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The intense plume activity at the South Pole of Enceladus together with the recent detection of libration hints at an internal water ocean underneath the outer ice shell. However, the interpretation of gravity, shape, and libration data leads to contradicting results regarding the depth of ocean/ice interface and the total volume of the ocean. Here we develop an interior structure model consisting of a rocky core, an internal ocean, and an ice shell, which satisfies simultaneously the gravity, shape, and libration data. We show that the data can be reconciled by considering isostatic compensation including the effect of a few hundred meter thick elastic lithosphere. Our model predicts that the core radius is 180–185 km, the ocean density is at least 1030 kg/m3, and the ice shell is 18–22 km thick on average. The ice thicknesses are reduced at poles decreasing to less than 5 km in the south polar region.

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SUMMARY We have investigated the impact of lateral viscosity variations (LVV) in the top 300 km of the mantle on the long‐wavelength gravitational response of the Earth. In contrast to the previous studies we demonstrate that the LVV may play a crucial role if a model with imposed plate velocities and partial layering is considered. Assuming LVV in the top mantle associated with the continental roots and the oceanic asthenosphere, we are able to explain a significant portion of the geoid (85 per cent) and of the free‐air gravity data (55 per cent) without invoking a complex radial viscosity profile or assuming a lithosphere with an unrealistically low uniform viscosity. The best fit to the data is found for models in which mass anomalies located at the boundary between upper and lower mantles reduce the mass flux across the 660 km discontinuity by a factor of 3. These models are characterized by a low average value of viscosity in the asthenosphere below the oceans (∼1019 Pa s) and a large viscosity contrast (>100) between the young suboceanic mantle and the deep continental roots. The viscosity in the deep upper mantle is found to be around 3 × 1020 Pa s while a value higher by at least two orders of magnitude is typical for the lower mantle. The predicted dynamic surface topography is influenced by the surface plate velocities and its amplitude amounts to a few hundred metres. Besides investigating the viscosity structures that reflect the different thicknesses of the lithosphere in continental and oceanic regions, we have searched for a large‐scale pattern of lateral viscosity variation in the top 300 km that yields the best fit to the geoid. The pattern obtained by this inversion shows a good correlation with the ocean–continent distribution and 90 per cent of the geoid and 67 per cent of the free‐air gravity can be explained.