Propagation Velocity of Pulse-Like Rupture with a Time-Weakening Friction Law

Abstract:

Pulse-like rupture propagation along a fault has been widely investigated. Especially, Rice et al. [2005] have revealed energetics of steady state slip pulse propagation under slip-weakening friction law theoretically. The propagation velocity of the pulse was, however, considered to be an arbitrary constant in their model, and understanding of what determines the velocity is still developing. For this understanding, we here propose a new model of such a pulse by taking into account the relaxation time of friction suggested by Hatano [2009]. Hatano [2009] has modeled a granular shear layer numerically and found that there exists a relaxation time independent of slip velocity for a transient process in which the slip velocity is instantaneously changed. We assume that the relaxation time corresponds to the passage time of the process zone located behind the leading edge of the pulse. According to Hatano [2009], moreover, the relaxation time depends on the thickness of the granular layer and pressure. Hence, we can derive a theoretical relation between the layer thickness $H_0$, pressure $P$, fracture energy $G$ and rupture velocity $v_r$. In this framework, for example, we can conclude that $v_r$ should be about 70 percent of the Rayleigh wave speed when $H_0 = 100$ [mm] and be close to the Rayleigh wave speed when $H_0 = 10$ [mm] if $P$ and $G$ are assumed to be $100$ [MPa] and $0.1$ [MJ/m${}^2$], respectively. This relationship suggests that the estimation of values of $P$ and $H_0$ could contribute to the estimation of a value of $v_r$, and vice versa.

References

Rice, J.R., Sammis, C.G., & Parsons, R., 2005, Off-fault secondary failure induced by a dynamic slip pulse, Bull. Seism. Soc. Am., 95(1) 109--134.

Hatano, T., 2009, Scaling of the critical slip distance in granular layers, Geophys. Res. Lett., 36, L18304.