Resumen
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.

Resumen
Refocusing for time reversed waves propagating in disordered media has recently been observed experimentally and studied mathematically. This surprising effect has many potential applications in domains such as medical imaging, underwater acoustics, and wireless communications. Time refocusing for one-dimensional acoustic waves is now mathematically well understood. In this paper the important case of one-dimensional dispersive waves is addressed. Time reversal is studied in reflection and in transmission. In both cases we derive the self-averaging properties of time reversed refocused pulses. An asymptotic analysis allows us to derive a precise description of the combined effects of randomness and dispersion. In particular, we study an important regime in transmission, where the coherent front wave is destroyed while time reversal of the incoherent transmitted wave still enables refocusing.