顾及地形效应的重力向下延拓模型分析与检验

doi:10.11947/j.AGCS.2016.20150453

测绘学报 ›› 2016, Vol. 45 ›› Issue (5): 521-530.doi: 10.11947/j.AGCS.2016.20150453

顾及地形效应的重力向下延拓模型分析与检验

刘敏¹, 黄谟涛^2,3, 欧阳永忠², 邓凯亮², 翟国君^2,3, 吴太旗²

1. 信息工程大学地理空间信息学院, 河南郑州 450001;
2. 海军海洋测绘研究所, 天津 300061;
3. 海军工程大学导航工程系, 湖北武汉 430033

收稿日期:2015-09-28 修回日期:2016-03-01 出版日期:2016-05-20 发布日期:2016-05-30
作者简介:刘敏(1980-),男,博士生,研究方向为海洋重力场测定理论方法及应用。E-mail: Ouyangyz@sohu.com
基金资助:
国家973计划(613219);国家自然科学基金(41474012;41174062;41374018);国家重大科学仪器设备开发专项(2011YQ12004503)

Test and Analysis of Downward Continuation Models for Airborne Gravity Data with Regard to the Effect of Topographic Height

LIU Min¹, HUANG Motao^2,3, OUYANG Yongzhong², DENG Kailiang², ZHAI Guojun^2,3, WU Taiqi²

1. Institute of Geospacial Information, Information Engineering University, Zhengzhou 450001, China;
2. Naval Institute of Hydrographic Surveying and Charting, Tianjin 300061, China;
3. Department of Navigation, Naval University of Engineering, Wuhan 430033, China Abstract

Received:2015-09-28 Revised:2016-03-01 Online:2016-05-20 Published:2016-05-30
Supported by:
The National Basic Research Program of China (973 Program) (No. 613219);The National Natural Science Foundation of China (Nos. 41474012;41174062;41374018);The Great Scientific Instrument Development Project of China (No.2011YQ12004503)

摘要/Abstract

摘要： 向下延拓是航空重力测量数据实际应用中必不可少的技术环节。向下延拓属于不适定反问题,其解算过程具有较大的不确定性,故该问题一直是大地测量领域国内外学者的研究热点。本文深入分析研究了当前国内外最具代表性的3种向下延拓计算模型的技术特点和适用条件,提出了应用超高阶位模型、局部地形改正和移去-恢复技术顾及地形效应,以及位场延拓结果球面化曲面的工程化方法,重点探讨了计算模型的稳定性及数据观测误差对延拓计算结果的影响。通过理论分析、数值仿真和实测数据计算等手段,定量评估了不同向下延拓模型的解算精度及其可靠性。其主要结论是:传统逆Poisson积分模型解严重受制于输入数据观测噪声的干扰,在现有作业条件下,该模型至多只能用于1 km以下高度的延拓解算;频谱截断积分和位模型加地改两种延拓新模型具有良好的计算稳定性,完全适用于2'分辨率和5 km飞行高度条件下的航空重力测量数据向下延拓解算,其延拓计算精度可达2×10^-5 m/s²,可满足各方面实际应用需求。

关键词: 航空重力测量, 向下延拓, 地形效应, Poisson积分, 有限带宽频谱, 超高阶位模型

Abstract: Downward continuation is an essential technical step of data processing in airborne gravimetry for further applications. It is known that the solution of downward continuation is uncertain due to its ill-posedness. So it has been a topic of general interest for many scholars at home and abroad in geodesy. The main purpose of this paper is to give 3 representative models for downward continuation including traditional inverse Poisson integration and two modern methods, and make a comprehensive comparison and analysis on their property and applicability among the different models. Ultra-high-degree geopotential model, local topographic correction and remove-restore technique are suggested to be used for regard to the effect of topographic height, and for the realization of downward continuation combining with a transformation from spherical to undulating surface. We pay our attention to the influence of surveyed data errors on the stability of downward continuation solutions. Theoretical analysis, simulated data and real numerical computations are carried out to evaluate the stability and accuracy of downward continuation models. And some useful conclusions are obtained. Under existing working conditions, the traditional inverse Poisson integration method can only be used to the continuation computation under 1 km due to the serious disturbing of surveying noise. Excellent computation stability can be achieved by using the band-limited spectrum and the geopotential model plus topographic correction methods. The two new models can be used to the downward continuation of airborne gravity data on 5 km height and 2' data resolution. And the accuracy of corresponding continuation solutions can be reach 2×10^-5 m/s². It can meet the requirements from different applications.

