Finite Size Effects on Seismicity Induced by Fluid Injection in a Discrete Fault Network With Rate-and-State Friction

The seismicity rate model of J. Dieterich (1994, A constitutive law for rate of earthquake production and its application to earthquake clusteringhttps://doi.org/10.1029/93jb02581) has been used extensively in recent years to model induced seismicity in fluid injection settings. In this study, we highlight its major assumptions and examine how they may bias the interpretations of inferred model parameters when applied to induced seismicity observed in real reservoirs. We do so by comparing the model to numerical simulations of induced earthquakes in a discrete fault network (DFN). The seismicity patterns show significant differences between the DFN and Dietrich model. In particular, DFN simulations show the development of a backfront during the injection due to the exhaustion of available nucleation sources and a shut-off of near-well seismicity due to aseismic slip at high pore pressure. When matched to the DFN catalogs, both the background seismicity rate parameter, R_b, and the direct effect rate-and-state friction parameter, a, of the Dieterich model both significantly underestimate the same parameters of the DFN. We recall the seismicity induced by the 1993 stimulation of the GPK1 injection well in Soultz-Sous-Forts for evidence of co-injection backfronts and aseismic slip among small faults. We do not discount the use of the Dieterich model—they successfully reproduce seismicity simulated from a wide range of initial conditions and fault network conditions—but emphasize that interpretations of inferred parameters must take into account finite size effects that are neglected by the model's original assumptions.