On the advantage of normal heights

Abstract

The author analyzes the arguments in the report by Robert Kingdon, Petr Vanicek and Marcelo Santos “The shape of the quasigeoid” (IX Hotin-Marussi Symposium on Theoretical Geodesy, Italy, Rome, June 18 June 22, 2018), which presents the criticisms for the basic concepts of Molodensky’s theory, the normal height and height anomaly of the point on the earth’s surface, plotted on the reference ellipsoid surface and forming the surface of a quasigeoid. The main advantages of the system of normal heights, closely related to the theory of determining the external gravitational field and the Earth’s surface, are presented. Despite the fact that the main advantage of Molodensky’s theory is the rigorous determining the anomalous potential on the Earth’s surface, the use of the system of normal heights can be shown and proved separately. To do this, a simple example is given, where the change of marks along the floor of a strictly horizontal tunnel in the mountain massif is a criterion for the convenience of the system. In this example, the orthometric heights show a change of 3 cm per 1.5 km, which will require corrections to the measured elevations due the transition to a system of orthometric heights. The knowledge of the inner structure of the rock mass is also necessary. It should be noted that the normal heights are constant along the tunnel and behave as dynamic ones and there is no need to introduce corrections. Neither the ellipsoid nor the quasi-geoid is a reference for normal heights, because so far the heights are referenced to initial tide gauge. The points of the earth’s surface are assigned a height value; this is similar to the ideas of prof. L. V. Ogorodova about the excessive emphasis on the concept of quasigeoid. A more general term is the height anomaly that exists both for points on the Earth’s surface and at a distance from it and decreases together with an attenuation of the anomalous field.