Deflection of the vertical and refraction in three-dimensional adjustment of terrestrial networks

Summary In this paper statistical tests are exploited in order to verify the hypotheses about the refraction and the deflection of the vertical pertaining to a geometrical model for the three-dimensional adjustment of terrestrial networks. The deflections of the vertical and the refraction coefficients can be assumed either as unknowns or fixed input data, at some or all the points of the network. The geometrical model, reported in the appendix for convenience, assumes as observables the slant distances, zenith and horizontal angles, without any reduction neither to the marks on the ground nor to the surface of reference. Further, the observation equations are derived and linearized in terms of Cartesian coordinates in Geocentric or Topocentric system; direction cosines of the vertical and of the ellipsoidal normal are adopted as the relevant direction parameters. Finally, an application to a network from Hradilek (1984), performed under different assumptions about the unknowns and the corrections of the angular observations due to the deflections of the vertical, shows the effectiveness of the proposed approach.