I know it’s a bit of a necro. But since this still comes up first in google search when searching concentric circles panning. Thought I’d share a slightly simpler basic approach.
The multiply or lerp would be to mask of the edges. And ceil, abs, 1-x nodes are just variations. You’d still want to plug these into a multiply or lerp to mask the outer corners)
(You can also UV anim the TexCoords to the Spheremask with a noise texture for wobbly circles)