Seismic common-depth-point (CDP) gathered data contain waves of various reflection phases other than the primary events of interest. Such waves often form distinctive, separate peaks in the velocity spectrum derived from the CDP gather, and their propagation modes can often be identified. To exploit such separation and identification, a method is developed to decompose the CDP-gathered data into several phases. The method combines normal moveout (NMO) removal, space-time filtering, and NMO restoration. The space-time operator central to this method is shown to have several useful properties. Its frequency response passes one quadrant pair in the frequency-wavenumber domain and rejects the other. A set of marine reflection records is used to demonstrate the usefulness of the decomposition approach, particularly for separating primary from nonprimary waves, and waves of possible marine PSSP mode from all others. Both examples may bear some exploration significance.