Geodetic singularities in the gravity field of a non-homogeneous planet

Summary. An inverse geodetic singularity problem is considered for a non-homogeneous spherical planet. The singularity condition is expressed in terms of the density distribution and of the geometrical parameters of the configuration; the condition for the density distribution is deduced which gives rise to singularities of parabolic type in the external gravity field of the planet. The structure of the gravity field in the neighbourhood of the singularities is investigated in detail together with the behaviour of the gradients of the disturbances in the geodetic coordinates.     

A comment on depths of sources of anomalies in the Earth's gravity field

Summary. One method to determine the depths of sources of anomalies in the Earth's gravity field is to plot log [(2 n + 1) σ _n ] versus n where σ _n is the n th term in the amplitude spectrum of the Earth's gravitational potential. This procedure assumes that the amplitude spectrum of the anomalous density variations does not vary with n. Such an assumption may not apply to the Earth.     

Isoparametric and isozenithal-type representations of the actual gravity field of the Earth

Summary. The first-order theory of three-dimensional representations of the actual gravity field of the Earth on the normal field given by Bocchio has been applied to the class of isoparametric-and of isozenithal-type mappings. The resulting linear and angular deformations together with the expressions for the gravity anomalies and disturbances have been compared and discussed and some invariant relations have been put into evidence.