Natural fault networks are geometrically complex systems that evolve through time. The evolution of faults and their off-fault damage patterns 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 is created to incorporate the 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 simulate sequences of episodic fault growth due to earthquakes and aseismic creep for the first time. 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 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 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.

中文翻译：

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传播断层的地震破裂和动态断层变形特征

自然断层网络是几何形状复杂的系统，会随着时间而发展。断层的演化及其断层破坏模式受地震期间的动态地震破裂和抗震变形的影响。为了更好地理解它们对断层的贡献，我们模拟了在受速率和状态依赖的摩擦的粘弹塑性地壳中的地震破裂动力学和长期变形。这里介绍的基于连续力学的数值模型包括三个新功能。首先，创建一个2.5D近似值，以合并有限深度以下的粘弹性下地壳基底的影响。其次，我们引入了一种动态自适应（取决于滑动速度）的断层宽度测量方法，以确保对于不断发展的断层，断层角的网格尺寸收敛。第三，实验室实验的结果是，塑性应变减弱了体积速率和状态摩擦参数，从而促进了断层的定位。这使我们第一次能够模拟由于地震和地震蠕变引起的断层增长。针对从持续速度减弱到速度增强的四种整体流变模拟了局部断层的生长。有趣的是，在这些主体流变中的每一种中，断层主要由于地震变形而定位并增长。然而，对于整体流变学，以从速度增强的摩擦过渡到速度减弱的摩擦，获得了更实际的增长率的周期性断层增长。断层的生长在里德尔和共轭角下发生，并向机翼裂纹过渡。断层变形，分布的和局部的，通常是在动态地震破裂期间形成的。模拟的断层形变结构范围从扇形分布形变到局部展状断层。我们观察到，由于震源区的有限深度，外部破坏区的断层正常宽度随着断层长度的增加而饱和。我们还观察到，相邻断层股线的动态和静态应力场影响一次和二次断层的生长，因此，正应力变化会影响地震序列。最后，我们发现断层变形量明显取决于断层相对于主要但动态变化的应力场的最佳程度。通常，我们在平行于加载方向的断层上模拟断层变形。这产生一个6。与最佳定向断层相比，断层的能量耗散高出5倍，而最佳定向断层的应力降大1.5倍。断层相对于静应力场的未对准因此促进断层变形。这些结果表明，断层几何形状弯曲，各个断层股相互作用，并且最佳方位和断层变形随空间和时间而变化。通过我们的工作，我们为受长期和短期动态影响的复杂演化故障网络的仿真和分析奠定了基础。最佳方向和断层变形会随时间和空间变化。通过我们的工作，我们为受长期和短期动态影响的复杂演化故障网络的仿真和分析奠定了基础。最佳方向和断层变形会随时间和空间变化。通过我们的工作，我们为受长期和短期动态影响的复杂演化故障网络的仿真和分析奠定了基础。