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

This study presents a novel hybrid implicit–explicit time-integration strategy for simulating injection-induced fault reactivation within a fully coupled poroelastodynamic extended finite element (XFEM) framework. Modeling these systems is inherently challenging due to the extreme separation of temporal scales – ranging from hours to days for fluid diffusion to milliseconds for dynamic rupture. Although the fully implicit formulation can provide enhanced numerical stability, stability alone does not guarantee sufficient temporal accuracy during nonlinear fault rupture. The results demonstrate close agreement between simulations with minimum time-step sizes of 10 ⁻⁵ and 10 ⁻⁶  s for the investigated slip and event-scale observables on the adopted spatial mesh, indicating temporal convergence for these quantities at 10 ⁻⁵  s. This time-step size is substantially smaller than the mesh-based explicit stability estimate. To reduce computational cost, the proposed strategy employs an implicit solver for quasi-static loading and nucleation and switches to a central-difference-based mechanical solver with implicit pressure integration once a prescribed slip-velocity threshold is exceeded. At a switching threshold of 0.01 m s ⁻¹ , the hybrid simulation requires approximately 10.0 h, compared with 26.4 h for the fully implicit reference, corresponding to a computational-time reduction of 62.12 %. The hybrid strategy reproduces the overall rupture sequence, stress evolution, final accumulated fault slip, and seismic moment. However, differences remain in the timing and magnitude of peak slip velocities, rupture-propagation speeds, and transient particle motion. These findings demonstrate the computational potential of the hybrid formulation for the investigated two-dimensional configuration, while highlighting the need for further assessment of transient dynamic accuracy and computational performance across different spatial discretizations and geological conditions.