My husband and I recently traveled to Arnold, California, and visited the Big Tree State Park. We were lucky enough to have a young lady join us who had just graduated from college with a degree in botany who was as amazed as we were to see trees like this. She thought it was probably some form of lichen, but wasn't sure. It seemed to originate at a spot where a limb had come off the tree and then make a circle around the tree from there. There were several trees like this in the immediate area.
I really don't know, the green rings actually look more like a moss to me, the lichen that I can see is a Usnea. The green rings do seem to occur at the branch whorls and may be related to annual growth cycle.