Halliday & Matthiessen (2014: 329):
We saw also that in circumstantial and possessive relational processes there are often close parallels between be + preposition and a verb, e.g.
the delay was because of a strike ~ was caused by a strike
a carpet was over the floor ~ covered the floor
the bridge is across the river ~ crosses/spans the river
a path is along(side) the wood ~ skirts the wood
a halo is around the moon ~ surrounds the moon
This similarity between verb and preposition can also be seen in cases where there is a close relationship between a prepositional phrase and a non-finite dependent clause:
he cleaned the floor with a mop ~ using a mop
grass grows after the rain ~ following the rain
In this way certain prepositions are themselves derived from non-finite verbs; e.g. concerning, according to, given, excepting. These considerations suggest that the nominal group stands to the preposition in some kind of transitivity relation, as well as in a relationship like that of Complement to Predicator in mood structure.