  Magnetic investigations of icy moons have provided some of the most
compelling evidence available confirming the presence of subsurface, liquid
water oceans. In the exploration of ocean moons, especially Europa, there is a
need for mathematical models capable of predicting the magnetic fields induced
under a variety of conditions, including in the case of asymmetric oceans.
Existing models are limited to either spherical symmetry or assume an ocean
with infinite conductivity. In this work, we derive an analytic result capable
of determining the induced magnetic moments for an arbitrary, layered body.
Crucially, we find that degree-2 tidal deformation results in changes to the
induced dipole moments. We demonstrate application of our results to models of
plausible asymmetry from the literature within the oceans of Europa and Miranda
and the ionospheres of Callisto and Triton. For the models we consider, we find
that in the asymmetric case, the induced magnetic field differs by more than 2
nT near the surface of Europa, 0.25$-$0.5 nT at 1 $R$ above Miranda and Triton,
and is essentially unchanged for Callisto. For Miranda and Triton, this
difference is as much as 20$-$30% of the induced field magnitude. If
measurements near the moons can be made precisely to better than a few tenths
of a nT, these values may be used by future spacecraft investigations to
characterize asymmetry within the interior of icy moons.
