As this image shows, the ring was black not blue which supports the view that it was not part of the livery.
The following explanation of the nose ring comes from Tony Anderson, via John Minski and Ansett historian Fred Niven:
The photos of the black ring around the radome are of Ansett 727 & 737 a/c brought back some memories of the avionic group’s early work with Omega navigation systems.
You are right, the black ring was not part of the Ansett livery, but was part of a black conductive paint scheme, that was all over the radome, so that the Omega system would operate better as it was susceptible to “p” precipitation static when Ansett use particular antennae for the system.
In theory the static discharge would stream back to the exposed black conductive surface and discharge it before it got too significant.
There was also the possibility of breakthrough through the white polyurethane over-coat, if it were a thin enough coat. Management decided that as Ansett was an all white livery they permited as a compromise, just to have a black ring showing as in the photos.
The use of H field omega antennae on some aircraft relieved the requirement, as they aren’t as susceptible to “p” static as the E field antennae that were initially installed to try to get Omega to successfully function.