The last confirmed sighting of the missing man, originally from Liverpool, is outside the town's Morrison's store shortly after 8.30am on March 11.
Inspector Ally Robertson of Tayside Police urged the marine, from 45 Commando at Condor in Angus, to let people know he is safe and well.
"This is a difficult and stressful time for Sarah as the birth of her child approaches and it is important that she has the people she needs most close with her. She is desperately worried about Ralph and needs him here at her side for what should be a joyous occasion for them both," he said.
Mr Hebden is 6ft 4in, has a muscular build and cropped fair hair. When last seen he was wearing black trainers, dark blue or black jogging bottoms, a blue fleece and a black beanie hat. He had a blue rain jacket with him when he left his home that morning.
Anyone who has information which could help police trying to trace him can call 101, or speak to any police officer.