Spatio-temporal chaos of one-dimensional thin elastic layer with the rate-and-state friction law

TL;DR

This paper investigates the spatio-temporal chaos in a one-dimensional elastic layer with rate-and-state friction law, using the complex Ginzburg-Landau equation to model oscillatory slip instabilities relevant to soft solids and slow earthquakes.

Contribution

It introduces a simplified elastic layer model incorporating rate-and-state friction, linking chaos theory with geophysical and soft matter slip phenomena.

Findings

Spatio-temporal chaos can be modeled by CGLE in elastic layers.

Rate-and-state friction influences oscillatory slip behavior.

Potential applications to slow earthquakes and soft solid interfaces.

Abstract

Independent of specific local features, global spatio-temporal structures in diverse phenomena around bifurcation points are described by the complex Ginzburg-Landau equation (CGLE) derived using the reductive perturbation method, which includes prediction of spatio-temporal chaos. The generality in the CGLE scheme includes oscillatory instability in slip behavior between stable and unstable regimes. Such slip transitions accompanying spatio-temporal chaos is expected for frictional interfaces of a thin elastic layer made of soft solids, such as rubber or gel, where especially chaotic behavior may be easily discovered due to their compliance. Slow earthquakes observed in the aseismic-to-seismogenic transition zone along a subducting plate are also potential candidates. This article focuses on the common properties of slip oscillatory instability from the viewpoint of a CGLE approach by introducing a drastically simplified model of an elastic body with a thin layer, whose local expression in space and time allows us to employ conventional reduction methods. Special attention is paid to incorporate a rate-and-state friction law supported by microscopic mechanisms beyond the Coulomb friction law. We discuss similarities and discrepancies in the oscillatory instability observed or predicted in soft matter or a slow earthquake.