Estimation of surface gravity at benchmarks is discussed for computing Helmert heights in Japan. A 3' x 3' grid of real Bouguer anomalies (Kuroishi, 1995) is used to restore surface gravity values. In comparison with the bilinear interpolation, we employ the biquadratic interpolation method to estimate real Bouguer anomalies at benchmarks. RMS discrepancies between the estimated and the observed gravity at 9, 329 benchmarks are found to be 2.5 mgal, which is comparable to RMS variations of 2.9 mgal in gravity within 3' x 3' cells and to RMS errors of 2.2 mgal of 3' x 3' grid anomalies. The heights of all national benchmarks distribute with a RMS value of 179.40 m and 95 percent of them are below 500 m. Under the assumption of no correlation among estimated gravity values, the RMS error induced from gravity estimation errors is expected to be 0.6 mm. Sample computations of differences of Helmet heights between with the observed and with the estimated gravity are carried out for leveling routes 187 and 204, which are considered to be of the biggest Helmert correction lines: the former includes the highest benchmark at Nomugi Pass and the latter runs from Matsumoto, Nagano to Itoigawa, Niigata. The results show 6 mm at the maximum difference and the errors in Helmert heights are expected to be less than 10 mm. That is comparable to the error of the Helmert height system and the estimated gravity, therefore, is precise enough to compute Helmert heights in Japan.
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