  We study experimentally the fluctuations of deformation along a shear fault
naturally emerging within a compressed frictional granular medium. Using laser
interferometry, we show that the deformation inside this granular gouge occurs
as a succession of localized micro-slips distributed along the fault. The
associated distributions of released seismic moments, the memory effects in
strain fluctuations, as well as the time correlations between successive
events, follow exactly the empirical laws of natural earthquakes. Using a
methodology initially developed in seismology and social science, we reveal,
for the first time at the laboratory scale, the underlying causal structure.
This demonstrates that the spatio-temporal correlations of the slip dynamics
effectively emerge from more fundamental triggering kernels. This formal
analogy between natural faults and our experimentally controllable granular
shear band opens the way towards a better understanding of earthquake physics.
In particular, comparing experiments performed under different imposed
deformation rates, we show that strain, not time, is the right parameter
controlling the memory effects in the dynamics of our fault analog. This raises
the fundamental question of the relative roles of strain-dependent structural
rearrangements within the fault gouge vs that of truly time-dependent,
thermally activated processes, in the emergence of spatio-temporal correlations
of natural seismicity.
