Newby modeling question here. I’m trying to create a similar effect as shown in the first image, but instead of creating a regular sphere I would like the lift-up to stop at the boundaries of the mesh. I’m using the warp modifier now, but when its radius goes beyond the boundaries of the mesh, it starts to lift the whole mesh up (as a new user I only can add one image, otherwise I would have added an other one to illustrate what I mean). Is there a way to lock the outer edges of the mesh and make the warp modifier stop at them ? Or is there an other way to achieve this instead of using the warp modifier ?
Thanks in advance.
Welcome 
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In 2D thsi is often done makeing something like a heightmap with image filters like bevel, emboss, convolve or even a blur filter and disgarding one side of the borders… maybe even “difference of gaussians”… all those follow the edges and make a “smoother junction”… so you may have a look into this…
If you select the border edges and maybe the next ones in, you can make a vertex group.
With that you can limit the influence of the modifier.
Thanks for the welcome and the answer. I’m a little bit confused by it. I’m familiar with bevel, emboss etc in Photoshop, but not in Blender. I’m using Blender mainly for some rather simple modelling/sculpting towards 3d-printing and my knowledge of it is limited to that. So I do not have a clue how to apply these effects on the job I have at hand here. Can you point me to some tutorials you think may be instructive ?
Thanks for your answer. I followed your advice to create a vertex group and the result is coming closer to what I’m trying to achieve, but I’m still not completely there. The edge of the lift up is now very harsh, is there a way to make it smoother ? Applying smooth modifiers afterwards doesn’t seem to work well.
Yeah, if you have enough vertices, you can change the weights of each successive outline, with the weight control under Object Data Properties > Vertex Groups > Weight… This is in edit mode. You could also weight paint with a radial gradient but I think the first idea is best.
Ohh… i meant using some 2D filter to generate somekind of displacment map…