航空重力测量数据向下延拓的改进Poisson积分迭代法

目前，航空重力测量是快速获取陆地和近海区域高精度、高分辨率重力场信息的非常有效的技术手段，向下延拓则是其数据处理中的关键环节，直接影响到测量结果的进一步应用。本文在对传统最小二乘法、改进最小二乘法、Tikhonov正则化法等延拓模型进行数值分析的基础上，根据调和函数的基本特性，提出并建立了Poisson积分迭代法和改进Poisson积分迭代法延拓模型。实测航空和地面重力测量数据的试验结果表明，本文新建的Poisson积分迭代法和改进Poisson积分迭代法延拓模型精度相当，比传统最小二乘法延拓模型精度提高了15.26 mGal，比改进最小二乘法延拓模型精度提高了0.21 mGal，比Tikhonov正则化法延拓模型精度略低0.13 mGal，从而证明了本文所建模型的正确性和有效性。

Downward Continuation of Airborne Gravimetry Data Based on Improved Poisson Integral Iteration Method

Airborne gravimetry is an effective technology to obtain the Earth's gravity field information of land and offing area in high precision and resolution quickly.Downward continuation is one of the key steps in airborne gravimetry data processing,and the quality of continuation results directly influence the further application of surveying data.Based on numerical analysis of the continuation models of traditional least squares method,improved least squares method and Tikhonov regularization method,and according to the basic characteristics of spherical harmonic function,the continuation models of Poisson integral iteration method and improved Poisson integral iteration method were proposed and deduced.For the testing area in this paper,the surveyed airborne and terrestrial gravimetry data prove that the precision of the new continuation models of Poisson integral iteration method and improved Poisson integral iteration method are equal.Compared with the continuation models of traditional least squares method and improved least squares method,of which the precision are improved about 15.26 mGal and 0.21 mGal,respectively.The precision of new continuation models are inferior to Tikhonov regularization method about 0.13 mGal.Therefore,the new continuation models proposed in this paper can not only be used to amend the ill-posed problem of the continuation model introduced by traditional Poisson integral discretization formula,but also be used to suppress the ill-posed problem of the continuation model itself.Therefore,the research achievements can be applied directly in the data processing of our country's airborne scalar and vector gravimetry.