Modeling precursory laboratory seismicity using a wear-based rate- and
state-dependent friction model
Abstract
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.