Yes friend, I believe it is the Ambergris. I wore Live Jazz a few days ago with about 6 or 7 sprays cause It's still cold and way dry here in Utah where I live. The air has no humidity at all. Anyway.. Once it starts to dry down, you will be hit with a baseball bat of warm, heavy, thick ambergris. I can sense a tiny bit if sweetness and vanilla, but mostly just a heavy thick creamy warm note. I've always thought of Ambergris as natural MSG for fragrance. It boosts and thickens whatever it's mixed with. They have chemicals that do this too, but I think Live Jazz is pretty raw and natural for the most part.
Oh yeah, you can see all fragrances with Ambergris if you click on Ambergris in the note pyramid on the Live Jazz page. Here are some that have it that might be good for you to try.
Bulgari Eau Parfumée au Thé Blanc
D&G The One for Men
Davidoff Cool Water Frozen
Kenneth Cole Black