航空重力测量数据向下延拓的改进Poisson积分迭代法

doi:10.11947/j.AGCS.2018.20170569

测绘学报 ›› 2018, Vol. 47 ›› Issue (9): 1188-1195.doi: 10.11947/j.AGCS.2018.20170569

航空重力测量数据向下延拓的改进Poisson积分迭代法

刘晓刚^1,2,3, 孙中苗^1,2, 管斌^1,2, 范昊鹏^1,2,4

1. 地理信息工程国家重点实验室, 陕西西安 710054;
2. 西安测绘研究所, 陕西西安 710054;
3. 大地测量与地球动力学国家重点实验室, 湖北武汉 430077;
4. 信息工程大学地理空间信息学院, 河南郑州 450052

收稿日期:2017-10-09 修回日期:2018-05-09 出版日期:2018-09-20 发布日期:2018-09-26
通讯作者: 孙中苗 E-mail:sun_szm@163.com
作者简介:刘晓刚(1983-),男,博士,助理研究员,主要从事重力、磁力测量及其数据处理技术研究。E-mail:liuxiaogang_1949@163.com
基金资助:
国家自然科学基金（41774018；41304022；41504018）；大地测量与地球动力学国家重点实验室开放基金（SKLGED2017-1-1-E）

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

LIU Xiaogang^1,2,3, SUN Zhongmiao^1,2, GUAN Bin^1,2, FAN Haopeng^1,2,4

1. State Key Laboratory of Geo-Information Engineering, Xi'an 710054, China;
2. Xi'an Research Institute of Surveying and Mapping, Xi'an 710054, China;
3. State Key Laboratory of Geodesy and Earth's Dynamics, Wuhan 430077, China;
4. Institute of Geospatial Information, Information Engineering University, Zhengzhou 450052, China

Received:2017-10-09 Revised:2018-05-09 Online:2018-09-20 Published:2018-09-26
Supported by:
The National Natural Science Foundation of China (Nos. 41774018;41304022;41504018);The Open Foundation of State Key Laboratory of Geodesy and Earth's Dynamics (No. SKLGED2017-1-1-E)

摘要/Abstract

摘要： 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。

关键词: 航空重力测量, 向下延拓, Poisson积分迭代法, 最小二乘法, Tikhonov正则化法

Abstract: 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.

Key words: airborne gravimetry, downward continuation, poisson integral iteration method, least squares method, tikhonov regularization method

中图分类号:

P228

刘晓刚, 孙中苗, 管斌, 范昊鹏. 航空重力测量数据向下延拓的改进Poisson积分迭代法[J]. 测绘学报, 2018, 47(9): 1188-1195.

LIU Xiaogang, SUN Zhongmiao, GUAN Bin, FAN Haopeng. Downward Continuation of Airborne Gravimetry Data Based on Improved Poisson Integral Iteration Method[J]. Acta Geodaetica et Cartographica Sinica, 2018, 47(9): 1188-1195.

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航空重力测量数据向下延拓的改进Poisson积分迭代法

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

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