On the Determination of the Terrain Correction Using the Spherical Approach

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.