Every body chases rings differently but the way I usually do it is sand down the end of the stave so I can get a clear view of the rings & choose the one I want with some wiggle room to go deaper if there are any suprises on that ring and I chase down to the ring above that one & depending on the ring thickness I scrape to the ring, if those rings are thin I personaly would not go near it with that rasp , can you post a pick of the sanded end grain so we can see your rings ? Also when Im done for the day I re shellac every thing to prevent checking !