Development of a Statistical Physics Approach to Multi-Scale Complexity in Earthquake Rupture Dynamics

地震破裂的一个最基本的特征是它具有时空复杂性。然而，理解自发破裂系统中混沌动力学的演化和含义还远未完成。由于完整的多尺度数值模拟的3-D介质是数值棘手的与目前的计算能力，本项目的目标是调查的可能性，构建？缩小模型？保留了这个复杂动力系统的基本物理特性。减少模型将被用来产生近似的，数值上有效的解决方案，预测断层滑动引起的自发动态摩擦滑动事件中存在的非均匀预应力（地震）。 研究人员将研究确定性和随机模型简化技术。减少哲学取决于一组变量的选择称为？粗糙变量？这平均（在适当的意义上）的精细尺度动力学和捕获所研究的动力系统的宏观特征。然后，可以计算滑移作为这些粗略变量的函数，而无需进行详细的模拟。 将使用一套不同的模拟工具，结合统计力学，非线性动力系统，随机建模和物理学的方法。将特别注意DARPA-Dynarum计划中正在开发的技术，该计划涉及马尔可夫学习方法，作为一个关键因素，粗变量从细尺度模拟中学习其动态。该项目将支持数学家和数学家之间的合作，并将资助一名研究生从事这一多学科项目。使用这些研究人员将探索的模型来理解地震的发生可能有助于提高我们对地震危害的认识。

One of the most fundamental features of Earthquake ruptures is that they exhibit spatial-temporal complexity. Yet understanding the evolution and implications of the chaotic dynamics in systems with spontaneous rupture is far from being complete. Since the full multi-scale numerical simulation of 3-D media is numerically intractable with current computational capabilities, the goal of this project is to investigate the possibility of constructing ?reduced models? that retain the essential physics of this complex dynamical system. The reduced models will be used to generate approximate, numerically efficient solutions that predict fault slip caused by spontaneous dynamic frictional sliding events in the presence of heterogeneous pre-stress (earthquakes). The researchers will investigate both deterministic and stochastic model reduction techniques. The reduction philosophy hinges on the selection of a group of variables called ?coarse variables? that average (in an appropriate sense) the fine scale dynamics and capture the macroscopic features of the studied dynamical system. Slip can then be calculated as a function of these coarse variables without resorting to detailed simulations. A diverse set of simulation tools will be used, combining methods from statistical mechanics, nonlinear dynamical systems, stochastic modeling and geophysics. Particular attention will be given to techniques being developed in the DARPA-Dynarum program that involves, as a key ingredient, the Markov learning methods, whereby the coarse variable learn their dynamics from fine scales simulations. The project will support a collaboration between geophysicists and mathematicians, and will fund a graduate student to work on this multi-disciplinary project. Understanding earthquake occurrence using the models these investigators will explore may help improve our knowledge of earthquake hazard.