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

TL;DR

This paper investigates how random inhomogeneities in underwater acoustic channels impair the spatial refocusing of time-reversed waves, contrasting with other media where randomness improves refocusing.

Contribution

It provides an asymptotic analysis of mode coupling in random underwater waveguides, revealing the detrimental effect of inhomogeneities on wave refocusing.

Findings

Random inhomogeneities deteriorate spatial refocusing.

Asymptotic form of coupled mode power equation derived.

Contradicts classical results in other configurations.

Abstract

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.