AI 中文总结
研究临界滑动距离\(D_c\)，通过第一性原理推导表明其是断层结构属性，证明速率-状态摩擦是底层动力学平均场极限并给出参数公式，引入“断层保持性”概念，强调评估断层稳定性要了解其层次结构。
AI 中文摘要
临界滑动距离\(D_c\)是地震破裂动力学中的关键参数，控制着成核过程和滑动演化。然而，其物理起源和尺度仍存在争议。本文提出第一性原理推导，表明\(D_c\)是断层的结构属性，由其属于Kardar-Parisi-Zhang普适类的自仿射粗糙度决定。还证明速率-状态摩擦是底层分形粗糙动力学的平均场极限，并给出其参数的解析公式。引入“断层保持性”概念，指出评估断层稳定性需了解断层系统的层次结构。
英文摘要
The critical slip distance $D_c$ - the characteristic displacement over which a fault dynamically weakens from peak to residual strength - is a key parameter in earthquake rupture dynamics, controlling the nucleation process and slip evolution. Nevertheless, its physical origin and scaling remain debated: Dc is observed to span from micrometers in lab experiments to meters on natural faults, a scaling which cannot be explained within the standard friction framework, which interprets Dc as a material constant related to the contact population and provides no mechanism linking it to fault structure or event size. Here, we propose a first-principles derivation showing that Dc is a structural property of faults, governed by their self-affine roughness belonging to the Kardar-Parisi-Zhang universality class. We further demonstrate that rate-and-state friction emerges as the mean-field limit of the underlying fractal asperity dynamics and provide analytical formulas for its parameters: the state variable represents the population-averaged contact age, while the critical distance identifies the geometric unlocking of the dominant pinning bumps. Rate-and-state friction is therefore an emergent phenomenology whose mathematical form reflects the statistical mechanics of the underlying contact population, and its parameter values are strictly scale-dependent. This allows us to better characterize fault stability from a multiscale perspective; hence, we introduce a new concept named "fault retentivity'': the ability of a fault to arrest a nucleated rupture before it degenerates into run-away via the multiscale barrier population encoded in the fault structure. Retentivity determines whether a fault hosts only small earthquakes or can occasionally nucleate large ones. The key implication is that assessing fault stability requires to understand the hierarchical architecture of the fault system.
Comments20 pages, 5 figures
