利用垂线偏差计算大地水准面中央区效应的改进方法

摘要

In order to improve the precision of the innermost area effects in geoid calculation using deflections of the vertical, components of deflections of the vertical were expressed as double quadratic polynomials regarding the innermost area as a rectangular one, and the formulae to calculate the innermost area effects were derived after the non-singular transformation was introduced. The analysis based on the theoretical model of deflections of the vertical shows that errors of traditional formulae depend on the latitude and the ratio of the change of the north- south deflection component along the meridian to that of the west-east deflection component along the parallel. A practical calculation was done based on deflections of the vertical data with a resolution of 2＇×2＇ in a middle latitude area. The results indicate that the maximal differences of the innermost area effects calculated by traditional and this formulae are several centimeters when the innermost area is only a grid including the calculation point. The formulae could provide theoretical basis for the calculation of the geoid innermost area effects with high precision.%为提高利用垂线偏差计算大地水准面中央区效应的精度，视中央区为矩形域，将垂线偏差分量表示成双二次多项式插值形式，引入非奇异变换，推导出中央区效应的计算公式。垂线偏差理论模型下的分析表明传统公式的误差与纬度以及垂线偏差子午分量沿经线方向的变化与卯酉分量沿纬线方向的变化之间的比值有关；以中纬度某区域分辨率为2’×2’的垂线偏差数据为背景场进行实际计算，结果表明当中央区为计算点所在的1个网格时，传统公式与该公式计算得到的中央区效应差值的最大值达数厘米。该公式可为大地水准面中央区效应的高精度计算提供理论依据。