Scholarly record
ON THE NORMAL HEIGHT DIFFERENCES DETERMINATION FROM GEOPOTENTIAL DIFFERENCES
Abstract
Calculation of normal heights and differences from known geopotential numbers and differences in geodetic practice is required when performing independent calculations: for control of levelling network adjustment made with different type heights – normal and geopotential; when using optical clocks technology for geopotential difference determinations; when performing precise engineering and geodetic works. It is well known that between two height types - normal heights and geopotential numbers exists theoretical equivalence when the same gravimetric and levelling data are used. In practice, this equivalence depends on the realized accuracy of the calculations. This requires the appropriate, substantiated calculation formulas. Transformation accuracy is connected to the degree of detail in description of the relationship between the two quantities. The accuracy of normal difference, determined by known geopotential difference is studied. The contribution of each individual term forming its mean square error is analyzed. The study is made under different conditions: heights, height differences, distances, orientation of levelling connection, and different errors in the height of the benchmarks. In the article briefly is presented the principle of geopotential difference determination, based on the gravitational Doppler effect. It occurs during the operation of two remote optical clocks, according to the General Theory of Relativity. The theoretical dependence between normal height differences and the frequency shifts of the optical clocks is also presented. In the article is discussed the transformation between the two equivalent quantity types, providing the necessary practical accuracy for the purposes of precise height determinations.
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