New determination of a marine geoid around Japan.

Abstract

A marine geoid around Japan is computed on the basis of 30' x 30' and 1 °× 1 ° block mean gravity anomalies. The 30’×30' block data are prepared by reading out the block-averaged gravity anomalies from the published gravity anomaly maps around Japan. The 1°X1° block data are prepared by taking averages of DMAAC's 1°x1° global gravity data and Watts and Leeds' 1°X1° block means. The geoidal heights are computed from the above terrestrial gravity data in combination with the GEM-10 satellite-derived global anomaly field. The GEM 10 model comprises a geopotential coefficient set which is complete up to degree and order 22. The radius of the circular cap area of the numerical Stokes’ integration is taken to be 20°. The marked features of the computed geoid are the dents over trench areas. The dents amount occasionally to more than 20 meters relative to the GEM-10 global geoid. The general geoidal high along island arcs is another marked feature of the calculated geoid. Geoid undulations on the land areas of Japan are compared with an astro-geodetic geoid of Japan (Ganeko, 1976). The standard deviation of the undulation differences is 1. 4 m, while the standard deviation decreases to 0. 8 m if the Hokkaido area is excluded. The astro-geodetic geoid in the Hokkaido area seems to have a tilt downward to the north relative to the gravimetric geoid. The gravimetricgeoid is compared with the Geos-3 altimetric sea surface heights. Altimeter data taken along 12 revolutions of the satellite passing over the region of the gravimetric geoid are used, and the comparison figures for each revolution are presented. The r. m. s. values of differences between altimetric sea surface heights and the gravimetric geoidal heights for each revolution vary within the range from 0. 6 to 1. 9 m except for tilts and constant biases. The total r.m.s. difference is around 1. 3 m. Differences seem to be large in the region where terrestrial gravity data are sparse and consequently gravimetric geoidal heights are poorly determined. Detailed investigations are carried out concerning the error sources involved in the procedure of computation of a gravimetric geoid by means of numerical integration of Stokes’ formula. The results of the investigations estimate the accuracy of the calculated gravimetric geoid to be around 1. 3 m in the area near Japan and to be around 1. 8 m in the gravity data-sparse areas. Terrestrial gravity data errors form the biggest error source under the present availability of the surface gravity data around Japan. The estimated accuracy of the gravimetric geoid is compatible with the comparison results between Geos-3 altimeter data and the gravimetric geoid. The accuracy of the geoidal height difference is also investigated. This kind of error estimation is meaningful because some of the error sources have long correlation distances, so that such error sources hardly affect the accuracy of the geoidal height difference. As for the calculated geoid, the accuracy of relative geoid undulations over 100 km distance is estimated to be around one meter. Detailed investigations concerning various error sources enable us to get a perspective of the geoid computation of the future. After an investigation of the statistical characteristics of the gravity anomaly field around Japan, we derive requirements for marine gravity surveys to achieve a 10 cm geoid. 10' block mean gravity anomalies with an accuracy better than 5 mGals must be prepared in the inner area of Stokes’ integration, i. e. inside and outside to 2° around the area where a 10 cm geoid is computed. These block data can be derived from profile gravity observations carried out along parallel ship tracks located every 10 nautical miles. Moreover, we need additional gravity surveys by profile observations made every 15 or 30 nautical miles depending on the roughness of the gravity anomaly field in the outer area extending to a distance of 20 to 30 degrees from the boundary of the inner area. Systematic errors larger than 0. 1 mGals in gravity observations must be avoided though a few mGals random errors of point gravity observations are acceptable. Stokes’ integration should be carried out in combination with a satellite-derived global gravitational field because long wavelength components of the geopotential field are well determined by the satellite trackings. The flattening of the earth and the sea surface topography must be taken into consideration in the computation of a 10 cm marine geoid.