ARMA 18 – 604 Modeling Induced Seismicity : Co-Seismic Fully Dynamic Spontaneous Rupture Considering Fault Poroelastic Stress

Pre-seismic poroelastic stress generated by quasi-static fluid perturbation is a centerpiece of information specific to injection-induced seismicity. To this day, there exists no fault rupture model that considers the fault poroelastic stress in the coseismic dynamic rupture process of an induced earthquake. To this aim, we develop a computational model of fluid-induced, fully dynamic and spontaneous co-seismic rupture under slip-weakening and an exact fault surface contact constraint. We show how the pre-seismic fault poroelastic stress enters the model formulation and discretization and how is it reflected on the computational procedures including linearization and preconditioner design. A numerical example is provided to demonstrate the impact of the fault poroelastic stress on the co-seismic fault rupture behavior and the associated dynamic changes of an induced earthquake. It is shown that including the fault poroelastic stress can lead to delayed nucleation of the rupture, promote the so-called supershear rupture and result in an overall stronger wavefield and a more profound stress loss near the fault. Additionally, when the pre-seismic transverse simple shear behavior of the fault is considered, the fault poroelastic stress with a steep gradient across the fault may also lead to asymmetric earthquake rupture propagation. mean stress and the volumetric strain of the hosting solid rock in a fully coupled manner. The latter process is typically considered as ‘undrained’ over the timescale relevant to a seismic event. The former is related to the latter in the following few ways. First, the former spatialtemporally alters the effective normal stress, shear stress and the resulting Coulomb stress on the fault, and therefore controls the time and location of nucleation of the rupture. Second and central to an induced seismicity problem, the accumulated fault poroelastic stress prior to nucleation of the rupture enters the co-seismic rupture process via the fault boundary condition (i.e., the consistency condition in plasticity theory). The fault stress profile when the rupture initiates has a fundamental control over the rupture style, rupture velocity and the associated seismic radiation pattern and wavefield, as has been amply demonstrated by many studies (e.g., Andrews, 1976; Dunham, 2007; Ampuero & Ben-Zion, 2008; Ben-David et al., 2010; Gabriel et al., 2012). Lastly, the poroelastic process also modifies the density of the fluid-solid mixture and must be taken into account in solving the fully dynamic rupture equation. Our Jin & Zoback (2017) paper describes in detail a nonlinear and fully coupled poromechanical model of an arbitrarily faulted and fluid-saturated quaso-static poroelastic system; the discretization and computational procedures are also given there. This computational model will be used for generating necessary inputs including the fault poroelastic stress for the study presented here. We hereinafter focus on the co-seismic fully dynamic spontaneous rupture problem only and we shall assume a plane-strain (in-plane fault slip) condition. Denote the model domain as Ω, the location within Ω as and the time as t, the conservation law we solve is the Cauchy equation of motion described by including the reference state at the end of the pre-seismic quasi-static process (i.e., when the rupture nucleates). It reads: ( , ) '( , *) ( , *) '( , ) ( , ) ( , *) ( , ) , *                     σ σ σ undrained