The six-part Amazon Prime Video series recently finished filming in Edinburgh.
The Rig tells the story of a North Sea oil rig off the Scottish coast which gets cut off from all communication with the shore and the outside world due to earth tremors.
“As the crew endeavour to discover what’s driving this unknown force, a major accident forces them to ask questions about who they can really trust,” according to a statement from the programme makers.
The crew “will be driven to the limits of both their loyalties and their endurance, into a confrontation with forces beyond their imagination”, it added.
The series, which was filmed entirely in Scotland, has been created by David Macpherson and is directed by John Strickland.
The Rig took over the former Pelamis building in Leith Docks, which Sir Sean Connery’s son Jason, who is an award-winning actor and director in his own right, and producer Bob Last run.
They secured it last year under a £1 million deal with the Scottish Government to get it off the ground.
It was previously used for the blockbuster Avengers: Infinity War.
Some scenes in series, which has been produced by Wild Mercury, makers of the Channel 4 drama Humans and the BBC-Netflix show Troy: Fall of a City, are expected to be shot on a real-life oil rig, again, in Scotland.
The new images show Mr Compston’s character working on board the oil rig.
The series also stars Game of Thrones ain Glen and Schitt’s Creek actress Emily Hampshire.
Glen plays the leader of the crew, while Hampshire takes on the role of a scientist and oil company rep and Compston depicts a communications officer.
Small Axe’s Rochenda Sandall, Game Of Thrones actor Owen Teale and Bridgerton star Richard Pepple will also feature in the series.
Calvin Demba, Emun Elliott, Abraham Popoola, Stuart McQuarrie and Molly Vevers will also appear.
Georgia Brown, director of European Amazing Originals for Amazon Prime Video, said: “The Rig is a brilliant story, expertly told, in the most dramatic of settings.
"It asks searching questions about nature and the environment, about what it takes to survive and to be human, which feels very pertinent to the world we are living in now.”