Periodicity and chaos in a one-dimensional dynamical model of earthquakes

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Abstract
We study the homogeneous one-dimensional dynamic Burridge-Knopoff stick-slip model for an earthquake fault with periodic boundary conditions. The dissipation is tuned such that the system is asymptotic to elasticity at all wavelengths. For an inhomogeneous distribution of prestress, after an initial transient that displays a power-law distribution of fracture sizes for cases of weak dissipation, the earthquake sequences settle into a periodic state of through-going ruptures; the power-law distributions are attributable to persistence effects. The transition time from the precursory chaotic regime to the periodic state generally increases with an increasing ratio of transverse to longitudinal spring constants, but nonmonotonically so in individual simulations. These results argue in favor of the importance of a mechanism for generating localization to suppress through-going events, if these models are to be used in earthquake simulations.

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