Marina dove into the ocean depths, her tail slapping the surface dismissively.
There are two clauses.
The first clause is a complete sentence:
- Marina dove into the ocean depths
The second clause is a participle clause, with subject her tail, and verb phrase slapping the surface dismissively. This is an adverbial,
so it may be placed either at the beginning or the end.
- Her tail slapping the surface dismissively, Marina dove into the ocean depths.
As with most adverb clauses, there is the possibility of introducing it with a preposition or conjunction. Here the usual preposition would be with
- Marina dove into the ocean depths, (with) her tail slapping the surface dismissively.
Nominative absolute is not a helpful phrase. It's not used in syntax (nominative is reserved for noun case, and absolute doesn't mean anything in particular), but rather is a handwaving term that refers mostly to participles in ancient literary forms. A syntactician would simply say it's a participle.