Quadra Magic is actually in a Materia Cave off Mideel not trhe crater, I've learned how to get that w/o a Special Chocobo thanks to a glitch & a tip-off.

Getting out of the Northern Crater is daunting when you first try it, but it's second nature to me now just go all the way down get everything, talk to your other charcters for more shtuff but DONT AND I MEAN DONT step down the glowing hole yet. You can walk/jump/climb all the way bk up, in involves going in & out of caves & jumping & falling a lot but it's worth it, especially if you want the KoR+HP Absorb combo mastered (God bless them Magic Pots). I could explain exactly how when I get home.