地球重力场模型计算点向径取值对模型重力场元影响

Influence of calculation point’s geocentric distance on gravity field elements for Earth’s gravity field model

利用地球重力场模型计算重力场元时,为提高计算速度,有时将计算点的高程近似为0,为提高精度,在球面对计算点高程进行泰勒级数展开。但是,考虑到地球表面真实情况,这种近似将会引入巨大的距离误差,同时也会影响计算点的地心纬度值。针对此,分析了计算点向径不同取值之间的差异及对计算点地心纬度、模型垂线偏差计算结果的影响,引入等效高程讨论了按照泰勒级数展开快速计算模型垂线偏差方法的适用性,采用实测数据比较了计算点向径不同取值计算模型垂线偏差的精度。实验结果表明:将计算点向径近似为地球长半轴与计算点高程之和,造成的距离误差可达20km,而近似为参考椭球面向径与地面点高程之和造成的距离误差最大不超过6cm,对模型垂线偏差的影响则不足0.05″,这为精确快速计算模型重力场元提供了参考。

When using the Earth’s gravity field model to calculate the gravity field elements,the elevations of calculation points are sometimes approximated as zero for increasing the computational speed,and Taylor formula expansion for calculation points’ elevations would be performed on the spherical surface for improving the accuracy.However,taking into account the real surface of the Earth,this approximation will introduce a huge distance error and also affect the geocentric latitude value of calculation points.Aiming at this problem,the differences among different calculation points’ geocentric distances as well as the influences on the calculation points’ geocentric latitudes and model vertical deflections are analyzed.Equivalent elevation has been introduced to study the applicability of the method for calculating the vertical deviation of the model based on Taylor series expansion.The measured data is used to compare the accuracies in calculating the model vertical deflections by using different geocentric distances of calculation points.Experiment results show that, approximating the calculation points’ geocentric distance to be the summation of the Earth’s semi-major axis length and calculation points’ elevation can cause an error of 20 km,while if approximating the geocentric distance to be the summation of reference ellipsoid’s geocentric distance and elevation of calculation point,the distance error will be less than 6 cm,and the influence on model vertical deflection will be no more than 0.05″. The proposed method provides a reference for accurate and fast calculating the model gravity field elements.