Journal of the Geodetic Society of Japan

The most accurate practical formula calculating normal heights, i.e., the working formula obtained by Eremeev in 1965 has been evaluated. Then the study estimates the accuracy of the gravity surveys along a leveling line required for the purpose of determining normal heights keeping the accuracy of geometrical leveling which has the highest accuracy among various geodetic surveys. Determinations of geodetic heights or normal heights at triangulation points by trigonometrical leveling are also important in mountainous countries such as Japan from the point of view of processing geodetic surveys by the projection method. The accuracies of height determinations in such cases have been discussed.

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In order to process geodetic surveys by the projection method it is necessary to know the distribution of astrogeodetic deflections of the vertical, i.e., inpractice to map the two deflection componentsξ, ηseparately by contour lines. For this it is the most efficient way to interpolate astrogeodetic deflections of the vertical by using gravity data. The main objective of the present work is to discuss the accuracies characterizing the deflection component maps obtained in such away. Deflections of the vertical can also bedetermined or interpolated by using astrogeodetic data such as by trigonometrical level in gand by using topographic data . The accuracies of determining deflections of the vertical in such cases have also been discussed .

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A program for the computer graphics of a Bouguer gravity iso-anomaly map in Sakurajima, Kyushu is constructed in BASIC. The interpolation of the gravity anomlies between mesh points is conducted through the least squares collocation with a local covariance function.

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To estimate an average mutual distance in a set of ground control points, a method in recent computer graphics was introduced. According to Dirichlet tessellation, whole area is divided into small domains, each of which has one control point in it. This is same as Voronoi diagram and Delaunay triangulation in an ideal case of geodetic triangulation net. If every Delaunay triangle is equilateral and every control point lies at each apex, length of a side is 1.075√A/N, where A is whole area and N number of total points. For a random distribution, an average length of Delaunay triangles is 1.13√A/N, which is 5.3% larger than the equi lateral case. As to the triangulation net in Japan, it was shown that areas of domains on outer part of the net along sea coast equals nearly to those of inside ones. The average side length of the second order net is apparently larger than 8 km which is the standard value and of the third order is smaller than 4 km.

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