Halliday & Matthiessen (2014: 419-20):
Premodifiers are grammatical items like not and rather and so; there is no lexical premodification in the adverbial group. What there is is therefore more like what we have called ‘submodification’ in the nominal group, with SubModifiers relating to an adjective as their SubHead.
We can represent the adverbial group as a logical structure as shown in Figure 6-24.