Comparison between thermal–viscous coupling and frictional sliding

Abstract

We investigated the similarity between thermal–viscous coupling (TVC) and frictional sliding, proposed by Kameyama and Kaneda [Pure Appl. Geophys. 159 (2002) 2011]. We consider a one-dimensional layer composed of viscous material, which is sandwiched and sheared by two thick elastic layers. The rate of viscous deformation depends on the temperature T c in the viscous layer as well as shear stress τ. The temperature T c changes owing to heating by viscous dissipation and conductive cooling. We carried out velocity-stepping tests for the steady-state deformation both numerically and analytically, and compared the temporal evolution of small perturbations with that of the spring-block model with rate- and state-dependent friction (RSF). We found that, as is the case of frictional slip stability, the manner of temporal evolution is classified into four regimes depending on whether it is stable or not and whether it is monotonous or oscillatory with time. By further interpreting TVC in terms of general RSF theory by Ruina [J. Geophys. Res. 88 (1983) 10359], we obtained the relations between the parameters appearing in the phenomenological RSF law and the nondimensional parameters which characterize the nature of TVC. A further improvement of this approach might be important for estimating the actual values of frictional constitutive parameters at the deeper portion of seismogenic faults of interplate or inland earthquakes where a ductile deformation is expected to be significant.