Characteristics of earthquake ruptures and dynamic off-fault deformation on propagating faults

Abstract

Abstract. Natural fault networks are geometrically complex systems that evolve through time. The evolution of faults and their off-fault damage pattern are influenced by both dynamic earthquake ruptures and aseismic deformation in the interseismic period. To better understand each of their contributions to faulting we simulate both earthquake rupture dynamics and long-term deformation in a visco-elasto-plastic crust subjected to rate-and-state-dependent friction. The continuum mechanics-based numerical model presented here includes three new features. First, a 2.5-D approximation to incorporate effects of a viscoelastic lower crustal substrate below a finite depth. Second, we introduce a dynamically adaptive (slip-velocity-dependent) measure of fault width to ensure grid size convergence of fault angles for evolving faults. Third, fault localization is facilitated by plastic strain weakening of bulk rate-and-state friction parameters as inspired by laboratory experiments. This allows us to for the first time simulate sequences of episodic fault growth due to earthquakes and aseismic creep. Localized fault growth is simulated for four bulk rheologies ranging from persistent velocity-weakening to velocity-strengthening. Interestingly, in each of these bulk rheologies, faults predominantly localize and grow due to aseismic deformation. Yet, cyclic fault growth at more realistic growth rates is obtained for a bulk rheology that transitions from velocity-strengthening friction to velocity-weakening friction. Fault growth occurs under Riedel and conjugate angles and transitions towards wing cracks. Off-fault deformation, both distributed and localized, is typically formed during dynamic earthquake ruptures. Simulated off-fault deformation structures range from fan-shaped distributed deformation to localized Riedel splay faults. We observe that the fault-normal width of the outer damage zone saturates with increasing fault length due to the finite depth of the seismogenic zone. We also observe that dynamically and statically evolving stress fields from neighboring fault strands affect primary and secondary fault growth and thus that normal stress variations affect earthquake sequences. Finally, we find that the amount of off-fault deformation distinctly depends on the degree of optimality of a fault with respect to the prevailing but dynamically changing stress field. Typically, we simulate off-fault deformation on faults parallel to the loading direction. This produces a 6.5-fold higher off-fault energy dissipation than on an optimally oriented fault, which in turn has a 1.5-fold larger stress drop. The misalignment of the fault with respect to the static stress field thus facilitates off-fault deformation. These results imply that fault geometries bend, individual fault strands interact and that optimal orientations and off-fault deformation vary through space and time. With our work we establish the basis for simulations and analyses of complex evolving fault networks subject to both long-term and short-term dynamics.

Characteristics of Earthquake Cycles: A Cross‐Dimensional Comparison of 0D to 3D Numerical Models

“…To accommodate more on‐ and off‐fault complexity, including variations in fault properties or geometry along strike, a three‐dimensional (3D) model with a 2D fault plane is also prevalent (e.g., Barbot et al., 2012; Chemenda et al., 2016; Erickson & Dunham, 2014; Jiang & Lapusta, 2016; Lapusta & Liu, 2009; Okubo, 1989). In certain scenarios a so‐called 2.5D model is used for the sake of affordable computational cost, which approximately accounts for the effect of a finite fault width (e.g., Lapusta, 2001; Preuss et al., 2020; Weng & Ampuero, 2019). To do better justice to the large amount of earthquake cycle papers, we refer the reader to a white paper on future challenges for earthquake modeling (Lapusta et al., 2019) and an overview of benchmarked modeling codes provided in Erickson et al.…”

Rate and State Friction as a Spatially Regularized Transient Viscous Flow Law

“…(2018); Preuss et al. (2019, 2020), who made the purely local substitution $$v0V\,\to \,{h}_{x}{\gamma }_{0}\gamma $$ and used a Drucker‐Prager elastoplastic model similar to the one set out in Section 2.4. Setting $${\lambda }_{0},\,\eta =0$$ and assuming that strain rate fully localizes into a discrete Dirac function sampled every $${h}_{x}$$, we find that the coefficients $${c}_{1}$$ and $${c}_{2}$$ become $${h}_{x}/{d}_{c}$$ and 1 respectively, substitution of which into Equation 16 yields Herrendörfer's version of the aging law.…”

“…Herrendörfer's model was subsequently applied in an unconstrained evolving continuum model in Preuss et al. (2019, 2020), but notwithstanding measures put in place that acknowledge the changing distribution of shear strain rate within a shear zone, their model ultimately lacks regularizations that remove mesh dependence. In the chapters titled “Localization of Deformation” and “Relationship of Localization to Instability” of his PhD thesis, Ruina (1980) gives a thoughtful take on aspects of the localization behavior of a strain rate formulation of rate and state friction (without spatial regularization), which is in some aspects in line with findings reported in this work, and complementary in others.…”

Rate and State Friction as a Spatially Regularized Transient Viscous Flow Law

“…The framework here proposed can be seen as a generalization of the work of Herrendörfer ically and effectively yielding a numerical method analogous to the stress glut method of Andrews (1999). Herrendörfer's model was subsequently applied in an unconstrained evolving continuum model in Preuss et al (2019Preuss et al ( , 2020, but notwithstanding measures put in place that acknowledge the changing distribution of shear strain rate within a shear zone, their model ultimately lacks regularizations that remove mesh dependence. In the chapters titled 'Localization of Deformation' and 'Relationship of Localization to Instability' of his PhD thesis, Ruina (1980) gives a thoughtful take on aspects of the localization behavior of a strain rate formulation of rate and state friction (without spatial regularization), which is in some aspects in line with findings reported in this work, and complementary in others.…”

“…et al (2018);Preuss et al (2019Preuss et al ( , 2020, who made the purely local substitution v 0 V → h x γ 0 γ and used a Drucker-Prager elastoplastic model similar to the one set out in Section 2.4. Setting λ 0 , η = 0 and assuming that strain rate fully localizes into a discrete Dirac function sampled every h x , we find that the coefficients c 1 and c 2 become h x /d c and 1 respectively, substitution of which into (16) yields Herrendörfer's version of the aging law.…”