Maximum Magnitude of Induced Earthquakes in Rate and State Friction Framework

We analyze the evolution of the rupture radius and maximum magnitude (M _max) of injection-induced earthquakes on faults obeying rates and state friction. We define the radii of two different slip modes, aseismic (R ^a) and seismic slip (R ^s), and derive an expression for maximum magnitude evolution. If the flow rate is sufficiently high, the seismic moment grows with the scaled injection volume, Qt/wS, as M~C _f(Qt/wS) ^3/2, in which C _f depends on the initial stress level, S is storage coefficient, and w is the thickness of the reservoir. These findings are confirmed using numerical simulations conducted with varied initial states. The simulations show that R ^s behaves as a rupture arrest radius and R ^a behaves as the minimum possible radius of aseismic creep at a given injection volume. The M _max evolution curve can be steeper if the fault is slightly critically stressed. A high-flow rate results in frequent seismic events, starting at relatively low-injected volume, which helps track the evolution of M _max, providing a way to anticipate the risk of a large event. Conversely, a low-flow rate allows for a larger volume injection without seismic events but may lead to sudden large events without precursory events.