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Synthetic aperture radar (SAR) single-aperture systems are designed to image fixed scenes. Dual-antenna along-track interferometric (ATI) SAR systems are designed to detect moving targets and estimate their motion parameters. Although SAR systems are not designed to characterize moving targets, for localized targets, such as vehicles or ships, this problem has been addressed in the literature with some success. Distributed moving targets are hard to characterize, even for ATI systems. Estimating surface water speeds is an ideal example of this since the water returns are generated from weak returns randomly distributed in both time and space. The question asked here is can one measure surface water speeds with a single-phase center SAR system? The answer presented is a qualified yes, with the aid of an upper bound on the water speed, but not with the same accuracy as an ATI system. This upper bound and the collection geometry provide design criteria for the filtering of the phase information. Time-frequency (TF) methods provide another speed estimate as well as a rough profile of the speed across the water channel. A robust nonparametric TF method was developed and applied to estimate the speed. Comparisons between the ATI estimate and single-phase estimates are made using data from an X-band ATI-SAR system.