Modelling precursory laboratory seismicity using a roughness-based rate- and state-dependent friction model

Abstract

We investigate experimental results from a direct shear friction apparatus, where a fault was formed by pressing mature, worn surfaces of two polymethyl methacrylate (PMMA) samples on top of each other in a dry environment. The fault was sheared until macroscopic stick-slip frictional failure occurred. Before the macro-failure small precursory seismicity nucleated from regions that also experienced aseismic slow slip. These precursory events did not cascade-up into gross fault rupture and arrested locally. Reasons as to why ruptures arrested are investigated using a 1-D rate and state friction (RSF) model. Surface profilometry of the fault surface taken \textit{a posteriori} revealed wear in the form of a bimodal Gaussian distribution of surface height. In our model, this unique distribution of surface roughness is determined to be a proxy for the heterogeneous spatial description of the critical slip distance $D_{c}$. We assume that smooth (polished) sections of fault exhibited lower $D_{c}$ than rougher sections of the bimodal Gaussian roughness profile. We used a quasi-dynamic RSF model that determined localized seismicity initiated at the smooth sections. Source properties: average slip $\delta$, seismic moment $M_{0}$, stress drop $\Delta \tau$ and fracture energy $G^{'}$, were determined for each event. We compare the numerically modeled source properties to experimental source characteristics inferred from seismological estimates using an array of acoustic emission sensors from a concerted study. We discuss similarities, discrepancies and assumptions between these two independent models (kinematic and dynamic) used to study earthquakes for the first time in the laboratory.