G. Manoussakis | Searcharxiv

arXiv2016

Gravimetric estimation of the Eötvös components

The elements of the Eötvös matrix are useful for various geodetic applications, such as the interpolation of the elements of the deflection of the vertical, the determination of gravity anomalies and the determination of geoid heights. A torsion balance instrument is customarily used for the determination of the Eötvös components. In this work, we show that it is possible to estimate the Eötvös components, at a point on the physical surface of the Earth, using gravity measurements at three nearby points, comprising a very small network. In the first part, we present the method in detail, while in the second part we demonstrate a numerical example. We conclude that this method is able to estimate the elements of the Eötvös matrix with satisfactory accuracy.

physics.geo-ph↗

arXiv2011

Formulae for the determination of the elements of the Eötvos matrix of the Earth's normal gravity field and a relation between normal and actual Gaussian curvature

In this paper we form relations for the determination of the elements of the Eötvös matrix of the Earth's normal gravity field. In addition a relation between the Gauss curvature of the normal equipotential surface and the Gauss curvature of the actual equipotential surface both passing through the point P is presented. For this purpose we use a global Cartesian system (X, Y, Z) and use the variables X, and Y to form a local parameterization a normal equipotential surface to describe its fundamental forms and the plumbline curvature. The first and second order partial derivatives of the normal potential can be determined from suitable matrix transformations between the global Cartesian coordinates and the ellipsoidal coordinates. Due to the symmetry of the field the directions of the local system (x, y, z) are principal directions hence the first two diagonal elements of the Eötvös matrix with the measure of the normal gravity vector are sufficient to describe the Gauss curvature of the normal equipotential surface and this aspect gives us the opportunity to insert into the elements of the Eötvös matrix the Gauss curvature.

math.DG↗