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[EE] Poster

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# [S-CG53] Science of slow earthquakes: Toward unified understandings of whole earthquake process

Wed. May 23, 2018 3:30 PM - 5:00 PM Poster Hall (International Exhibition Hall7, Makuhari Messe)

convener:Satoshi Ide(Department of Earth an Planetary Science, University of Tokyo), Hitoshi Hirose(Research Center for Urban Safety and Security, Kobe University), Kohtaro Ujiie(筑波大学生命環境系, 共同), Takahiro Hatano(Earthquake Research Institute, University of Tokyo)

# [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

A slow earthquake [1] is a type of shear slip observed at plate boundaries similar to regular earthquakes. However, slow earthquakes show different scaling from regular earthquakes, not only their characteristically long durations [2]. It is also known that their cumulative number of observation is an exponential function of the released energy [3]. This shows distinctive contrast with regular earthquakes that have Gutenberg-Richter law. Since slow earthquakes release the energy stored, simple description of their dynamics will be helpful to predict the spatio-temporal dynamics of the stress distribution along subduction zones.
In order to understand physical aspects of slow earthquakes, we analyze the rate and state friction model [4]. 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 [5]. 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.

[Reference]
[1] K. Obara, Science 296 1679 (2002).
[2] S. Ide et al., Nature 447 76 (2007).
[3] S. Yabe and S. Ide, J. Geophys. Res. Solid Earth 119 8171 (2014).
[4] J. H. Dietrich, J. Geophys. Res. 84, 2161 (1979), J. R. Rice, A. L. Ruina, J. Appl. Mech. 50 343 (1983).
[5] J. M. Carlson and J. S. Langer, Phys. Rev. Lett. 62 2632 (1989), H. Kawamura, et al., Rev. Mod. Phys. 83, 839 (2012).