多源重力数据球冠谐模型抗差融合法

doi:10.11947/j.AGCS.2015.20140345

测绘学报 ›› 2015, Vol. 44 ›› Issue (9): 952-957.doi: 10.11947/j.AGCS.2015.20140345

多源重力数据球冠谐模型抗差融合法

王燚, 姜效典, 李德勇

中国海洋大学海洋地球科学学院, 山东青岛 266100

收稿日期:2014-06-25 修回日期:2014-12-09 出版日期:2015-09-24 发布日期:2015-09-24
作者简介:王燚(1974—),男,博士,讲师,研究方向为地球物理勘探方法与信息技术。E-mail:wyfox009@163.com
基金资助:
海洋公益性行业科研专项经费(201305029-02)

The Robust Fusion of Multi-source Gravity Data Based on the Spherical Cap Harmonic Model

WANG Yi, JIANG Xiaodian, LI Deyong

College of Marine Geo-science, Ocean University of China, Qingdao 266100, China

Received:2014-06-25 Revised:2014-12-09 Online:2015-09-24 Published:2015-09-24
Supported by:
The Oceanic Publical Nonprofit Research Project(No.201305029-02)

摘要/Abstract

摘要： 提出了一种基于球冠谐模型的抗差岭估计数据融合算法,并通过数值计算对算法的有效性进行验证。结果表明融合后的球冠谐模型不仅能够抵抗系数阵的病态性,而且能够有效地消除观测粗差的影响。最后就观测噪声大小对融合结果的影响进行了探讨。

关键词: 球冠谐分析, 最小二乘法, 抗差岭估计, 球谐模型, 边界效应

Abstract: A robust ridge estimation multi-source data fusion algorithm is proposed based on spherical cap harmonic analysis.The effectiveness is verified through numerical calculations. It is shown that this fused model can not only resist the ill-conditioning of coefficients array but also eliminate the observation errors. Finally, it is analyzed the influence of the observation noise size on the fusion results.

Key words: pherical cap harmonic analysis, least squares, robust ridge estimation, spherical harmonic model, boundary effect

中图分类号:

P223

王燚, 姜效典, 李德勇. 多源重力数据球冠谐模型抗差融合法[J]. 测绘学报, 2015, 44(9): 952-957.

WANG Yi, JIANG Xiaodian, LI Deyong. The Robust Fusion of Multi-source Gravity Data Based on the Spherical Cap Harmonic Model[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(9): 952-957.