Key words: airborne gravimetry, downward continuation, terrain effect, Poisson integration, band-limited spectrum, ultra-high-degree geopotential model

中图分类号:

P223

刘敏, 黄谟涛, 欧阳永忠, 邓凯亮, 翟国君, 吴太旗. 顾及地形效应的重力向下延拓模型分析与检验[J]. 测绘学报, 2016, 45(5): 521-530.

LIU Min, HUANG Motao, OUYANG Yongzhong, DENG Kailiang, ZHAI Guojun, WU Taiqi. Test and Analysis of Downward Continuation Models for Airborne Gravity Data with Regard to the Effect of Topographic Height[J]. Acta Geodaetica et Cartographica Sinica, 2016, 45(5): 521-530.

参考文献

[1] 李建成, 陈俊勇, 宁津生, 等. 地球重力场逼近理论与中国2000似大地水准面的确定[M]. 武汉: 武汉大学出版社, 2003. LI Jiancheng, CHEN Junyong, NING Jinsheng, et al. Theory of the Earth's Gravity Field Approximation and Determination of China Quasi-geoid 2000[M]. Wuhan: Wuhan University Press, 2003.
[2] 黄谟涛, 翟国君, 管铮, 等. 海洋重力场测定及其应用[M]. 北京: 测绘出版社, 2005. HUANG Motao, ZHAI Guojun, GUAN Zheng, et al. The Determination and Application of Marine Gravity Field[M]. Beijing: Surveying and Mapping Press, 2005.
[3] 王彦飞. 反演问题的计算方法及其应用[M]. 北京: 高等教育出版社, 2007. WANG Yanfei. Computational Methods for Inverse Problems and Their Applications[M]. Beijing: Higher Education Press, 2007.
[4] PELLINEN L P. Accounting for Topography in the Calculation of Quasigeoidal Heights and Plumb-line Deflections from Gravity Anomalies[J]. Bulletin Géodésique, 1962, 63(1): 57-65.
[5] BJERHAMMAR A. Gravity Reduction to a Spherical Surface[R]. Stockholm: Royal Institute of Technology, 1962.
[6] HEISKANEN W A, MORITZ H. Physical Geodesy[M]. San Francisco: Freeman W H and Company, 1967.
[7] JEKELI C. The Downward Continuation of Aerial Gravimetric Data without Density Hypothesis[J]. Bulletin Géodésique, 1987, 61(4): 319-329.
[8] WANG Y M. The Effect of Topography on the Determination of the Geoid Using Analytical Downward Continuation[J]. Bulletin Géodésique, 1990, 64(3): 231-246.
[9] MARTINEC Z. Stability Investigations of a Discrete Downward Continuation Problem for Geoid Determination in the Canadian Rocky Mountains[J]. Journal of Geodesy, 1996, 70(11): 805-828.
[10] XU Peiliang. Truncated SVD Methods for Discrete Linear Ill-posed Problems[J]. Geophysical Journal International, 1998, 135(2): 505-514.
[11] NOVÁK P, KERN M, SCHWARZ K P. Numerical Studies on the Harmonic Downward Continuation of Band-limited Airborne Gravity[J]. Studia Geophysica et Geodaetica, 2001, 45(4): 327-345.
[12] MUELLER F,MAYER-GUERR T.Comparison of Downward Continuation Methods of Airborne Gravimetry Data[C]//Proceedings of the International Association of Geodesy IAG General Assembly Sapporo. Berlin: Springer, 2005, 128: 254-258.
[13] KERN M. An Analysis of the Combination and Downward Continuation of Satellite, Airborne and Terrestrial Gravity Data[D]. Calgary: University of Calgary, 2003.
[14] ALBERTS B, KLEES R. A Comparison of Methods for the Inversion of Airborne Gravity Data[J]. Journal of Geodesy, 2004, 78(1-2): 55-65.
