Macroscopic friction in the framework of the Frenkel-Kontorova model: application to dynamics of crustal faults

控制摩擦的经济和技术效益是巨大的。例如，动摩擦对材料能量耗散和磨料降解的影响在1)机械和材料工程以及2)机器性能和寿命中是普遍存在的。此外，摩擦是控制地震孕育和发展的主要机制。后者影响着全球数百万人的生活。更好地了解规则地震和瞬时断层滑动的出现和动力学条件，将朝着预测大灾难地震发生地点和时间的长期目标又迈进一步。摩擦理论是物理和地球物理中的一个基本问题。宏观摩擦是一个高度非线性的过程，在实验室或地壳断层尺度上都没有描述它的控制方程。然而，在特定的背景下，各种模型被用来描述摩擦。我们的初步研究表明，Frenkel-Kontorova(FK)模型也是一种合适的摩擦模型，该模型最初是用来描述晶体中的塑性的。在连续介质极限下，FK模型用Sine-Gordon(SG)方程描述，SG方程是数学物理中完全可积的非线性方程之一。由于其在物理学中的特殊重要性和普适性，该方程得到了深入的研究。FK模型和SG方程在以前的各种应用中得到的结果和发展的数学工具将在这个项目中用于描述摩擦，并与实验室实验的结果进行比较。此外，还将考虑该模型的两个具体应用：(1)幕式地震和滑移(ETS)；(2)触发非火山地震。最近发现的ETS现象是一个很有希望的工具，可以用来监测以前无法获得的地壳区域。一次ETS事件由两部分组成：非火山地震和慢滑。这些是耦合的地震和大地测量现象，在空间和时间上广泛相关，在卡斯卡迪亚北部和日本西南部俯冲带具有惊人的周期性。最新的观测揭示了ETS事件期间地震的复杂迁移模式。滑动脉冲如何产生震颤仍然是一个悬而未决的问题；然而，这个问题将在FK模型和SG方程的框架下在这个项目中被考虑。后者的解析解(允许清楚地分析参数相关性)将连接滑移脉冲和抖动参数。在此基础上，对地震的迁移规律进行了详细的分析。此外，越来越多的证据表明，远震和潮汐触发了非火山地震，但这些现象的机制尚不清楚。我们认为，潮汐或远距离地震可能通过与滑动脉冲的相互作用来影响地震的产生，这一假设将在我们的模型中得到验证。

The economical and technological benefits of controlling friction are enormous. For example, the effects of kinetic friction on energy dissipation and abrasive degradation of materials is ubiquitous in 1) mechanical and material engineering and 2) machine performance and lifetime. In addition friction is a major mechanism controlling the nucleation and development of earthquakes. The latter impacts the lives of millions of people around the globe. A better understanding of conditions responsible for the appearance and dynamics of regular earthquakes and transient fault slip will be one more step toward the long-term goal of prediction of the place and time of large catastrophic earthquakes.The theory of friction is a fundamental problem in physics and geophysics. Macroscopic friction is a highly nonlinear process for which there are no governing equations describing it at either laboratory or crustal-fault scales. However, various models have been used to describe friction in a specific context. Our preliminary studies suggest that the Frenkel-Kontorova (FK) model, which was originally introduced to describe plasticity in crystals, is also an appropriate tool to model friction. In the continuum limit the FK model is described by the sine-Gordon (SG) equation, one of the fully integrable nonlinear equations of mathematical physics. This equation has been intensely investigated due to its exceptional importance and universality in physics. The results obtained and mathematical apparatus developed in various prior applications of both the FK model and the SG equation will be applied in this project to describe friction and compared with the results from laboratory experiments. In addition two specific applications of the model will be considered: (1) Episodic Tremor and Slip (ETS), and (2) triggering of non-volcanic tremor. The recently discovered phenomenon of ETS is a promising tool for monitoring previously unavailable regions of the Earth's crust. An ETS event consists of two parts: non-volcanic tremor and slow slip. These are coupled seismic and geodetic phenomena that are broadly correlated in space and time and strikingly periodic in the northern Cascadia and southwest Japan subduction zones. The latest observations reveal a complicated migration pattern of tremor during an ETS event. How a slip pulse generates tremor remains an open question; however, this question will be considered in this project in the framework of the FK model and the SG equation. Analytical solutions of the latter (allowing a clear analysis of parameter dependencies) will connect slip pulse and tremor parameters. Based on this, the migration pattern of tremor will be analyzed in detail. Also, there is growing evidence of teleseismic and tidal triggering of non-volcanic tremor, but the mechanisms of these phenomena are not clear. We suggest that tides or distant earthquakes may affect tremor production through interaction with slip pulses and this hypothesis will be examined in our model.