Trying to understand the way Saturn's ring look in this famous Cassini image

What's going on with the distortion of the rings on the upper half when they (presumably) cross in front of Saturn?

The brownish areas you see on Saturn are ring light, analogous to seeing the Earth by moonlight. Saturn's rings light up Saturn's night sky, particularly just after sunrise and just before sunset. The two dark bands across the face of Saturn are the A ring (upper dark band) and B ring (lower dark band). Of all of Saturn's rings, these two are the most opaque. The parts of Saturn underneath those two dark bands are brilliantly lit by ring light, but Cassini can't see those parts of Saturn because the opaque A and B rings block that light.

For a much better and more thorough explanation of all of the features in this incredible image, I suggestion you spend eleven minutes watching this youTube video by Emily Lakdawalla.

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^{_{This is one of the very few times I will post a link to a youTube video. It is worth every eleven minutes.}}