Time reversal mirrors have been demonstrated to focus acoustic energy in the ocean at ranges of tens of kilometers from a probe source [W. A. Kuperman et al., J. Acoust. Soc. Am. 103, 25–40 (1998)]. Time reversal has also been exploited to focus acoustic energy at discrete scatters of unknown location using the eigenvectors of the time reversal operator which can be formed by measuring the interelement transfer function of a source/receiver array [C. Prada et al., J. Acoust. Soc. Am. 99, 2067–2076 (1996)]. This paper extends these principles to the case of reverberation from a rough interface in a waveguide. The reverberation data collected on a source/receiver array are used to form a time reversal operator. The most energetic eigenvector of this operator focuses to a specific range along the rough interface. Improved signal-to-noise measurements of the time reversal operator can be obtained by probing the water column with orthogonal array beams. Since this method does not depend upon a priori environmental information, it is applicable to complex shallow water environments. Numerical simulations with a Pekeris waveguide are used to demonstrate this method. [Work supported by ONR.]