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Here, a member of the ship's crew shows off the various thicknesses of cable that are deployed from the Ile de Batz.
The different sizes are used at different depths, although surprisingly the larger diameters are used closer to the surface. The top example in this picture is the lightweight cable that Alcatel-Lucent uses in very deep oceans, where ships' anchors pose no threat. The shallower the waters, the more heavily-armoured the cable needs to be, as depicted in this progression of thickness.
If cut, the cable can be repaired — Alcatel-Lucent has more ships on standby around the world for this purpose — but each reconnection degrades the system gain of the cable. The system is designed with enough headroom to tolerate a certain number of repairs.