In truth, this started out as a kind of 3D doodle. At it's core, this is just a hollowed out cube, with a bunch of modifiers:
I elongated a cube, removed two sides, added a solidify mod (to give the remaining faces some thickness), two Array mods (to create a wall of these cubes), a Curve Mod (to create the arc), a couple of subsurf mods (because why not?), and another couple of array mods (to create the radial pattern that defines the layered dome shape). This was not the most efficient scene. It took an unreasonably long time to render (15+ hours), even for the size of the image. Plus, the way I used the mods eliminates this scene from being shown from any other angle, without killing the illusion of a dome. In reality, when viewed from a different location (from outside of this inner curve), this looks a bit like a mushroom cloud. I really like the architectural effect & may try this again, but better.