- create a sparse image:
hdiutil create -size 600g -type SPARSEBUNDLE -fs "HFS+J" NAME_XXXXXXX.sparsebundle -volname 'untitled' -encryption
- ideally the sparse bundle should have about twice the size of your Mac's storage
- copy sparse bundle to the network and then mount it:
rsync -aE NAME_XXXXXXXXXXXX.sparsebundle /Volumes/DRIVE/.
- remove the sparse bundle from machine:
rm -rf NAME_XXXXXXXXXXXX.sparsebundle
- tell time machine to backup your mounted drive:
sudo tmutil setdestination /Volumes/TimeMachine
- head to System preferences, then open Time Machine settings; you should see your virtual drive as the default backup destination