Summary: We consider an active source embedded in a randomly layered medium. We study the cross-correlation functions of the signals recorded at a series of points located at the surface. We show that this information can be processed to locate and identify the source inside the medium. The analysis is based on a separation of scales technique and limit theorems for random differential equations. The statistical stability of the imaging method is proved. The analogy with the time reversal of waves is enlightened, but the main difference is also put forward: we propose a passive way of imaging an unknown medium without the use of any active device. Finally, we extend these ideas for the location of a scatterer illuminated by a controlled source located at the surface or by a set of unknown sources generating random noise.