Halliday & Matthiessen (2014: 294-5):
In the ‘possessive’ type, the relationship between the two terms is one of ownership; on entity possesses another … In addition to possession in the narrow sense of ‘owning’, the category of ‘possessive’ clauses also includes possession in a broader, more generalised sense — possession of body parts and other part–whole relations, containment, involvement and the like … Possession thus has to be interpreted quite broadly, in the sense of ‘extension’: one entity is construed as being extended by another.
Just like ‘circumstantial’ clauses, ‘possessive’ ones are construed in both the ‘attributive’ and ‘identifying’ modes.