Loss of Resolution for the Time Reversal of Waves in Random Underwater Acoustic Channels

In this paper we analyze a time-reversal experiment in a random underwater acoustic channel. In this kind of waveguide with semi-infinite cross section a propagating field can be decomposed over three kinds of modes: the propagating modes, the radiating modes and the evanescent modes. Using an asymptotic analysis based on a separation of scales technique we derive the asymptotic form of the the coupled mode power equation for the propagating modes. This approximation is used to compute the transverse profile of the refocused field and show that random inhomogeneities inside the waveguide deteriorate the spatial refocusing. This result, in an underwater acoustic channel context, is in contradiction with the classical results about time-reversal experiment in other configurations, for which randomness in the propagation medium enhances the refocusing.