Refinement of the normal Eötvös matrix and its influence on the estimation of the deflections of the vertical

Abstract The elements of the Eötvös matrix, usually determined by torsion balance measurements, are useful in many geodetic applications. We present a method for the computation of the elements of the normal Eötvös matrix at a point on the Earth’s physical surface, resulting in an improvement in the determination of the deflection of the vertical at intermediate points of a network. In the process, we also present analytical expressions for the computation of the components of the deflection of the vertical. From those expressions and using also a numerical example, we show that the proposed refinement is not completely negligible.