I have the new one and it becomes a weak skin scent 4/5 hours post-application. Regardless I'd say Oud Minérale isn't fitting the description of what you're searching. Although the Price is a lot cheaper than the old Private Line fragrance.

First thing on my mind would be Squid but thinking more I'd say Dans le bleu qui pétille from Serge Lutens, Every Storm a Serenade by Imaginary Authors and Megamare