Conducting bodies exposed to time-varying magnetic fields induce secondary magnetic fields from movement of eddy currents. In the case of spherically symmetric conducting bodies, matching magnetic solutions at the boundary results in relatively simple relations between the excitation field and the induced field. For a non-spherical conducting body, such as an ocean with a tidal bulge, the induced magnetic field necessarily becomes more complicated. In this work, we determine the induced magnetic field from near-spherical layered conducting shells, where each boundary is expanded in spherical harmonics. Under the approximation that the average radius of each boundary is large compared to its perturbation from spherical symmetry, we have derived a versatile method by which the induced magnetic field may be evaluated for an arbitrary conductivity structure described by expanding the radii of the conducting shell boundaries in spherical harmonics.
Many moons in the Solar System are tidally locked and contain subsurface oceans; asymmetries in gravitational field, thermodynamics, and composition will result in deviation from spherical symmetry by the outer boundary of these oceans. Dissolved salts expected to be present in the oceans of these moons are effective electrical conductors. The nearly spherical shape of their oceans and strength of applied magnetic oscillations make several moons promising candidates for study using the method we describe. Deviation from spherical symmetry of subsurface oceans has never been included in past studies. For Europa in particular, a careful analysis of Galileo magnetometer data allows us to place constraints on the amount of asymmetry that may be present in its ice−ocean boundary. Induced magnetic fields are determined using our method, for exaggerated versions of candidate interior structures; induced fields are then compared to Galileo data to determine the maximum asymmetry that may be consistent with magnetic field measurements. Similar applications may be made to Ganymede and Callisto, and Enceladus, which may be subjected to oscillatory magnetic fields owing to libration. The method we describe permits magnetic studies of the effects of symmetry breaking in these bodies for the first time.