The field/hinterland, or area of control; see Bilgim (2007) Pol. Geog. 26, 7 on Turkey’s ‘natural sphere of influence’. Referring to the Ukraine crisis of 2014, Thomas Donilon, former US national security adviser, said ‘with respect to Putin my observations [are]…that for him, these concepts of balance of power, spheres of influence, are quite real concepts. And quite relevant to how he views the world…he regards it as an element of the Russian sphere of influence’ (Brookings.edu).
The term is also used for the urban field of a city; see Ma (2005) Pol. Geog. 24, 4.