Time-reversal refocusing for point source in randomly layered media

This paper demonstrates the interest of a time-reversal method for the identification of source in a randomly layered medium. An active source located inside the medium emits a pulse that is recorded on a small time-reversal mirror. The wave is sent back into the medium, either numerically in a computer with the knowledge of the medium, or physically into the real medium. Our goal is to give a precise description of the refocusing of the pulse. We identify and analyze a regime where the pulse refocuses on a ring at the depth of the source and at a critical time. Our objective is to find the location of the source and we show that the time-reversal refocusing contains information which can be used to this effect and which cannot be obtained by a direct arrival-time analysis. The time-reversal technique gives a robust procedure to locate and characterize the source also in the case with ambient noise created by other sources located at the surface.