Determine a radius on terrain and lerp the border to smooth the height flattening

I know it looks like a complex question so here's what I'm doing. Currently I can determine an area, get the terrain heights in that area, filter the results to fit inside a circle and then set a flat height to those. Which gives me the 2nd result in the image. Just a flat height inside a circle.

Question is, how can I smooth the height around that circle so that it looks like number 3? My math check cannot roll high enough for this battle :)

My Current code:

 float[,] heightsAroundBuilding =
                 _mainTerrainData.GetHeights(terX - radius/2, terZ - radius/2, radius, radius);
             
             float heightScale = 1.0f / _mainTerrainData.size.y;
             for (int i = 0; i < radius; i++)
             {
                 for (int j = 0; j < radius; j++)
                 {
                     float heightToSet = (spawnPosition.y - heightOffset) * heightScale;
                     if ((i - radius / 2) * (i - radius / 2) + (j - radius / 2) * (j - radius / 2) < radius * 2)
                     {
                         //SMOOTHING LOGIC HERE probably via lerp?
                         heightsAroundBuilding[i, j] = heightToSet;
                     }
                 }
             }
             _mainTerrainData.SetHeights(terX - radius/2, terZ - radius/2, heightsAroundBuilding);