This is an update: I believe I have figured this out, at least for what I need to do. I'll work on it tonight and let you know. Thanks to all.
Thanks for the suggestions so far. I need to say that this is a picture of a quilt I found on-line, it's not one I've made. Unfortunately, when I went back to try and find it, so I could contact the person who made it, I couldn't find this quilt anywhere. So far, I've tried using a 4" center and sewing 2 rounds of logs and then cutting the block in half and re-sewing. The center matches up fine, but the logs don't line up.
So I'm hoping that my friend's quilt will look a lot like this one, but this one belongs to someone else!! I'm going to keep thinking about it.