Algebraic Theory of the Marussi Tensor

Abstract

The Marussi tensor, or the tensor of gravity gradients, or simply the gravity tensor, has long been regarded as the centerpiece of differential geodesy. It was introduced in Marussi (1949) primarily by using the homographic calculus and in Marussi (1951a) he called it the Eötvös tensor since, as he noted, “… it was this geodesist who gave the first systematic consideration to the application of the second derivatives of the potential to geodetic and geophysical problems.” In his formulation the theory of the tensor is essentially that of the Eötvös and generalized Burali-Forti homographies. As he noted, up to second order this tensor systematically synthesizes all of the dynamical and geometric properties of the Earth’s gravity field.