Imagine instead that each ring is joined by a set of springs, which can be compressed down to zero and extended to the difference in the grid snapping between the 2 rings. As the rings snap to different grids the springs extend and contract to fill the gaps. Now place some vertices on these springs and you have a terrain mesh, where the majority of vertices are snapped to locations depending on the LOD, except those joining the rings, which such that the transitions between the layers are seamless