基于逆Vening-Meinesz公式的测高重力中央区效应精密计算

Precise Calculation of Innermost Area Effects in Altimetry Gravity Based on the Inverse Vening-Meinesz Formula

为提高利用逆Vening-Meinesz公式反演测高重力中央区效应的精度,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,推导出了重力异常的计算公式。以低纬度区域2′×2′的垂线偏差实际数据为背景场进行了计算,结果表明,当中央区包含4个网格时,传统公式与推导出的重力异常计算公式误差的最大值大于1 mGal。推导出的公式可为高精度测高重力中央区效应的计算提供理论依据。

In order to improve the precision of the innermost area effects in altimetry gravity computed by the inverse Vening-Meinesz formula, deflections of the vertical are expressed as bi-quadratic polynomials regarding the innermost area as a rectangular one, and the formulas to calculate gravity anomaly of this area are derived after the non-singular transformation is introduced. A practical calculation is done based on deflections of the vertical data with a resolution of in the low latitude area. The results indicate that the maximal difference between the contributions of the innermost area including four grids calculated by traditional formulas and this paper’s formulas is greater than 1 mGal. The formulas derived in this paper can provide theoretical basis for the innermost area effects in altimetry gravity with high precision.