International audienceVarious papers have discussed the forward relationships between internal density anomalies of a planet and its external gravity field. The inverse modeling, i.e. finding the internal density anomalies from the external potential is known to be highly non unique. In this research note, we explain how a 3D basis can be built to represent the internal density variations which includes a subset that explicitly spans the kernel of the forward gravity operator. This representation clarifies the origin of the non-uniqueness of the gravity sources and implies the existence of a natural minimal-norm inverse for the internal density. We illustrate these ideas by comparing a tomographic model of the mantle to the minimal norm density
