推证顾及地形与完全球面布格异常梯度改正的完全到一阶项的物理大地测量边值问题的严密解式，并在某试验区综合利用地形、重力、GPS／水准等数据进行区域似大地水准面的计算与检验。通过对高程异常计算绝对与相对精度的比较分析，结果表明，完全球面布格异常梯度改正项对高程异常的影响能够达到厘米的量级。因此，提高区域似大地水准面的建模精度，尤其是在地形起伏较大的区域，除需顾及地形改正项影响外，还应考虑完全球面布格异常梯度改正项对高程异常的影响。%The rigorous formulae of the boundary value problem （BVP） of physical geodesy complete to the first- order solution were derived considering corrections of terrain and complete spherical Bouguer anomaly＇s gradient term, The formulae were tested through computation of a regional quasi-geoid based on terrain, gravity and GPS/ leveling observations within a selected experiment area, Comparison and analysis of the calculated height anomalies in term of absolute and relative accuracy show that the effect of complete spherical Bouguer anomaly＊s gradient term on height anomaly could reach centimeter level, Therefore, besides the effect of terrain corrections, the effect of complete spherical Bouguer anomaly＇s gradient term on height anomaly should also be taken into account in order to improve the accuracy of regional quasi-geoid modeling especially in areas with rolling terrain.
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