Precise Interpolation of Deflections of the Vertical.

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  • 鉛直線偏差の精密な内挿
  • エンチョクセン ヘンサ ノ セイミツ ナ ナイ ソウ

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The Geographical Survey Institute has carried out astronomical observations at 454 stations between 1947 and 1992. The density of the stations is one station per approximately 30 km×30 km. Interpolation is one of the best ways to obtain a dense estimation. The observed deflections of the vertical are affected very strongly by topography, so that the interpolation accuracy depends on the topographic irregularity. To eliminate the interpolation error due to the topographic effects, the following steps have been performed: (1) The topographic effects are removed computationally by subtracting them from the observed deflections of the vertical. (2) After removing the topographic effects, interpolation is made at an unknown station by the method of least squares interpolation. (3) As the final step of this method, the topographic effects are restored by adding them to the interpolated values at unknown stations. Residual, the difference between the interpolated and observed values, is computed at each astronomical observation station to estimate the interpolation error. The rms value of residuals is 2.6 seconds in this precise method, and is 4.4 seconds in the direct interpolation. These results show that the direct interpolation leads to poor results because of topographic irregularity, and that it is extremely advisable to factor the topographic effects into the interpolation. Mean interpolation error is estimated to be around 2.0 seconds at unknown stations among the observation stations.

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