How is damage from proximity AoEs calculated?

[Delphor]

I survive just sitting in the centre of that all the time. The moves aren't inherently lethal, they just deal higher damage the closer you are to them.

Depends if you're a tank though or if you have high defense values. I've seen tanks take the sandpit attack from Arachne Eve right close to the center and survive, whereas if it was a squishier caster or healer, they'd be dead if they're on par with the item level for the encounter.