New Pieces in the Picture Puzzle of an Astrogeodetic Geoid Map of the World
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Irene FISCHER, Mary SLUTSKY, F.R. SHIRLEY, P.Y. WYATT lit Army Map Service, Washington, D.C. NEW PIECES IN THE PICTURE PUZZLE OF AN ASTROGEODETIC GEOID MAP OF THE WORLD Abstract The astrogeodetic geoid map presented to the IUGG at Helsinki in 1960 has been updated to reflect the accumulation of new data. The geoid map of North America has been recomputed, that of South and Central America enlarged. A geoid chart of Australia has been added. Various other improvements were made. Terrestrial gravity was used for interpolation, and satellite observations for inter- continental connection. World datum parameters were derived in various solutions. Satellite positioning of the major astrogeodetic datum blocks leads to an equatorial radius a = 6378142 m for a flatteningf = 1/298.25. If surface gravity is included, the radius is larger. A reference figure a = 6378150 m and f = 1/298.3 is recom- mended for practical applications ? 1. Introduction Quite a few geoid charts are to be found in the current technical literature. They were derived from satellite data and cover the world. Why should we still be interested in the laborious process of piecing an astrogeodetic chart together. While such comments are heard occasionally, astrogeodetic charts are nonetheless used as standard for comparing the various satellite charts. One reason is the variety of these charts depicting presumably the same geoidal surface : the charts look similar at first sight, but less so if specific geoidal heights at specific places are needed. The limitations of the classical astrogeodetic method to land areas permit a direct comparison only for stations within the same datum, after allowing for the difference in reference system. The land limitations are relaxed somewhat through the use of HIRAN, stellar triangulation, and SECOR, that is through geometric techniques by which the area of a specified geoidal datum can be extended. If such extension is carried far enough so as to overlap with the area of another geodetic datum, conversion formulae can be derived to put both areas on the same datum. Also dynamic satellite results in the form of geoid charts or tracking station coordinates can be used to connect the isolated astrogeodetic datum blocks. Furthermore, dynamic results provide the relation to the center of 199 6 Irene FISCHER, Mary SLUTSKY, F.R. SHIRLEY, P.Y. WYATT III mass of the earth. The advice received from these various satellite results on how the astrogeodetic blocks should be put together in relation to each other and to the center of mass is, however, not exactly the same at this time. The construction of astrogeodetic geoid charts for the purpose of detailed local information as well as for the derivation of world geodetic systems has been carried out at the Army Map Service within a series of studies of the Figure of the Earth over several years. The present study is but one of this series. For proper perspective some highlights of the series are briefly recapitulated here. When the two long meridional arcs from Canada to Chile and from Finland to South Africa were completed in 1953 and 1954, a tentative size of the earth was derived from astrogeodetic deflections of the vertical, indica[ing that the equatorial radius of the International ellipsoid was much too large [ 1 ]. Then the method was changed from deflections to geoidal heights [ 2 ] . All available geoid charts were collected and new ones constructed, and the Molodenskiy correction was introduced to cope with scale distortions in poorly fitting extended nets. The result upheld that of the previous study, suggesting that also the International flattening was too large. For various reasons, however, the conventional flattening 1/297 paired with an equatorial radius of a = 6378270 m (the Hough ellipsoid) was adopted for the Vanguard Datum and the Tentative World Datum [ 3 ], although the free-air solutions had shown smaller values. Soon after that the first satellites went up. The analysL of observations from the Vanguard satellite yielded the value 1/298.3 for the flatt~,ning [ 4 ] , which v~as adopted for the Figure of the Earth studies. The mathematical relationship between values of the flattening and of the radius for the same observational material would automatically yield a smaller radius. A recomputation, incorporating all astrogeodetic, gravimetric, and satellite data available at that time, was presented to the IUGG at Helsinki in 1960 [ 5 ] . The results were confirmed by also using elaborate statistical methods on the same data [ 6 ] . The Mercury Datum (a = 6378166 m for f = 1/298.3) is solution 4 in reference 5b, using gravimetric orientation. The ellipsoid used in the South Asia Datum (a = 6378155 m for f = 1/298.3) is solution 3, derived purely astrogeodeti- cally. A third solution a = 6378160 m (p. 249, s was submitted to the Working Group on Astronomical Constants of the International Astronomical Union, Hamburg 1964. The present study updates the Helsinki paper. The astrogeodetic geoid chart has been extended to formerly blank areas, and satellite results were used for intercontinental connections. 