Gravimetric estimation of the E\"otv\"os components

The elements of the E\"otv\"os 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 E\"otv\"os components. In this work, we show that it is possible to estimate the E\"otv\"os 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 E\"otv\"os matrix with satisfactory accuracy.