On the Advantage of Normal Heights
This paper analyzes the arguments in the report “The shape of the quasigeoid” by Robert Kingdon, Petr Vaníček, Marcelo Santos presented in Rome (IX Hotin-Marussi Symposium on Theoretical Geodesy, Italy, Rome, June 18–June 22, 2018), which contains the cri
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In memory of Prof. Lyudmila V. Ogorodova
Abstract
This paper analyzes the arguments in the report “The shape of the quasigeoid” by Robert Kingdon, Petr Vaníˇcek, Marcelo Santos presented in Rome (IX Hotin-Marussi Symposium on Theoretical Geodesy, Italy, Rome, June 18–June 22, 2018), which contains the criticisms of the basic concepts of Molodensky’s theory: 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. Also are presented the main advantages of the system of normal heights. They are closely related to the theory of determination of the external gravitational field and the Earth’s surface, are presented. Despite the fact that the main core of Molodensky’s theory is the rigorous determining of the anomalous potential on the Earth’s surface, the advantage of the normal heights system can be shown and proved separately. And this can be easily demonstrated by a simple hypothetical example of the spherical non-rotating Earth where the change of marks along the floor of a strictly horizontal tunnel in the spherical mountain massif serves as criterion for the convenience of the system. In this example, the difference in orthometric heights comes up to 3 cm per 1.5 km. It will require the same corrections to the measured elevations what with the effect of the orthometric heights system. Also the knowledge of the inner structure of the rock mass is necessary. In turn, 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 surface for normal heights, because until now the heights are referenced to the initial tide gauge. The numerical values of heights are assigned to the physical surface. This is similar to the ideas of prof. L. V. Ogorodova about the excessive emphasis on the concept of quasigeoid itself. According to prof. V. V. Brovar the 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. Keywords
Geoid Height systems Modelling method Normal height Orthometric height Quasigeoid
1 V. V. Popadyev () Federal Scientific-Technical Center of Geodesy, Cartography and Spatial Data Infrastructure, Moscow, Russia e-mail: [email protected]
Introduction
The main disadvantage of the quasi-geoid boils down to the well-known fact that near the singular points of the earth’s surface (conical cusps and faces) the gravitational field also
International Association of Geodesy Symposia, https://doi.org/10.1007/1345_2019_74, © Springer Nature Switzerland AG 2019
V. V. Popadyev
has a special feature. Since the normal field is smooth, the surface of the quasigeoid heights D W U also has the peculiarity. Here we should remember that the solution of the boundary value problems of the Newton potential in all cases requires that the earth’s surface shou
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