Efforts to recover four anchors from the Stena Spey platform that detached during Storm Babet have begun.
The anchors detached themselves due to the severe weather on Saturday morning.
All 89 men on board the North Sea rig were accounted for, although the coastguard moved quickly to evacuate 45 of the non-essential workers to nearby platforms as a result of the incident.
The other half of the crew remained on the platform more than 140-miles east of Aberdeen.
Stena Drilling Ltd have since confirmed that an operations to reattach the anchors is underway.
A spokesman for the company said: "Stena Drilling’s priorities continue to be the safety of all personnel and the company is working closely with partner organisations and relevant authorities, including the Health and Safety Executive to ensure the safety of all involved.
"A tow line was successfully attached from a towing vessel to the Drilling Unit yesterday. The Drilling Unit remains in a secure position.
"Two anchor handling vessels have arrived at the location today to begin anchor recovery operations. The Stena Spey is safe and the well remains secure."