How do you make a ring thinner?

[Ofnuts]

• Make sure the image is square and the ring is centered in it (for this image, just crop the top)
  
• Filters>Distorts>Polar coordinates, and untick the "To Polar". This will transform your ring into a rectangle at the bottom
  
• Select the resulting rectangle (no need ot be too accurate), and scale it down vertically using the Scale tool
  
• Commit/Anchor the transform (Ctr-H) and remove the selection Select>None
  
• Filters>Distorts>Polar coordinates again, and tick the "To Polar".