Considerations in Obtaining Detailed Surveys of the Form of the Quasigeoid and of the Deflection of the Vertical (I)

Abstract

In general, given the error of representation or the error of interpolation, the sufficient and economic distribution of gravity observations for a prescribed accuracy for astrogravimetric leveling or the interpolation of the deflection of the vertical can be' determined. This report discusses in what way and with what accuracy detailed surveys of the form of the quasigeoid and of the deflection of the vertical should be obtained. The folllowing conclusions were obtained. 1. It is advisable to use the indirect method of interpolation of the freeair anomalies, , which makes use of the fact that Bouguer anomalies are in general far less correlated with elevation than free-air anomalies (our system of computing astrogravimetric leveling applies this method). 2. The error of representation and the error of interpolation in north Kanto aree three or four times larger than those obtained by the Russian geodetists on the basis of the dence gravity-station nets of the U.S.S.R. 3. In general, these errors will depend not only on the size of the variations of the gravity anomalies but also on its irregularities. Thus the coefficient k of the righthand side of the empirical formula of the form (1), or (2), which expresses the error of representation or the error of interpolation, should be considered not to be constant but to be variable. Before the astrogravimetric leveling is carried out, therefore, we must have a guarantee that some local gravity surveys already exist, from which the value of k can be determined. 4. On the basis of the error of representation in north Kanto, which may represent eastern Japan approximately, in order to obtain the results of astrogravimetric leveling with an accuracy of ±0"6.21, it is necessary, say, that a regional gravity survey with a density of 1 point per 60 km² exists out to 41 from the middle point between astronomical stations and that the neighborhood of the astronomical station is covered by a gravity station net-1 point per 5-10, km2 in a circle of 8 km radius. Further if gravity observations at an average distance of 7 km for lowlands and mountains, and of 3-4 km for high mountains can be get, the deflections of the vertical with an accuracy of 1" will be obtained. 5. If studied area has a rather smooth gravity-anomaly field, as is true in western Japan, the necessary deflections of the vertical can be adequately obtained on the basis of a rather widely spaced gravity-station net.