https://en.wikipedia.org/wiki/Compression_ratio
If you work on the basis of an average / new Nissan diesel compression ratio the only unknown quantity you will have will be Vc - clearance volume.
The clearance volume will include not just the cylinder head total volume but also the area that is not swept by the piston, head gasket, piston tops etc. When you calculate this and then subtract the volume you have recessed (that will be the area you have machined out (pye r squared x depth) you will arrive at the slightly greater value of Vc.
Then do the calculation again where the compression ratio is unknown but other values are. This will give you the new compression ratio - you will then compare that to the first figure you used. This can then be used to give you a % change in compression ratio.
If the maths defeats you PM me with the dimensions you have cut out & I will give it a go for you. Dont forget if it has been rebored the swept volume will be greater.