2, Geoid Charts The North American geoid chart presented at Toronto 1957 has been recomputed with some deflection values and a new method [ 7 ]. Geoidal profiles along meridians and parallels spaced 1~ apart were computed by formulas conform- ing to the projection method, and the geoidal height values at the intersection points were adjusted with weights reflecting the number of given deflection values pertinent to the adjacent l~ sections. The geoid profile along the 35 th 200 NEW PIECES IN THE PICTURE PUZZLE ... parallel, observed and computed by the Coast and Geodetic Survey [ 8 ], was held fixed after the reference was changed to conform with zero meters at the origin Meades Ranch. As a second backbone a dense meridional geoid profile in the center of the country was constructed by gravimetric interpolation of the astrogeodetic deflections. The southern part of this profile was computed by the Coast and Geodetic Survey, using the circular template method. For the northern part the Coast and Geodetic Survey had observed a 200-mile wide band of gravity values ; the profile was computed by the Army Map Service [ 9 ] with a new automated method of small uniform rectangular template compartments [ 10 ] . The North American Datum was tentatively extended along the North Atlantic HI RAN path through utilizing the six deflections on the icecap observed by the 1959 Interna- tional Glaciological Expedition to Greenland, together with the astronomic positions observed by the Army Map Service at some HI RAN stations. Also stellar triangulation provided some geoidal heights. With more deflections in Mexico and Central America the geoid compu- tation was extended to South America. A geoid chart of South America on 1956 Provisional South American Datum and also on the more suitable Corrego Allegre Datum was prepared for the Pan American Consultation in Guatemala City, 1965, with all deflections available at that time [ 11 ]. Since then more values in eastern and southern Brazil became available and the chart could be extended through Uruguay and along the 25th parallel in Paraguay. It is hoped that in the near future an Argentinian geoid profile from the border with Uruguay to the border with Chile will become available and will strengthen the huge loop around the continent. Transformation formulae between 1956 SAD and 1927 NAD were derived at the junctions in Nutibara, Colombia, and in Trinidad. Figure 1 shows the geoid contours in the Western Hemisphere on 1927 North American Datum. Figure 2 shows the geoid contours on European Datum for Europe, Asia, and Africa. The chart for Europe is very similar to G. Bomford's more detailed chart of 1963. Spain has been recomputed. New deflections in southern Italy and corrections to some Greek values have lowered the geoidal height at Athens by several meters. A loop around the Mediterranean Sea has been attempted by extending Dufour's geoid contours in Morocco, Algeria and Tunisia to Libya and Egypt, then using Tengstr6m's gravimetric profile from El Alamein to Athens [ 12 ] . There is still a misclosure of ten meters, the African route yielding a negative value of about - 6 m. For the time being the value of zero meters with an uncertainty of + 5 m was adopted at Athens. This lowers the profile through Turkey and Iran by ten meters and slightly changes the transformulation formulas at Koh-i-Malik between South Asia Datum and European Datum to the following : A N ( E D--SA D ) = + 112 cos ~ cos ~ + 49 cos ~ sin ~k + 116 sin r + 94 sin2 ~ _ 233 South Asia Datum itself is, of course, not affected. Geoid contours on that datum were extended to Thailand and West Malaysia (Figure 3), and then 201 Irene FISCHER, Mary SLUTSKY, F.R. SHIRLEY, P.Y. WYATT III converted to European Datum by the above formula. The ED contours in the USSR were recomputed, replacing Dubovkiy's chart with Molodenskiy's. The Manchurian tie was strengthened considerably by establishing transformations between horizontal positions on Iman Datum, Svobodny Datum, Manchurian Principal System, and Pulkovo 1942 Datum [ 13 ]. A three-dimensional transformation between Pulkovo 1942 Datum and Manchurian Principal System could now be derived, based on position and height differences at Svobodny, and strengthened by height differences along the two arcs from Vladi- vostok to Khabarovsk and along the Amur, This changed somewhat the transfor- mation between Tokyo Datum and European Datum. New deflections permitted an extension of the geoid chart of Japan to the south, including the Ryukyu Islands. In Africa, data outside the 30th meridian are beginning to come in slowly but surely. A geoidal profile along the 30th parallel south was observed and computed by B.M.