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

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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.