Time Reversal for Waves in Random Media

TL;DR

This paper provides a theoretical and numerical analysis of how time reversal techniques improve wave focusing in heterogeneous media, revealing that multiple scattering enhances resolution beyond the diffraction limit.

Contribution

It offers a quantitative explanation of time reversal and refocusing phenomena for classical waves in complex media using high-frequency asymptotic analysis.

Findings

Multiple scattering improves spatial resolution in time reversal.

Refocusing can surpass the diffraction limit in heterogeneous media.

Numerical experiments support the theoretical predictions.

Abstract

In time reversal acoustics experiments, a signal is emitted from a localized source, recorded at an array of receivers-transducers, time reversed, and finally re-emitted into the medium. A celebrated feature of time reversal experiments is that the refocusing of the re-emitted signals at the location of the initial source is improved when the medium is heterogeneous. Contrary to intuition, multiple scattering enhances the spatial resolution of the refocused signal and allows one to beat the diffraction limit obtained in homogeneous media. This paper presents a quantitative explanation of time reversal and other more general refocusing phenomena for general classical waves in heterogeneous media. The theory is based on the asymptotic analysis of the Wigner transform of wave fields in the high frequency limit. Numerical experiments complement the theory.