空域法恢复CHAMP重力场的误差分析

Error Analysis on Space -wise Approach for CHAMP Gravity Field Recovery

空域法是CHAMP重力场恢复的常用方法之一，本文针对空域法中的延拓误差和格网化误差展开讨论。结果表明：延拓误差中的截断误差部分影响量级约0．001m^2／s^2（均方误差意义下），最大误差仅为0．11m^2／s^2，可完全忽略；延拓误差中的参考重力场模型误差影响随参考场选取的不同而有所差异，整体而言小于0．1m^2／s^2，但最大误差可达1．3m^2／s^2，采用高精度的参考重力场模型能大大减小延拓误差影响。对于CHAMP卫星而言，延拓计算中，参考重力场模型的阶数取60阶便可满足精度要求。目前最常用的格网化方法包括加权平均方法和最小二乘配置方法，计算表明，利用30天的CHAMP数据进行2°×2°格网化处理，加权平均法的格网化误差在0．13m^2／s^2量级，最大误差可达1．58m^2／s^2，而最小二乘配置法的格网化误差在0．006m^2／s^2量级，最大误差仅为0．15m^2／s^2，明显优于加权平均法。

Space - wise approach is one of the most common methods used for CHAMP gravity field recovery. In this paper, the up/downwards continuation errors and gridding errors of space - wise approach are discussed. The computation implies that the influence of truncation error of up/downwards continuation is about 0. 001 m^2/s^2 （in the sense of RMS） , and the maximum error is only 0.11 m^2/s^2, which can be ignored in CHAMP gravity field recovery. The influence of the reference gravity field error of up/downwards continuation is less than 0. 1m^2/s^2 in general, but the maximum error can reach 1.3m^2/s^2. To reduce this error, a high - precision gravity field model should be used in the up/downwards continuation. The maximum degree of reference gravity field can be chosen 60 for the up/down- wards continuation, which is enough for CHAMP gravity field. The weighted means and least squares collocation （LSC） are two gridding methods which are commonly used. The computation shows that the gridding error of weighted method is about 0.13m^2/s^2 , and the maximum error is about 1.58 m^2/s^2 using 30 - day CHAMP data to form a grid with 2 - degree spacing in longitude and latitude. The gridding error of LSC method is about 0. 006 m^2/s^2, and the maximum error is about 0.15 m^2/s^2, which shows that it is obviously superior to the weighted method.