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Coherence of broad-band acoustic waves for mid-to-high frequencies (0.6-18 kHz) is obtained for a very shallow-water (15-m-deep) waveguide over a wide band of environmental conditions and for a source-receiver range of 387 m. Temporal behavior is sampled at two different rates: one that resolves at fractions of a second over intermittent periods of 40 s and another that resolves at 10 min over periods of several days. Spatial behavior is sampled in the vertical by hydrophones with spacings of the order of meters. The effect of environmental variability on coherence, in particular, soundspeed fluctuations in the water column and wind-induced modulations of the air-sea interface, is noted as a function of acoustic frequency and ray path. Analysis of the acoustic fluctuations over short time scales more accurately resolves the temporal decorrelation of the received signal due to sea surface waves. The vertical sampling of the received signal permits an analysis of arrival-angle fluctuations. The dependence of coherence on the number of surface bounces is studied by comparing arrivals that have zero, one, two, and three surface bounces.