[SCG53-P22] Are slow earthquakes spatio-temporal chaos?-Reproducing slow earthquakes as the Benjamin-Feir instability
Keywords:rate and state friction, Benjamin-Feir instability, complex Ginzburg Landau equation
In order to understand physical aspects of slow earthquakes, we analyze the rate and state friction model . The rate and state friction model is a widely used mathematical model for a rock friction, which was introduced by Dietrich. Interestingly, it is known to reproduce slow earthquake near the instability threshold. To understand underlying mechanisms, we first derive a simplified expression of the rate and state model near Hopf bifurcation point. This simplified expression can be used to adopt spatial dimension as well.
We, as a first step, incorporate the rate and state friction model into a thin 1-dimensional elastic layer, which has local coupling . We simplify the thin 1-dimensional elastic layer with the rate and state friction into the complex Ginzburg Landau equation. We confirm that this simplified equation shows the Benjamin-Feir instability at an appropriate condition, leading to spatio-temporal chaos. We further discuss some characteristic features of slow earthquakes from the view point of such spatio-temporal chaos.
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