Abstract The complex process of tip-propagation and growth of natural faults remains poorly understood. We analyse field structural data of strike-slip faults from the Atacama Fault System using fracture mechanics theory to depict the mechanical controls of fault growth in crystalline rocks. We calculate the displacement-length relationship of faults developed in the same rock type and tectonic regime, covering a range of five orders of magnitude, showing a linear scaling defined by d max = 0.0337 L 1.02 . A multiple linear regression approach based on the cohesive end zone (CEZ) crack model was formulated to estimate the range of possible effective elastic moduli, cohesive endzone lengths, stress drops, and fracture energies from displacement distributions mapped on natural faults. Our results challenge the existent paradigm wherein the self-similarity of fault growth is only achieved under the condition of invariable stresses and elastic properties. We propose a model of self-similar fault growth with scale-dependent evolution of shear modulus, cohesive end zone length and stress drop. These results also have implications for determination of stress drop for small earthquakes that are consistent with recent advances in observational seismology.

中文翻译：

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通过依赖于尺度的生长过程实现的自相似长度位移尺度：来自阿塔卡马断层系统的证据

摘要 自然断层尖端传播和生长的复杂过程仍然知之甚少。我们使用断裂力学理论分析了来自阿塔卡马断层系统的走滑断层的现场结构数据，以描述结晶岩断层生长的机械控制。我们计算了在相同岩石类型和构造体制中发育的断层的位移-长度关系，覆盖了五个数量级的范围，显示了由 d max = 0.0337 L 1.02 定义的线性标度。制定了基于粘性端区 (CEZ) 裂纹模型的多元线性回归方法，以估计可能的有效弹性模量、粘性端区长度、应力降和映射到天然断层上的位移分布的断裂能的范围。我们的结果挑战了现有的范式，其中断层生长的自相似性仅在恒定应力和弹性特性的条件下实现。我们提出了一种自相似断层生长模型，其具有剪切模量、粘性端区长度和应力降的尺度相关演变。这些结果也对确定小地震的应力降有影响，这与观测地震学的最新进展是一致的。