New dynamical systems modeling helps explain mega-earthquakes

Self-organized criticality (SOC) is a phenomenon of dynamical systems with extended degrees of freedom that tend to evolve spontaneously towards a stationary state. The phenomenon follows a power law, and was first introduced in 1987. Recently, researchers from Warsaw, Poland extended a simply cellular automaton — the one-dimensional forest-fire model — to the case of two self-organized critical states, where automaton states from one SOC migrates to the other. They report their findings in Chaos: An Interdisciplinary Journal of Nonlinear Science.

Building on the analysis of cellular automata conducted in the past five years, Zbigniew Czechowski and his co-author Agnieszka Budek studied features of steady states for two cases. They derived time-evolution equations modelling the cellular automaton around the steady states, and subsequently tested them against advanced computer simulations. The stationary and the verified dynamical equations “enable us to make the one-to-one relation between forms of microscopic rules and the macroscopic behavior manifesting in avalanches,” Czechowski said.

The two self-organized critical states model sheds light on earthquake supercycles, consecutive occurrences of several large earthquakes. The model exhibits a long migration of seismic activity increasing strain energy from one criticality to another, which then returns to the former criticality in a large seismic event. The model furthermore shows that such a behavior is statistically periodic, consisting of recurrences of slow buildups with rapid releases.

Source: “Bi-SOC-states in one-dimensional random cellular automaton,” by Zbigniew Czechowski and Agnieszka Budek, Chaos: An Interdisciplinary Journal of Nonlinear Science (2017). The article can be accessed at https://doi.org/10.1063/1.4997680 .