Geodetic singularities

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Abstract
Both general and local coordinate systems for geodesy are usually defined in terms of the gravity vector and on the basis of the assumption of the ‘convexity’ of the equipotential surfaces of the gravity field, which ensures the uniqueness of the coordinates of geodetic type. Two formulations of the singularity condition which have been deduced starting from two different approaches to the geodetic singularity problem, that is, the local‐operational and the global‐geometrical approaches, are discussed. A geodetic singularity problem and the related inverse problem are also discussed for a homogeneous and a nonhomogeneous planet; in particular, the existence of geodetic singularities is shown in connection with a perturbing field with a very simple geometry, and the density distribution is deduced which gives rise to geodetic singularities in the external gravity field of the planet. The structure of the gravity field in the neighborhood of the singularities is investigated in detail together with the behavior of the gradients of the disturbances in the geodetic coordinates, and the scale of the perturbed zone is deduced in connection with a given perturbation.

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