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The effects of source and receiver motion have been discussed by a number of authors. However, no attention has been paid to the influence of marine currents, which can attain velocities approaching typical seismic shooting speeds. It is argued that such currents may have a significant effect for OBN analysis, 4D surveys and reconciling data shot in opposing current directions. A theoretical basis is introduced that systematically applies Galilean transformations and wave extrapolations to describe the effects of this motion that includes source and receiver motion. The results are completely consistent with the theory of Doppler (1842) and agree with the theory of Hampson & Jakubowicz (1995) . Several methods are described to compensate for the distorting effects of these currents.