For a typical two-dimensional (2-D) marine multichannel seismic reflection survey, cross currents cause receiver cable side drift, and data collection becomes a limited swath 3-D survey. Processing of swath marine survey data using standard 2-D imaging procedures can create spurious discontinuities and wipeouts in the images of reflection events. These anomalies are commonly attributed to geology and tectonics during interpretation. We show how discontinuous reflections and wipeouts are created wherever subsurface structures have significant cross-profile dip. We also show that more accurate imaging can be achieved by cross-dip processing, which takes into account the 3-D character of the data and of the geology. The final products are a much improved stack, determinations of structural dips at right angles to the survey line, and an improved velocity model. We apply this cross-dip processing to data from the eastern Nankai Trough, SW Japan. Improved imaging combined with the new cross-dip information allows us to constrain better the 3-D character of the deformation in the accretionary prism and oceanic crust. In particular, the extracted structural cross-dip values provide evidence that supports two hypotheses related to the underthrusting of a large oceanic ridge (Paleo-Zenisu ridge) underneath the accretionary wedge: (1) Parts of the accretionary wedge basins have been uplifted and deformed due to the subduction of a volcano on the ridge. (2) The early phase of oceanic lithosphere shortening, which produced the underthrusted Paleo-Zenisu ridge, was related to N-S compression oblique to the general plate motion in this region.