In this work we introduce a scheme of reverse time migratio n specially designed for offshore data acquired with a single boat pulling one or two air-guns and some streamers of receivers. 2-D and 3-D depth migrations are performed using the concept of areal shot record, as it was introduced in (Berkhout, 1992). In our scheme, an areal shot record is computed through the sum of convolutions between the seismograms registered along a sail line and a synthesis operator, which is designed in order to form a specific wave front just above the target zone (controlled illumination). All extrapolations are performed solving the acoustic two-way wave equation without any assumption in relation to the macro-velocity field. We illustrate the method with an application on the 3-D SEG-EAGE Overthrust model and 2-D Marmousi model. Except for some small artifacts, less than forty areal shot records were enough to image the main interfaces. The execution time was considerably lesser than the one required to reserve time migrate all seismograms independently.