广义带限航空矢量重力确定大地水准面的两步积分法

A two-step integral method for geoid determination using generalized band-limited airborne vector gravity data

依据物理大地测量学的广义带限水平边值问题理论,本文提出了基于带限航空矢量重力水平分量确定大地水准面的两步积分法。首先,依据广义带限水平边值问题解将带限航空矢量重力水平分量转化为飞行高度面上的带限扰动位;然后,利用带限Dirichlet边值问题解将飞行高度面上的带限扰动位向下延拓到海平面(海拔高程起算面,也称平均海面)上的带限扰动位;最后,依据Bruns公式将海平面上的扰动位转化为大地水准面高度。利用EGM2008重力位模型开展数值仿真计算试验,结果表明,广义带限水平边值问题解具有较好的低通滤波特性,能有效抑制观测高频噪声的影响;当带限航空矢量重力水平分量观测误差取3×10^(-5)m/s 2、测量飞行高度取6 km时,基于带限Dirichlet边值问题解的带限大地水准面计算精度优于3 cm,初步验证了两步积分法的计算稳定性和有效性。

According to the generalized band-limited horizon boundary value theory of physical geodesy survey,a two-step integral method is proposed to determine the geoid based on the horizontal component of band-limited airborne vector gravity data.Firstly,based on the solution of generalized band-limited horizon boundary value problem,we transform the horizontal component of band-limited airborne vector gravity data into a band-limited disturbing gravity potential at flight level.Secondly,the band-limited disturbing gravity potential is continued downward to the sea level by using the solution of the band-limited Dirichlet boundary value problem.Finally,according to the Bruns formula,the band-limited disturbing gravity potential at sea level is converted to the geoid.Simulation experiments using EGM2008 gravity field model show that the solution of generalized band-limited horizontal boundary value problem has a good low-pass filtering characteristic,which can weaken the effect of high-frequency noises in the observed value.The accuracy of the band-limited geoid obtained by the solution to the band-limited Dirichlet boundary problem is better than 3 cm when the error of the horizontal component of band-limited airborne vector gravity data is taken as 3 mGal and the flying height as 6 km.It indicates that the two-step integral method has good stability and effectiveness.