Contribution au calcul simplifié de la correction orthométrique en nivellement de précision

Abstract

The height of a point, generally useful to ensure the direction of runoff waters, is the coordinate which is expressed by the vertical distance between this point and a reference surface. Thus, several types of heights are defined. As for orthometric heights, the considered reference surface is an equipotential surface of the Earth's gravity field, corresponding approximately to the mean sea level (geoid).
The equipotential surfaces are not parallel; it is not possible to set the altitude as a simple geometric height above a reference surface. Thus, the geometric height differences between points measured step by step from a fundamental point with a precision leveling method should be corrected by taking into account the variations of gravity. The estimation of this correction, known as orthometric correction, that we will have to make to the measured height differences can be done through two approaches. The first known as the normal orthometric correction is based on normal gravity (or theoretical). The second form is a rigorous approach that includes the real gravity measurements in leveling.
This paper has therefore examined the theory and practical possibility to estimate the orthometric corrections for precise leveling networks. A computer program dedicated to numerical estimation of normal orthometric corrections in its three possible forms and the so-called Helmert correction was developed. Leveling data set covering the Perth area Australia was used to validate the reliability of this program, which provides conclusive results.
Key words: height, observed gravity, normal gravity, normal orthometric correction, Helmert's orthometric correction.