Published in Journal of Geodesy
The ellipsoidal Stokes problem is one of the basic boundary-value problems for the Laplace equation which arises in physical geodesy. Up to now, geodecists have treated this and related problems with high-order series expansions of spherical and spheroidal (ellipsoidal) harmonics. In view of increasing computational power and modern numerical techn...
Published in Journal of Geodesy
Motivated by the existing theory of the geometric characteristics of linear generalized inverses of linear mappings, an attempt is made to establish a corresponding mathematical theory for nonlinear generalized inverses of nonlinear mappings in finite- dimensional spaces. The theory relies on the concept of fiberings consisting of disjoint manifold...
Published in Journal of Geodesy
GPS has become an essential tool for the precise determination of point positions. Since GPS campaigns for geodynamic purposes – such as the monitoring of recent crustal movements – require major financial efforts, it is essential to ensure already in the planning phase a good network quality and the attainment of the scientific goals in a reasonab...
Published in Journal of Geodesy
The second Baltic Sea Level (BSL) GPS campaign was run for one week in June 1993. Data from 35 tide gauge sites and five fiducial stations were analysed, for three fiducial stations (Onsala, Metsähovi and Wettzell) fixed at the ITRF93 system. On a time-scale of 5 days, precision was several parts in 109 for the horizontal and vertical components. A...
Published in Journal of Geodesy
In this contribution we consider the precision of the floated and the fixed GPS baseline for the case of weighted ionosphere. Canonical forms of the baseline variance matrices are developed for different measurement scenarios. These forms make the relation between the various variance matrices transparent and thus present a simple way of studying t...
Published in Journal of Geodesy
Recurrence relations have been derived for truncation error coefficients of the extended Stokes' function and its partial derivatives required in the computation of the disturbing gravity vector at any elevation above the earth's surface. The corresponding formulae, the example of values of the truncation error coefficients for H=30.1 km and ψ0=30∘...
Published in Journal of Geodesy
Published in Journal of Geodesy
In precise geoid determination by Stokes formula, direct and primary and secondary indirect terrain effects are applied for removing and restoring the terrain masses. We use Helmert's second condensation method to derive the sum of these effects, together called the total terrain effect for geoid. We develop the total terrain effect to third power ...
Published in Journal of Geodesy
In the determination of the preliminary geoid over Zambia, we compare three methods of the modified Stokes formula: that of Vincent and Marsh, a modified Wong and Gore method, and a modified spectral weighting method, with the final solution being estimated by the modified Wong and Gore procedure. The geoid over Zambia (based on GRS80) is rising fr...
Published in Journal of Geodesy
The contribution of bathymetry to the prediction of quantities related to the gravity field (e.g., gravity anomalies, geoid heights) is discussed in an extended test area of the central Mediterranean Sea. Sea gravity anomalies and a priori statistical characteristics of depths are used in a least-squares collocation procedure in order to produce ne...
