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退化的影响在1)机械和材料工程以及2)机器性能和寿命中无处不在。此外，摩擦力是控制地震成核和发展的主要机制。后者影响着全球数百万人的生活。更好地了解导致常规地震和瞬态断层滑动的出现和动态的条件，将是向预测大灾难性地震的地点和时间的长期目标又迈进了一步。摩擦理论是物理学和地球物理学中的一个基本问题。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，不同的模型被用来描述特定情况下的摩擦。我们的初步研究表明，最初用于描述晶体塑性的Frenkel-Kontorova （FK）模型也是模拟摩擦的合适工具。在连续体极限下，FK模型用数学物理中完全可积非线性方程之一的sin - gordon （SG）方程描述。由于这个方程在物理学中的特殊重要性和普遍性，人们对它进行了深入的研究。本项目将应用FK模型和SG方程在各种先前应用中获得的结果和开发的数学装置来描述摩擦，并与实验室实验的结果进行比较。此外，将考虑该模型的两个具体应用：(1)幕式震颤和滑动（ETS），以及(2)非火山震颤的触发。最近发现的ETS现象是一种很有前途的工具，可以用来监测以前无法探测到的地壳区域。ETS事件由两部分组成：非火山震动和慢滑。在卡斯卡迪亚北部和日本西南部的俯冲带，这些是地震和大地测量耦合现象，在空间和时间上具有广泛的相关性，并且具有显著的周期性。最新的观测结果揭示了ETS事件中复杂的地震迁移模式。滑动脉冲如何产生震颤仍然是一个悬而未决的问题；然而，本项目将在FK模型和SG方程的框架内考虑这个问题。后者的解析解（允许参数依赖关系的清晰分析）将连接滑移脉冲和震颤参数。在此基础上，详细分析了地震的迁移模式。此外，越来越多的证据表明，远震和潮汐引发的非火山震动，但这些现象的机制尚不清楚。我们认为潮汐或遥远的地震可能通过与滑动脉冲的相互作用影响震颤的产生，这一假设将在我们的模型中进行检验。

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.