It's very doable in Rhino, and there are multiple ways to accomplish it.
Make a sphere.
Draw some curves on a side view to where you want the growth rings. You probably want the winter wood to be thin, and the summer wood to be thick for a realistic effect.
You can use wirecut to slice the sphere into slices. The result will be polysurfaces. (The original surface was only a single surface.)
You can use scale2d to resize the winter wood slices to make them a little smaller.
If I were going to make a mesh with the result, and wanted the result a single polysurface, you can union the slices again.
As long as you are careful with the slices and the unit accuracy is not dauntingly high, Rhino should be able to union the slices.
But if the union fails, because you are resizing sections, you may cause nearly coplanar surfaces which may be difficult to union.
You may have to keep the unit accuracy moderate and not .000001mm, or make sure the slices interfere with one another.
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Another way to go about it is to create a displacement or height map with you can deform a section like a half of the sphere at a time. The advantage here is you can include endgrain in your result.
Though, you are going the be throwing a lot of nodes in the result.
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A 3D scanner can scan the surface and create a detailed triangle mesh that could be imported into Rhino as well, though you would be limited to what a triangle mesh could do. Still, you could merge your NURBS geometry and the triangle mesh on export, so when you carve, you can have it.