区域重力大地水准面确定的相对精度估计

Relative Accuracy Estimation for Determining Regional Gravimetric Geoid

以频域解析方法,研究由地面重力数据、全球位模型确定区域重力大地水准面的相对精度估计。首先由Stokes公式的数值积分推导地面重力数据与球谐系数的精度关系;再由"移去-恢复"方法的空域截断逼近模式和协方差函数的球谐表达,分别推导内区地面重力数据之误差、外区全球位模型之误差与区域重力大地水准面之相对精度的解析关系;为便于计算,提出将内区地面重力数据和外区全球位模型的频域截断误差合并,再按频段重新划分为两部分:①全球范围——地面重力数据对应频率以上的截断;②外区范围——介于全球位模型最高频率与地面重力数据对应频率之间的截断,以经验阶方差模型分别估计之。模拟计算显示了地面重力数据之精度、分辨率、积分半径和全球位模型之精度、分辨率与区域重力大地水准面之相对精度的具体对应关系。本文研究同样适用于区域重力似大地水准面的确定。

Relative accuracy of regional gravimetric geoid determination is estimated by an frequency domain analysis,which is determined by regional terrestrial gravity measurements and geopotential model.First,the accuracy relationship between terrestrial gravity measurements and spherical harmonic coefficients is deduced based on the Stokes formula.Second,based on the truncated approach of ＂remove-restore＂ and spherical harmonic expansion of the covariance function,the analytical relationships among errors of inner terrestrial gravity measurements, errors of outer geopotentialmodeland relative accuracy of regionalgravimetricgeoid are deduced respectively. Thirdly, for convenience of calculation, it is proposed that frequency truncation errors of inner terrestrial gravity measurements and outer geopotential model be merged and then reclassified in two parts; （1）at frequencies higher than inner gravity data in global area; （2） at frequencies between inner gravity data and geopotential model in outer area. They are estimated respectively by using empirical degree-variance model. Simulation indicates the corresponding relationships among terrestrial gravity measurements accuracy, resolution and integral radius, geopotential model accuracy and resolution and the relative accuracy of regional gravimetric geoid determination. The study can be used to regional gravimetric quasi-geoid determination.