac, 2012).

Identifying parameters that control magnitudes and their statistics is a key point for evaluating the seismic hazard of fluid injections. Similarly to the tectonic seismicity, statistics of the induced seismicity can be rather well described by the Gutenberg–Richter frequency–magnitude distribution (Shapiro et al., 2007, 2010, 2011; Shapiro and Dinske, 2009a,b; Dinske and Shapiro, 2013). However, large-magnitude events deviate from it (Shapiro et al., 2011). In this chapter we analyze the influence of fluid injections on the frequency–magnitude statistics of induced events. We start with a model of point-like independent seismic events. This model describes the statistics of numerous small-magnitude earthquakes well. The model allows us to formulate a simple description of the seismicity rate and to introduce parameters quantifying the seismo-tectonic state of a fluid-injection site. One such useful parameter is the seismogenic index. This helps to predict the probability of given-magnitude events. However, the model of point-like events tends to overestimate the probability of significant magnitudes.