Distortion when using displacement modifier So I'm modeling a ring for myself, and I'm using a moon surface texture as a displacement map using a UV unwrap of just the outside of the mesh.
But the displacement modifier seems to be afftecting parts of the mesh I don't want. You can see below that the internal diameter increases.



And I don't want this as obviously it will chance the ring size and it won't fit.
Also I'm wanting the displacement to only affext the surface and for it to stay flush with the top of the ring but it has these sides that I want to get rid of.



Any help or tips will be greatly appreciated!
A way to obtain a smooth transition from a displaced surface to the non displaced parts is to use a vertex group and to assign the good value for the vertex weights:



Here is a view of the weights (blue = the smallest value = 0, red = the highest value = 1):



This is done with the following steps (some of them will depend on your actual mesh and the way the ring is modeled):


Create a vertex group: in the property panel, use the "plus" button as below





In the displacement modifier, assign the group:





Now we have to assign vertices to the group and fix their weights


This part depend on how the model is done. 
Here I used a parallelepiped base, set an array on it, then subsurface and a curve:



To assign the wanted vertices:


Select them
Tune the value of the weight
And assign




So going progressively to the border, while decreasing the weight value to 0, you obtain a smooth edge.

The values are visible vertex per vertex on the right side panel:



The blend file