You can't, I'm afraid, there's no solution. Sometimes, if you know there's an old tree stump or something beneath the ground, removing that makes a difference, but that doesn't always work either.

According to "The Lawn Expert" by Dr. D.G. Hessayon, you could try iron sulphate (1/2oz in a gallon of water per sq. yard) but the real answer is to remove the turf and topsoil to a depth of 1ft. The area of excavation should extend to 1ft beyond the inner and outer edges of the ring, and all the earth should be moved well away from the lawn - take care not to spill any on the turf. Fill the hole with clean topsoil and then re-turf the area.
Sounds like a big job to me, depending on the size of the ring!

And doesn't always work, either.