Abstract
We present a systematic analysis of the dynamical behavior introduced by fault zone heterogeneities, using a simple mass-spring model with velocity-weakening friction. The model consists of two sliding blocks coupled to each other and to a constant velocity driver by clastic springs. The state of this system can be characterized by the positions of the two blocks relative to the driver. Symmetry stabilizes the system and generates only cyclic behavior. For an asymmetric system where the frictional forces for the two blocks are not equal, the solutions exhibit chaotic behavior. The transition from stable cyclic behavior to chaos is characterized by the period-doubling route to chaos. Lyapunov exponents are computed to quantify the deterministic chaos and to locate the onset of the chaotic evolution in parameter space. In many examples of deterministic chaos, chaotic behavior of a low-order system implies chaos in similar higher order systems. Thus, our results provide substantial evidence that crustal deformation is an example of deterministic chaos.
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Huang, J., Turcotte, D.L. Chaotic seismic faulting with a mass-spring model and velocity-weakening friction. PAGEOPH 138, 569–589 (1992). https://doi.org/10.1007/BF00876339
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DOI: https://doi.org/10.1007/BF00876339