  In this paper, the propagation of water surface waves over one-dimensional
periodic and random bottoms is investigated by the transfer matrix method. For
the periodic bottoms, the band structure is calculated, and the results are
compared to the transmission results. When the bottoms are randomized, the
Anderson localization phenomenon is observed. The theory has been applied to an
existing experiment (Belzons, et al., J. Fluid Mech. {\bf 186}, 530 (1988)). In
general, the results are compared favorably with the experimental observation.
