A staggered vertical marine seismic source contains upper and lower arrays (10, 11) of emitters of seismic energy (S11, S12; S21, S22). The upper array (10) is horizontally displaced relative to the lower array (11). The source is used in a marine seismic surveying arrangement that has means for moving the source and at least one seismic receiver. In use, the source is moved through the water in a direction parallel to the direction in which the two arrays are displaced. The arrays (10, 11) are fired sequentially, and the time delay between the firing of the first-fired array and firing of the second-fired array is chosen such that each seismic emitter in one array is fired at the same x- and y-co-ordinates as the corresponding emitter in the other array. The seismic wavefields generated by firing the two arrays are thus generated at the same x- and y-co-ordinates, but at different depths. The seismic data recorded at the receiver(s) as a consequence of firing the first array can be used to de-ghost the seismic data acquired as a result of firing the second array or vice-versa, thereby eliminating or reducing the effect of source-side ghost reflections and reverberations.