Shallow-water noise can come from waves scattering from a sunken ship or from the side of an island or iceberg several kilometers to the side of the survey line. Think of boulders strewn all over a shallow sea floor, not only along the path of the ship, but also off to the sides. (Reality is more impressive. Wind blown ice flows drag themselves along the bottom making huge scars in it.) The travel-time curves for reflections from the boulders nicely matches the random point-scatterer model. Because of the long wavelengths of seismic waves, our sending and receiving equipment does not enable us to distinguish waves going up and down from those going sideways.
Imagine one of these shallow scatterers several kilometers to the side of the ship. More precisely, let the scatterer be on the earth's surface, perpendicular to the midpoint of the line connecting the shot point to the geophone. A common-midpoint gather for this scatterer is a perfect hyperbola, as from the deep reflector contributions on Figure 20. Since it is a water-velocity hyperbola, this scatterered noise should be nicely suppressed by CDP stacking with the higher, sediment velocity. So the ``streaking'' scatterers in Figure 22 are not sidescatter.
The ``streaking'' scatterers are those neither along the survey line nor those perpendicular to it. The ``in-line'' scatterers have infinite velocity (on the flat spot). The scatterers perpendicular to the survey line have the water velocity. Scatterers at other angles have inbetween velocities and they stack strongly at the sediment velocity and account for the streaks.