It has been pointed out that very long baseline interferometry (VLBI) is less accurate in determining the station positions in a vertical axis than in a horizontal plane. However, possible applications of VLBI for sea level monitoring, terrestrial reference frame for astrometry and earth rotation studies, etc., require accurate determination of the station position in the vertical axis as well as in the other axes. I propose three different approaches to improve the accuracies of the estimated vertical site positions, that is, to control the vertical elongation of the positional error ellipsoids by low elevation observations, to reduce the size of the ellipsoids by decreasing the residuals, and to select a "right" atmospheric mapping function to avoid systematic errors in vertical positions.

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Japan University Consortium for GPS Research operated the Sagami Bay GPS Campaign with thirty GPS receivers both in December 1988 and in December 1989 to monitor crustal movement. This paper concerns only the data obtained during these campaigns by sixteen Trimble 4000SD dual-frequency receivers. The observations were conducted over a five day period in each year campaign. At the 1988 campaign the satellite constellation over Japan was very poor and four satellites were visible only for several tens of minutes. After the beginning of launch of block II satellites, the satellite visibility has been much improved even in Japan, and five satellites were available in the campaign of 1989. The number of baselines for which four (not five) satellites were available in analyses was only 53 in 1989 campaign, while it became 105 over for five satellites in 1989 campaign. The short term repeatability of baseline length was generally less than 1 ppm in 1988 campaign and it is shown that it has been improved to be less than 0.5 ppm for every baseline triangle in 1989 campaign. Although the changes of baseline lengths from December 1988 amount to 2.0 ppm, it can be interpreted that it is caused by poor satellite constellations in 1988 campaign and remain as apparent. The remarkable repeatability of 0.5 ppm in the 1989 campaign promises that GPS provides us the efficient observation means for the crustal motion in a wide area.

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The numerical example shown in the report indicates that we can not get a unique solution by iterative method in case of the free-network adjustment,

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A special technique of network adjustment is developed for analysis of leveling data that are obtained in the area where the remarkable crustal movements are prevailing. We applied velocity model in which not only corrections to the assumed height but also rate of vertical deformation linear with time at the bench marks are assumed to be unknowns in order to take into considerations of the effect of rapid vertical crustal movements to the results of survey. On the other hand, we have sometimes tidal stations along the sea coast of the discussed region and vertical rate of crustal move ments are able to be deduced from analysis of tidal data. Thus it is desirable to com bine the determined rates at some tidal stations with the leveling data in the network adjustment. The type of present adjustment with velocity model is proved to be a specialized case of least square adjustment of network with signals under deterministic approach. Let X be corrections to the assumed coordinates, a vertical rate of deformation, and f numerical term relating to the survey data and approximated coordinates, then the observation equation is generallyV+AX+Ha=fwhere A and H are coefficient matrices of vector X and a, V is residual vector applied to the observational results. We apply least squares collocation to the above equation. In numerical calculation, we have four fundamental cases. Except the case of all free parameters in which none of X and a are fixed and A as well as H are singular, we can apply reduced normal equation for obtaining X and a separatelly. According to the type of network with some fixed heights or fixed velocities and both A and H or one of them is regular, we apply different formulas. Thus formulas for all four cases are given in the text for obtaining X and a as well as their variance-covariance matrices.

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The conventional concept of geoid may be obsolete with the recent development of GPS technique in height determinations. We reexamine the significance of gravity anomaly and geodetic boundary-value problem from a standpoint of this new height system.

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This document is the quadrennial report of gravimetric works made in Japan during the period from April 1986 to March 1990. It has been prepared to submit to the International Gravity Commission of the International Association of Geodesy at its 13th meeting held in Toulouse, France, from September 11 to 14, 1990. A few of works and publications not included in the previous report presented to the 12th meeting are also supplemented. It summarizes gravimetric works such as international and domestic connections of gravity networks, absolute and relative gravity measurements, tidal and nontidal gravity changes, gravity surveys in Japan and foreign countries, data handling and mapping, geophysical interpretation of gravity data, theoretical researches of gravity field, etc. Complete references of the related articles are found in the bibliography towards the end of this report. The report was compiled by the editor from manuscripts submitted by various Research Institutes and University research groups. The editor is grateful to Drs. Y. GANEKO, Y. HAGIWARA, K. KAMINUMA, C. KITSUNEZAKI, M. KOMAZAWA, Y. KONG, M. KOSUGA, M. MISHINA, H. MURAKAMI, I. NAKAGAWA, S. NAKAI, S. NISHIMURA, I. OHNO, S. OKUBO, M. SATOMURA, J. SEGAWA, K. TSUKAHARA, A. YAMAMOTO and A. YOSHIDA for their assistance.

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