Static stress changes following large earthquakes are known to affect the rate and distribution of aftershocks, yet this process has not been thoroughly investigated for nanoseismicity and picoseismicity at centimeter length scales. Here we utilize a unique data set of M-3.4 earthquakes following a M-w 2.2 earthquake in Mponeng gold mine, South Africa, that was recorded during a quiet interval in the mine to investigate if rate- and state-based modeling is valid for shallow, mining-induced seismicity. We use Dieterich's (1994) rate- and state-dependent formulation for earthquake productivity, which requires estimation of four parameters: (1) Coulomb stress changes due to the main shock, (2) the reference seismicity rate, (3) frictional resistance parameter, and (4) the duration of aftershock relaxation time. Comparisons of the modeled spatiotemporal patterns of seismicity based on two different source models with the observed distribution show that while the spatial patterns match well, the rate of modeled aftershocks is lower than the observed rate. To test our model, we used three metrics of the goodness-of-fit evaluation. The null hypothesis, of no significant difference between modeled and observed seismicity rates, was only rejected in the depth interval containing the main shock. Results show that mining-induced earthquakes may be followed by a stress relaxation expressed through aftershocks located on the rupture plane and in regions of positive Coulomb stress change. Furthermore, we demonstrate that the main features of the temporal and spatial distributions of very small, mining-induced earthquakes can be successfully determined using rate- and state-based stress modeling.
