When a signal is emitted from a source, recorded by an array of transducers,
time reversed and re-emitted into the medium, it will refocus approximately on
the source location. We analyze the refocusing resolution in a high frequency,
remote sensing regime, and show that, because of multiple scattering, in an
inhomogeneous or random medium it can improve beyond the diffraction limit. We
also show that the back-propagated signal from a spatially localized
narrow-band source is self-averaging, or statistically stable, and relate this
to the self-averaging properties of functionals of the Wigner distribution in
phase space. Time reversal from spatially distributed sources is self-averaging
only for broad-band signals. The array of transducers operates in a
remote-sensing regime so we analyze time reversal with the parabolic or
paraxial wave equation
