  Recovering spherical magnetizations $m$ from magnetic field data in the
exterior is a highly non-unique problem. A spherical Hardy-Hodge decomposition
supplies information on what contributions of the magnetization $m$ are
recoverable but it does not supply geophysically suitable constraints on $m$
that would guarantee uniqueness for the entire magnetization. In this paper, we
focus on the case of induced spherical magnetizations and show that uniqueness
is guaranteed if one assumes that the magnetization is compactly supported on
the sphere. The results are based on ideas presented in Baratchart et al.
(2013) for the planar setting.
