航空重力梯度数据的模拟研究

Simulation of airborne gravity gradient tensor observations

针对提高模拟航空重力梯度的精度研究不足的现状,文章运用地球重力场模型构建了计算单点的扰动重力梯度分量的数学模型,推导了Legendre函数及其导数的无奇异性递推计算公式,克服了计算高阶次Legendre函数Pnm(cosθ)的下溢问题,随之对数学模型进行优化;最后利用EGM2008地球位模型模拟生成4km飞行高度处的扰动重力梯度张量作为航空重力梯度观测值。模拟试算表明,该模型能够满足当前航空重力梯度测量的精度要求。

Aiming at the insufficiency of studying the precision of simulated airborne gravity gradient, the paper utilized Earth＇s Gravity Field model to construct the mathematical model of calculating the gravi- ty disturbances gradient components of the single point, deduced the non-singular computational calcula- tion formulas of the Legendre functions and the derivation which overcome the underflow of Legendre function when computing ultra-high degree and order, subsequently optimized the mathematical model. Finally, simulated gravity disturbance gradient tensors at 4kin flight altitude generated by EGM2008 were seen as the airborne gravity gradient observations. Numerical tests showed that the model could fulfill the precision demand of the current airborne gravity gradient survey.