Header for non-logged in users and header for logged in users, possible?

This is something I have never even thought of before tonight, please excuse me while I try to explain what I am attempting to do.

I am working with the Divi theme located on seoinerg.com(non-production site). I would like to show non-logged in user the header that is there now, but when a user logs in I would like to a completely different header to appear.. something I can make more custom for a members area I am creating. Not sure how to go about this..

Is this where a child theme comes into play?

Can you help me understand how to do this? Or is this not possible?