Earthquake nucleation on faults with rate- and state-dependent friction: a dynamical system's approach to instability

地震科学中的一个突出问题是断层滑动如何从缓慢蠕变或接近锁定状态转变为引起地震的断层动态破裂。最基本的问题是不断变化的断层摩擦如何允许并决定滑动不稳定性的发展，最终形成动态破裂；断层上的条件如何影响这种发展；以及对地震周期的影响以及对地震早期阶段的识别。社会和科学界对了解地震是如何开始的很感兴趣。如果不了解动态断层破裂是如何开始的，我们就不可能可靠地了解对早期预警系统至关重要的最早地震信号的来源。通过最近的工作，我们对弹性体界面上的滑动不稳定形成有了革命性的理解，弹性体的摩擦遵循普遍的滑动率，并且在低地震间滑动率的实验室摩擦实验中表明状态依赖。将滑动断层视为一个非线性动力系统，我们发现了在这种界面上地震成核滑动不稳定性发展的方式。在动力系统背景下，发展对应于定点吸引。我们的新方法开辟了新的途径，以严格的细节来解决有关成核的几个基本问题：是否存在优先成核位置，如果确定，它们如何在地震循环中表达，以及它们可能暗示的局部强度的分布速率减弱或速率增强行为；成核过程是否可能是一个混沌的过程，以至于在滑移不稳定性开始时初始条件的微小变化可能导致动态破裂之前的力矩的巨大差异；以及断层性质和条件（如断层泥组成和厚度、环境温度和孔隙流体压力）的空间变化如何控制成核。

An outstanding problem in earthquake science is how fault slip transitions from slow creep or a nearly locked state to an earthquake-generating dynamic rupture of the fault. Fundamental questions are how an evolving fault friction allows for and determines the development of a slip instability that ultimately nucleates dynamic rupture; how conditions on the fault affect that development; and what are the consequences for the seismic cycle and the discernment of earthquakes at their earliest stages. There is societal and scientific interest in understanding how earthquakes start. Without an understanding of how dynamic fault rupture is initiated, it is unlikely we will reliably understand the origin of the earliest seismic signals that are crucial for early warning systems.Through recent work, we have developed a transformative understanding of slip instability formation on interfaces of elastic bodies whose friction follows the prevalent slip rate- and state- dependence indicated by laboratory friction experiments at low, interseismic slip rates. Treating a slipping fault as a nonlinear dynamical system, we have found the manner by which earthquake-nucleating slip instabilities develop on such interfaces. In the dynamical system context, the development corresponds to fixed-point attraction. Our novel approach has opened up new avenues to address, in rigorous detail, several of the fundamental issues concerning nucleation: whether preferential nucleation sites can exist and, if identified, how they may be expressed in the seismic cycle and what they may imply about the distribution of the local intensity of rate-weakening or rate-strengthening behavior; whether the nucleation process may be a chaotic one, such that small changes in initial conditions at the onset of a slip instability may result in large differences in the moments immediately preceding dynamic rupture; and how spatial variations of fault properties and conditions (such as fault gouge composition and thickness, ambient temperatures and pore fluid pressures) control nucleation.