  Classical analogs of the quantum mechanical concepts of the Loschmidt Echo
and quantum fidelity are developed with the goal of detecting small
perturbations in a closed wave chaotic region. Sensing techniques that employ a
one-recording-channel time-reversal-mirror, which in turn relies on time
reversal invariance and spatial reciprocity of the classical wave equation, are
introduced. In analogy with quantum fidelity, we employ Scattering Fidelity
techniques which work by comparing response signals of the scattering region,
by means of cross correlation and mutual information of signals. The
performance of the sensing techniques is compared for various perturbations
induced experimentally in an acoustic resonant cavity. The acoustic signals are
parametrically processed to mitigate the effect of dissipation and to vary the
spatial diversity of the sensing schemes. In addition to static boundary
condition perturbations at specified locations, perturbations to the medium of
wave propagation are shown to be detectable, opening up various real world
sensing applications in which a false negative cannot be tolerated.
