Dynamic and Quasi-Dynamic Modeling of Injection-Induced Earthquakes in Poroelastic Media

Earthquake ruptures in poroelastic media involve a suite of complex phenomena arising from stick-slip frictional instabilities and thermo-hydromechanical couplings. In this study we propose a fully implicit, time-adaptive, and monolithically coupled finite element model to simulate dynamic earthquake sequences in poroviscoelastic media. We consider a Kelvin-Voigt viscoelastic material and characterize the impact of inertial effects on injection-induced earthquakes. We present, for the first time, dynamic simulations of ruptures in rate-and-state faults in poroelastic media. Our simulations resolve the full earthquake cycle, including the interseismic, spontaneous earthquake nucleation, and dynamic rupture phases. We compare dynamic simulations with quasi-dynamic ones, in which inertial effects are neglected and the slip singularity is resolved through a radiation damping approximation. Viscous dissipation models the physical process of seismic wave attenuation: As viscous damping increases, the patch size and the maximum fault slip become smaller, hence decreasing the expected earthquake magnitude. From a computational perspective, viscoelasticity helps avoid spurious high-frequency oscillations during wave propagation. By including inertial effects, the dynamic model accounts for transient fluctuations of pressures and solid stresses during rupture, which are neglected in the quasi-dynamic approach. Understanding these transient perturbations may shed light on the role of pore pressure in the mechanism of dynamic earthquake triggering. The poroviscoelastic dynamic approach is a good compromise between the inviscid, fully dynamic model, and the quasi-dynamic one. A small amount of viscous damping allows us more efficient calculations, while preserving the most relevant features of dynamic ruptures, in particular slip velocities, accumulated slip, and seismic moment released.