  We measure experimentally the rearrangements due to a small localized cyclic
displacement applied to a packing of rigid grains under gravity in a 2D
geometry. We analyze the evolution of the response to this perturbation by
considering the individual particle displacement and the coarse grained
displacement field, as well as the mean packing fraction and coordination
number. We find that the displacement response is rather long ranged, and
evolves considerably with the number of cycles. We show that a small difference
in the preparation method (induced by tapping the container) leads to a
significant modification in the response though the packing fraction changes
are minute. Not only the initial response but also its further evolution change
with preparation, demonstrating that the system still retains a memory of the
initial preparation after many cycles. Nevertheless, after a sufficient number
of cycles, the displacement response for both preparation methods converges to
a nearly radial field with a 1/r decay from the perturbation source. The
observed differences between the preparation methods seem to be related to the
changes in the coordination number (which is more sensitive to the evolution of
the packing than the packing fraction). Specifically, it may be understood as
an effect of the breaking of local arches, which affects the lateral
transmission of forces.
