Does Shear Heating of Pore Fluid Contribute to Earthquake Nucleation?

Abstract

Earthquake nucleation requires reduction of frictional strength \(\tau = \mu (\sigma - p) \) with slip or slip rate, where \(\mu, \sigma_n\), and \(p\) are the friction coefficient, normal stress, and fluid pressure, respectively. For rate state \(\mu\) at fixed \((\sigma - p)\), instabilities can occur when \(d \mu_{ss}/dv<0\), where \(\mu_{ss}\) is the steady state friction and \(v\) is slip rate. Shear heating increases \(p\) and, if dilatancy and pore pressure diffusion are limited, will cause \(\tau\) to decrease. We examine how frictional weakening, shear heating, and dilatancy determine stability in simplified fault models. Mature faults have a thin (<1 mm) shear zone on which slip is concentrated, embedded within a \(∼0.1\) m wide fault core with permeability of order \(10^{−21}\) to \(10^{−19} m^2\), surrounded by rock of variable but higher permeability. Faults with \(d \mu_{ss}/dv>0\) are linearly stable at all wavelengths to adiabatic perturbations when v is near a plate rate if the wall rock permeability exceeds a critical value that is orders of magnitude less than inferred. Thus shear heating alone cannot then nucleate unstable slip; frictional weakening is required. However, shear heating can produce inertial instability on velocity strengthening faults following strong stress perturbations. On faults with \(d \mu_{ss}/dv<0\), shear heating increases pore pressure faster than is dissipated by Darcy flow at slip speeds of order \(1\) mm \(s^{−1}\). For faults bounding half-spaces with uniform thermal and hydraulic properties, \(\mu \dot{p}\) exceeds \(\dot{\mu}(\sigma - p)\) during nucleation for slip speeds in excess of \(10^{−2}\) to \(10^1\) mm \(s^{−1}\), depending on parameters chosen. Thus thermal effects are likely to dominate late in the nucleation process, well before seismic waves are radiated, as well as during fast seismic slip. By the time shear heating effects dominate, inertial slip is imminent \((∼10^{−1} s)\), so that time-to-failure calculations baseed on rate state friction are not biased by thermal pressurization.