We develop a rate- and state-dependent friction (RSF) model to investigate a compendium of recent experiments performed in the laboratory. In the documented experiments, a fault was sheared until macroscopic stick-slip frictional failure. Before macro-failure, small precursor seismicity nucleated from regions that also experienced aseismic slow slip. This behavior requires heterogeneity and is defined in our model as local variation in frictional parameters inferred from the roughness. During sliding wear introduced a smooth-polished surface onto a previously rough surface and was quantified using a bimodal Gaussian distribution of surface heights. We used spatial distribution of the smooth and rough sections to impose binary partitioning in critical slip distance $D_{c}$ to a planar frictional model. Simulations revealed that local seismicity nucleated on the “smooth’ sections, while the larger “rough’ section hosted aseismic slip. As the level of heterogeneity between smooth and rough sections increased, the model transitioned from a predominantly stick-slip to creeping. The simulations produced a dominant asperity, which appeared to control aspects of rupture nucleation: ($i$) weak heterogeneity caused the dominant asperity to generate foreshocks but also “ignite’ cascade-up fault-wide event, while ($ii$) strong heterogeneity led to constrained repeaters. Seismic source properties: average slip $\delta$, seismic moment $M_{0}$, stress drop $\Delta \tau$ and fracture energy $G^{’}$, were determined for each event and agreed with separate kinematic estimates made independently from seismic measurements. Our numerical calculations provide insight into rate-dependent cascade-up nucleation theory where frictional heterogeneity here was associated with wear of solid frictional contacts in the laboratory.

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.