Journal
GEOPHYSICAL JOURNAL INTERNATIONAL
Volume 189, Issue 3, Pages 1797-1806Publisher
WILEY-BLACKWELL
DOI: 10.1111/j.1365-246X.2012.05464.x
Keywords
Fractals and multi-fractals; Non-linear differential equations; Self-organization; Friction; Earthquake dynamics
Categories
Funding
- National Science Foundation
- Southern California Research Center
- Gordon and Betty Moore Foundation (the Caltech Tectonics Observatory)
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We investigate the chaotic behaviour of slip pulses that propagate in a spring block slider model with velocity weakening friction by numerically solving a computationally intensive set of n coupled non-linear equations, where n is the number of blocks. We observe that the system evolves into a spatially heterogeneous pre-stress after the occurrence of a sufficient number of events. We observe that, although the spatiotemporal evolution of the amplitude of a slip pulse in a single event is surprisingly complex, the geometric description of the pulses is simple and self-similar with respect to the size of the pulse. This observation allows us to write an energy balance equation that describes the evolution of the pulse as it propagates through the known pre-stress. The equation predicts the evolution of individual ruptures and reduces the computational time dramatically. The long-time solution of the equation reveals its multiscale nature and its potential to match many of the long-time statistics of the original system, but with a much shorter computational time.
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