The following SQL query could be run to determine which index volume belongs to an archive:

USE EnterpriseVaultDirectory
SELECT IndexVolume.IndexVolumeIdentity, IndexVolume.RootIdentity, IndexVolume.IndexRootPathEntryId,
IndexVolume.FolderName, IndexVolume.OldestItemDateUTC, IndexVolume.YoungestItemDateUTC,
Archive.ArchiveName
FROM IndexVolume INNER JOIN Root ON IndexVolume.RootIdentity = Root.RootIdentity INNER JOIN
Archive ON Root.RootIdentity = Archive.RootIdentity

This query will provide an output with different columns including one called ArchiveName.

In addition, it is possible to search for one index volume in particular adding the following WHERE clause:

WHERE (IndexVolume.IndexVolumeIdentity =  )

Note:  Replace with the IndexVolumeIdentity value from the IndexVolume table of the EnterpriseVaultDirectory database.