We analyze the phenomenon of super-resolution in time-reversal acoustics. A signal recorded by an array of transducers and sent back reversed in time approximately refocuses on the original source point. The refocusing resolution is improved in an inhomogeneous medium when the pulse has rich frequency content. We show that the back-propagated signal is self-averaging in this situation. This explains the statistical stability of the time-reversal refocusing and super-resolution.