参考文献

[1] ZHAI Zhenhe, SUN Zhongmiao. The Adaptive Fusion of Multi-source Gravity Data in Bohai Gulf[J]. Acta Geodaetica et Cartographica Sinica, 2010, 39(5): 444-449. (翟振和, 孙中苗. 渤海湾多源重力数据的自适应融合处理[J]. 测绘学报, 2010, 39(5): 444-449.)
[2] ZHAI Zhenhe, SUN Zhongmiao. Combining Airborne Gravity Data and Terrestrial Gravity Data Based on Least Squares Collocation[J]. Geomatic Science and Engineering,2008, 28(1): 10-14. (翟振和, 孙中苗. 基于最小二乘配置的航空和地面重力数据融合处理[J]. 测绘科学与工程, 2008, 28(1): 10-14.)
[3] HAO Yanling, CHENG Yi, LIU Fanming, et al. Simulation of Combination Algorithm for Heterogeneous Marine Gravity Data[J]. Journal of System Simulation, 2007, 19(21): 4897-4900. (郝燕玲, 成怡, 刘繁明, 等. 融合多类型海洋重力数据算法仿真研究[J]. 系统仿真学报, 2007, 19(21): 4897-4900.)
[4] WANG Xichen, WANG Guangjie, LI Tonglin, et al. Extracting Different Wavelength Gravity Anomaly by the Spherical Cap Harmonic Analysis Method[J]. Global Geology, 1996, 15(3): 80-83. (王喜臣, 王光杰, 李桐林, 等. 利用球冠谐分析方法提取不同波长重力场异常[J]. 世界地质, 1996, 15(3): 80-83.)
[5] HAINES G V. Spherical Cap Harmonic Analysis[J]. Journal of Geophysical Research, 1985, 90(B3): 2583-2591.
[6] HWANG C, CHEN S K. Fully Normalized Spherical Cap Harmonics: Application to the Analysis of Sea-level Data from TOPEX/POSEIDON and ERS-1[J]. Geophysical Journal International, 1997, 129(2): 450-460.
[7] ZHANG Qin, ZHAO Chaoying. The Spherical Cap Harmonic Analysis Method for Crust Vertical Deformation Field Fitting[J], Acta Geodaetica et Cartographica Sinica, 2004, 33(1): 39-42. (张勤, 赵超英. 地壳垂直形变场逼近的球冠谐分析法[J]. 测绘学报, 2004, 33(1): 39-42.)
[8] CHEN Bin, GU Zuowen, GAO Jintian, et al. Analyses of Geomagnetic Field and Its Secular Variation over China for 2005. 0 Epoch Using Spherical Cap Harmonic Method[J]. Chinese Journal of Geophysics, 2011, 54(3): 771-779. (陈斌, 顾左文, 高金田, 等. 2005. 0年代中国地区地磁场及其长期变化球冠谐和分析[J]. 地球物理学报, 2011, 54(3): 771-779.)
[9] LI Jiancheng. Spherical Cap Harmonic Expansion for Local Gravity Field Representation[J]. Manuscripta Geodaetica, 1995(20): 265-277.
[10] YOUNIS G K A, JGER R, BECKER M. Transformation of Global Spherical Harmonic Models of the Gravity Field to a Local Adjusted Spherical Cap Harmonic Model[J]. Arabian Journal of Geosciences, 2013, 6(2): 375-381.
[11] WU Zhaocai, LIU Tianyou, GAO Jinyao. Derivative Calculation and Applicationin Spherical Cap Harmonic Analysis of Local Gravity Field[J]. Oceanologia et Limnologia Sinica, 2006, 37(6): 488-492. (吴招才, 刘天佑, 高金耀. 局部重力场球冠谐分析中的导数计算及应用[J]. 海洋与湖沼, 2006, 37(6): 488-492.)
[12] ZHAO Jianhu, WANG Shengping, LIU Hui, et al. Study on Establishing Local Geomagnetic Model Using Spherical Cap Harmonic Analysis[J]. Science of Surveying and Mapping, 2010, 35(1): 51-53. (赵建虎, 王胜平, 刘辉, 等. 海洋局域地磁场球冠谐分析建模方法研究[J]. 测绘科学, 2010, 35(1): 51-53.)
[13] WANG Sanjun. The Spherical Cap Harmonic Analysis of GPS Leveling Height[J]. Science of Surveying and Mapping, 2008, 33(2): 13-14. (王三军. 利用球冠谐模型研究GPS水准问题[J]. 测绘科学, 2008, 33(2): 13-14.)
[14] CAO Yueling, WANG Jiexian. Application of Spherical Cap Harmonic Analysis to Fit GPS Level Height[J]. Geomatics and Information Science of Wuhan University, 2008, 33(7): 740-743. (曹月玲, 王解先. 利用球冠谐分析拟合GPS水准高程[J]. 武汉大学学报: 信息科学版, 2008, 33(7): 740-743.)
[15] DESANTIS A. Translated Origin Spherical Cap Harmonic Analysis[J]. Geophysical Journal International, 1991, 123(6): 253-263.
[16] PENG Fuqing, YU Jinhai.The Characters and Computation of Legendre Function with Non-integral Degree in SCHA[J]. Acta Geodaetica et Cartographica Sinica, 2000, 29(3): 204-208. (彭富清, 于锦海. 球冠谐分析中非整阶Legendre函数的性质及其计算[J]. 测绘学报, 2000, 29(3): 204-208.)
[17] WEI Bocheng, LU Guobin, SHI Jianging. Introduction to Statistical Diagnostics[M]. Nanjing: Publishing House of Dongnan University, 1991. (韦博成, 鲁国斌, 史建清. 统计诊断引论[M]. 南京: 东南大学出版社, 1991.)
[18] KORTE M, HOLME R. Regularization of Spherical Cap Harmonics[J]. Geophysical Journal International, 2003, 153(1): 253-262.
[19] YANG Yuanxi, SONG Lijie, XU Tianhe. Robust Parameter Estimation for Geodetic Correlated Observations[J]. Acta Geodaetica et Cartographica Sinica, 2002, 31(2): 95-99. (杨元喜, 宋力杰, 徐天河. 大地测量相关观测抗差估计理论[J]. 测绘学报, 2002, 31(2): 95-99.)
[20] YANG Yuanxi. Robust Estimation and Its Applications[M]. Beijing: Bayi Publishing House, 1993. (杨元喜. 抗差估计理论及其应用[M]. 北京: 八一出版社,1993.)
[21] WANG Guisong. Theory and Application of Liner Model[M]. Hefei: Press of Anhui Education, 1987. (王松桂. 线性模型理论及其应用[M]. 合肥: 安徽教育出版社, 1987.)
[22] GAO Rui, XIONG Xiaosong, LI Qiusheng, et al. The Moho Depth of Qinghai-Tibet Plateau Revealed by Seismic Detection[J]. Acta Geoscientica Sinica, 2009, 30(6): 761-773. (高锐, 熊小松, 李秋生, 等. 由地震探测揭示的青藏高原莫霍面深度[J]. 地球学报, 2009, 30(6): 761-773.)
[23] TIAN Qianning, GENG Tao, YANG Huiqun, et al. Gravity Anomalies Forward Fitting and Geological Explanation in the Western Qinghai-Tibet Plateau[J]. Geological Bulletin of China, 2008, 27(12): 2108-2116. (田黔宁, 耿涛, 杨汇群, 等. 青藏高原西部重力异常剖面拟合及其地质解释[J]. 地质通报, 2008, 27(12): 2108-2116.)

多源重力数据球冠谐模型抗差融合法

The Robust Fusion of Multi-source Gravity Data Based on the Spherical Cap Harmonic Model

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