On the Determination of the Terrain Correction Using the Spherical Approach
In the classical approach of planar representation of the Bouguer plate the terrain correction including all its components is always positive and quickly converges with growing radius of integration of topography heights referred to the Bouguer plate. Wh
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On the Determination of the Terrain Correction Using the Spherical Approach G. Kloch and J. Krynski
Abstract In the classical approach of planar representation of the Bouguer plate the terrain correction including all its components is always positive and quickly converges with growing radius of integration of topography heights referred to the Bouguer plate. When, however, the Bouguer plate is considered spherical, some components of the terrain correction as well as the resultant terrain correction may become negative. The terrain correction determined using spherical approach does not exhibit the evidence of convergence in distant zones with growing radius of integration. It makes thus difficult to determine the limitation for the area of integration of topography to compute the terrain correction of the required accuracy. The paper presents the results of research concerning the occurrence of negative components of the terrain correction and their contribution to the resultant terrain correction considering different range of roughness of topography. The convergence of the terrain correction with growing integration radius was investigated in both planar and spherical approach and the differences between the solutions obtained using those approaches were discussed. Special attention was paid to both analytical and empirical investigations of the convergence of the terrain correction when using spherical approach. Numerical tests were performed with the use of DTMs and of real data in a few test areas of Poland that are representative in terms of the variety of topography as well as with the use of simple artificial terrain models.
G. Kloch () Institute of Geodesy and Cartography, Warsaw, PL 02-679, Poland e-mail: [email protected]
52.1 Introduction One of the components of gravity anomalies that are appropriate for modelling precise geoid with the use of Stokes formula is the terrain correction c that represents the deviation of the actual topography from the Bouguer plate of a gravity station P in terms of gravitational attraction (Heiskanen and Moritz, 1967). Computation of terrain corrections is one of the most laborious tasks in precise geoid modelling. It requires the knowledge of the height H of a gravity station P above the geoid, the characteristics of heights of the terrain within a certain radius from P as well as the density ρ of the upper crust of the Earth. Particularly important is a very good knowledge of topography around the gravity station P (Sideris, 1984). The extensive research on methodology of terrain corrections computation was conducted in the framework of the project on modelling centimetre geoid in Poland in 2002–2005 led by the Institute of Geodesy and Cartography, Warsaw, (Krynski and Lyszkowicz, 2006; Krynski, 2007). Most of numerical experiments with computing the terrain corrections were performed using the classical rectangular prism method. The results obtained illustrated the relation between the mean dispersion of heights H = 50 m in the area of integration, the
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