  Time reversal (TR) focusing of ultrasound in granular packings is
experimentally investigated. Pulsed elastic waves transmitted from a
compressional or shear transducer source are measured by a TR mirror, reversed
in time and back-propagated. We find that TR of ballistic coherent waves onto
the source position is very robust regardless driving amplitude but provides
poor spatial resolution. By contrast, the multiply scattered coda waves offer a
finer TR focusing at small amplitude by a lens effect. However, at large
amplitude, these TR focusing signals decrease significantly due to the
vibration-induced rearrangement of the contact networks, leading to the
breakdown of TR invariance. Our observations reveal that granular acoustics is
in between particle motion and wave propagation in terms of sensitivity to
perturbations. These laboratory experiments are supported by numerical
simulations of elastic wave propagation in disordered 2D percolation networks
of masses and springs, and should be helpful for source location problems in
natural processes.
