Geometrical Scaling of the Magnitude Frequency Statistics of Fluid Injection Induced Earthquakes and Implications for Assessment and Mitigation of Seismic Hazard

Abstract:

To study the influence of size and geometry of hydraulically perturbed rock volumes on the magnitude statistics of induced events, we compare b value and seismogenic index estimates derived from different algorithms. First, we use standard Gutenberg-Richter approaches like least square fit and maximum likelihood technique. Second, we apply the lower bound probability fit (Shapiro et al., 2013, JGR, doi:10.1002/jgrb.50264) which takes the finiteness of the perturbed volume into account. The different estimates systematically deviate from each other and the deviations are larger for smaller perturbed rock volumes. It means that the frequency-magnitude distribution is most affected for small injection volume and short injection time resulting in a high apparent b value. In contrast, the specific magnitude value, the quotient of seismogenic index and b value (Shapiro et al., 2013, JGR, doi:10.1002/jgrb.50264), appears to be a unique seismotectonic parameter of a reservoir location. Our results confirm that it is independent of the size of perturbed rock volume. The specific magnitude is hence an indicator of the magnitudes that one can expect for a given injection. Several performance tests to forecast the magnitude frequencies of induced events show that the seismogenic index model provides reliable predictions which confirm its applicability as a forecast tool, particularly, if applied in real-time monitoring. The specific magnitude model can be used to predict an asymptotical upper limit of probable frequency-magnitude distributions of induced events. We also conclude from our analysis that the physical process of pore pressure diffusion for the event triggering and the scaling of their frequency-magnitude distribution by the size of perturbed rock volume well depicts the presented relation between upper bound of maximum seismic moment and injected fluid volume (McGarr, 2014, JGR, doi:10.1002/2013JB010597), particularly, if nonlinear effects in the diffusion process are considered. The interaction of fluid volume, pressure diffusion, hydraulic properties (permeability, anisotropy), and seismotectonic state (fracture concentration, rock strength) controls geometry and size of the perturbed volume. The perturbed volume is in turn a controlling factor of the maximum magnitude of induced events.