Hybrid implicit–explicit XFEM simulation of injection-induced seismicity: resolving multi-scale rupture nucleation and dynamics

Abstract. This study introduces a new hybrid implicit–explicit (IMEX) time-integration method for simulating injection-induced fault reactivation within a fully coupled hydromechanical extended finite element (XFEM) framework. Modeling these systems is inherently difficult because of the extreme difference in temporal scales – ranging from days for fluid diffusion to less than milliseconds for dynamic rupture. While fully implicit schemes provide unconditional stability, our results show that numerical accuracy during rupture nucleation is strictly controlled by the minimum time step used. Under-resolving these rapid transients causes delayed instability, lower slip rates, and underestimated seismic moments. Importantly, the temporal resolution needed to accurately capture rupture propagation is approximately the same as the critical time step set by the Courant–Friedrichs–Lewy (CFL) condition. To address this, the proposed IMEX strategy uses an implicit solver for quasi-static loading and switches smoothly to a fully dynamic explicit update once a slip-velocity threshold is reached. This hybrid approach significantly reduces computational costs – by 60–77 % compared to fully implicit simulations – while still accurately capturing fault slip, stress changes, and seismic magnitudes. Fully implicit solutions tend to predict slightly higher peak slip velocities and rupture speeds, but event timing and final deformation are consistent across both methods. Additionally, we show that the efficiency of the IMEX framework scales independently of the calculation of the complex slip tangent operator, providing a robust and efficient solution for multi-scale subsurface hazard assessment.