Depth is determined by species you are dealing with.
Moles and Gophers tunnel deeper than Voles,
mice and rats tend to run on the surface.
If you are not going to bury mesh the recommended 2 feet deep then you will need to cover the entire underside of the bed with mesh and it needs to extend above the surface at least 8 inches to prevent climb over.
We are having to rebuild some of our raised beds due to
wood rot and we will be making the new ones 16 inches tall above ground level, the 1/4 inch 19 gauge mesh will be sunk 2 feet or to bed rock which ever comes first.
This combination
should take care of the issues we have been having this year with voles and moles. Currently we stomp down all tunnels we find instead of resorting to mole traps.
Redhawk