Why not add ‘the’ before ‘North’ in the sentence:
So it comes as a surprise to learn that giant fish are terrifying the divers on North Sea oil rigs.
If there is not ‘oil rigs’, I think it is no need to add the ‘the’ before ‘North’ too.
Normally when referring to oceans or seas you would use the word "the". For example, you would write:
The Titanic sunk in the Atlantic Ocean.
rather than:
The Titanic sunk in Atlantic Ocean.
However, in your example "North Sea" is not being used to refer to the sea itself. It is being used as a descriptor of the oil rigs. I.e. these were not just regular oil rigs, but specifically North Sea oil rigs. That being the case, we have to instead determine whether "oil rigs" (with a descriptor) should get the word "the" in front of it. And that would depend on whether the sentence is referring to (North Sea) oil rigs in general, or some set of specific (North Sea) oil rigs.
In this case the point of the sentence is that divers on North Sea oil rigs in general are getting terrified, rather than that divers on some specific North Sea oil rigs are getting terrified; thus, the word "the" is not used.
When place names that usually have "The" are used as modifiers in phrases, they usually drop the "the":
Atlantic trade
Pacific islands
United States envoy
Amazon rainforest
Mediterranean coast
To extend Alex's excellent answer
the is used before a noun to highlight it is that exact item
the door to the left of the room
There is only 1 door, on the only left of the exact room we are discussing
but there are many "north sea oil rigs" and this sentence is discussing all of them.
