@thecrease: It is an adverbial phrase, but also a prepositional phrase. I know, it sounds confusing.
Adverbial phrase describes the function of the phrase as a whole, as a constituent of the sentence. You could say it is a description of its "external" function.
Prepositional phrase, however, describes its "internal" structure: it just means any phrase governed by a preposition, so any phrase beginning with a preposition. The "internal" structure has no bearing on its "external" function, there is no direct relation. —
Cerberus 48 secs ago