ABSTRACT Marine seismic data acquired with a moving vibrator suffer phase dispersion caused by Doppler shifting of the source sweep function. The dispersion, which can be as large as several hundred degrees, is a function of frequency, ship speed, sweep type, and the time dips of reflection events. In a constant-offset section, the Doppler factor for an event is the product of ship speed and the event's time dip. That key relationship allows the derivation of a two-dimensional filter that removes Doppler phase dispersion from seismic data. Both synthetic data and a Gulf of Mexico test line show that the phase-correcting filter is required for accurate steep-dip imaging with a moving vibrator source. INTRODUCTION Interest in marine vibrators has increased recently within the industry (Houston, 1987; Baeten, Fokkema, and Ziolkowski, 1987; O'Brien, 1986; Haldorsen, Desler, and Chu, 1985); and, in fact, a few seismic marine crews presently have the capability to acquire production lines with vibrator sources. Nevertheless, marine vibrators are still widely viewed as being exotic, experimental devices. As yet, they are not even close to having the industry-wide acceptance enjoyed by their land counterparts. One reason for this is that marine vibrators have a peculiar disadvantage not suffered by either impulsive marine sources or land vibrators: Doppler phase dispersion. In the usual production mode of marine operations, the seismic ship, the source, and the receivers move continuously through the water as data are recorded. Because of that motion, a correlated marine vibrator wavelet can contain phase dispersion due to classical Doppler frequency shifting. The size of the Doppler effect in any particular situation is proportional to the ratio of the speed of the motion (about 5 knots, or 2.6 m/s for a seismic ship) to the speed of sound in the surrounding medium (about 1500 m/s for water). Since, here, that ratio is small (about 0.0017), one might conclude at first that the Doppler effect is not important in marine vibrator data. The first of the two theory sections of this paper shows that conclusion to be, unfortunately, wrong. Phase dispersion as large as several hundred degrees can be observed at frequencies well within the seismic band. The second theory section proves the key result of this paper: when viewed in constant-offset gathers, phase dispersion caused by the Doppler effect is a function of only the apparent time dip of the reflection events, the type of vibrator pilot sweep, and the speed of the seismic ship. That result leads to a solution of the phase dispersion problem - a two-dimensional, phase-correcting filter that is applied in the frequency wavenumber domain. The performance of the phase-correction algorithm is demonstrated by applying it to some synthetic data that contain known Doppler effects. Finally, the filter is applied to field data from the Gulf of Mexico that show clear-cut examples of Doppler phase dispersion in the steeper reflections. The filter removes the phase dispersion.