Final answer:
Undercutting of a sea-side cliff leads to mass movements and the collapse of materials, generating turbidity currents which form turbidite sedimentary deposits on the sea floor.
Step-by-step explanation:
Undercutting of a sea-side cliff by erosion from waves and tidal action typically leads to mass movements where the unsupported materials collapse. In this scenario, the most likely type of mass movement would be rock falls, which are a subset of landslides. However, from the given options, the process that corresponds with sediment moving swiftly into the sea due to landslides, resulting in turbidity currents, is the closest match. Turbidity currents are submarine flows of turbid (or murky) water caused by greater-density sediment mixed within the water rushing down a slope.
Turbidite sedimentary deposits are formed when these currents lay down layers of sediment on the sea bottom, sorted by density. The undercutting of cliffs and the subsequent movement of material could lead to a massive slope failure, initiating these currents as material finds its way down to the deep sea-bed. This depositional process is integral in forming the geomorphological features of the underwater landscape and contributes significantly to sedimentary layering observed in marine geological studies.