Maximum Magnitude of Induced Earthquakes 2 in Rate and State Friction Framework

We analyze the evolution of the rupture radius and maximum magnitude (Mmax) of injection-induced earthquakes on fault obeying rates and state friction. We define the radii of two different slip modes, aseismic (Ra) and seismic slip (Rs), 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~Cf(Qt/wS)3/2, where Cf 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 Rs behaves as a rupture arrest radius and Ra behaves as the minimum possible radius of aseismic creep at a given injection volume. The Mmax 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 Mmax, 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.