Inspector Keith Bendall said: "This is an unusual incident in Orkney and we would urge anyone who has information which could assist our enquiries to come forward.
"Anyone with information can contact Police Scotland on 101, quoting incident NK97/19, or call Crimestoppers anonymously on 0800 555 111."
Prior to the theft, Gareth Derbyshire, chair of the Royal Oak Association, had spoken of his hope that the survey would reveal details of huge historical value:
"There are few details of the ship in the public domain, despite the huge loss of life.
"We believe that the survey will not only be of significant interest to those with a decent connection to the ship, but also act as an important means of ensuring that the history of the ship and the circumstances of its loss are available to future generations."