Wave propagation in randomly layered media with an application to time reversal

We describe the propagation of acoustic waves through randomly layered media over distances much larger than the typical wavelength of a pulse that is emitted from a point source. The layered medium is modeled by a smooth reference background modulated by fast random small-scale variations. Using asymptotic methods, we arrive to the O'Doherty-Anstey (ODA) formula which describes the coherent part of the pulse in a deterministic expression up to a small random time correction. An application on time-reversal is presented, where a pulse is sent through the medium, recorded in a small window, time-reversed, and then sent back towards the source. The striking phenomenon of enhanced refocusing occurs, where the randomness in the medium actually improves the spatial refocusing around the initial source