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

地震破裂最基本的特征之一是它们表现出时空复杂性。然而，对自发破裂系统中混沌动力学的演化及其意义的理解还远远不够。由于三维介质的全多尺度数值模拟在目前的计算能力下在数值上是难以处理的，本项目的目标是研究构建？减少模型?保留了这个复杂动力系统的基本物理原理。简化的模型将用于生成近似的、数值上有效的解决方案，以预测在非均匀预应力（地震）存在的自发动态摩擦滑动事件引起的断层滑动。研究人员将研究确定性和随机模型简化技术。约简哲学取决于一组变量的选择，这些变量被称为？粗变量?这（在适当的意义上）平均了精细尺度动力学，并捕获了所研究的动力系统的宏观特征。然后，滑移可以作为这些粗变量的函数来计算，而无需诉诸详细的模拟。将使用多种模拟工具，结合统计力学、非线性动力系统、随机建模和地球物理学的方法。将特别关注DARPA-Dynarum项目中正在开发的技术，其中包括作为关键成分的马尔可夫学习方法，即粗变量从精细尺度模拟中学习其动态。该项目将支持地球物理学家和数学家之间的合作，并将资助一名研究生从事这个多学科项目。利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.