[15] TZIAVOS I N, ANDRITSANOS V D, FORSBERG R, et al. Numerical Investigation of Downward Continuation Methods for Airborne Gravity Data[C]//GGSM 2004 IAG International Symposium Porto. Berlin Heidelberg: Springer, 2005, 129: 119-124.
[16] ALBERTS B. Regional Gravity Field Modeling Using Airborne Gravimetry Data[C]//Publications on Geodesy 70. Delft: Netherlands Geodetic Commission, 2009.
[17] 石磐, 王兴涛. 利用航空重力测量和DEM确定地面重力场[J]. 测绘学报, 1997, 26(2): 117-121. SHI Pan, WANG Xingtao. Determination of the Terrain Surface Gravity Field Using Airborne Gravimetry and DEM[J]. Acta Geodaetica et Cartographica Sinica, 1997, 26(2): 117-121.
[18] 沈云中, 许厚泽. 不适定方程正则化算法的谱分解式[J]. 大地测量与地球动力学, 2002, 22(3): 10-14. SHEN Yunzhong, XU Houze. Spectral Decomposition Formula of Regularization Solution for Ill-posed Equation[J]. Journal of Geodesy and Geodynamics, 2002, 22(3): 10-14.
[19] 王兴涛, 石磐, 朱非洲. 航空重力测量数据向下延拓的正则化算法及其谱分解[J]. 测绘学报, 2004, 33(1): 33-38. WANG Xingtao, SHI Pan, ZHU Feizhou. Regularization Methods and Spectral Decomposition for the Downward Continuation of Airborne Gravity Data[J]. Acta Geodaetica et Cartographica Sinica, 2004, 33(1): 33-38.
[20] 王振杰. 测量中不适定问题的正则化解法[M]. 北京: 科学出版社, 2006. WANG Zhenjie. Regularization Methods for Ill-posed Problem in Survey[M]. Beijing: Science Press, 2006.
[21] 顾勇为, 归庆明. 航空重力测量数据向下延拓基于信噪比的正则化方法的研究[J]. 测绘学报, 2010, 39(5): 458-464. GU Yongwei, Gui Qingming. Study of Regularization Based on Signal-to-noise Index in Airborne Gravity Downward to the Earth Surface[J]. Acta Geodaetica et Cartographica Sinica, 2010, 39(5): 458-464.
[22] 蒋涛, 李建成, 王正涛, 等. 航空重力向下延拓病态问题的求解[J]. 测绘学报, 2011, 40(6): 684-689. JIANG Tao, LI Jiancheng, WANG Zhengtao, et al. Solution of Ill-posed Problem in Downward Continuation of Airborne Gravity[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(6): 684-689.
[23] 邓凯亮, 黄谟涛, 暴景阳, 等. 向下延拓航空重力数据的Tikhonov双参数正则化法[J]. 测绘学报, 2011, 40(6): 690-696. DENG Kailiang, HUANG Motao, BAO Jingyang, et al. Tikhonov Two-parameter Regulation Algorithm in Downward Continuation of Airborne Gravity Data[J]. Acta Geodaetica et Cartographica Sinica, 2011, 40(6): 690-696.
[24] 蒋涛, 党亚民, 章传银, 等. 基于矩谐分析的航空重力向下延拓[J]. 测绘学报, 2013, 42(4): 475-480. JIANG Tao, DANG Yamin, ZHANG Chuanyin, et al. Downward Continuation of Airborne Gravity Data Based on Rectangular Harmonic Analysis[J]. Acta Geodaetica et Cartographica Sinica, 2013, 42(4): 475-480.
[25] 孙文, 吴晓平, 王庆宾, 等. 航空重力数据向下延拓的波数域迭代Tikhonov正则化方法[J]. 测绘学报, 2014, 43(6): 566-574. DOI: 10.13485/j.cnki.11-2089.2014.0080. SUN Wen, WU Xiaoping, WANG Qingbin, et al. Wave Number Domain Iterative Tikhonov Regularization Method for Downward Continuation of Airborne Gravity Data[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(6): 566-574. DOI: 10.13485/j.cnki.11-2089.2014.0080.
[26] 刘晓刚, 李迎春, 肖云, 等. 重力与磁力测量数据向下延拓中最优正则化参数确定方法[J]. 测绘学报, 2014, 43(9): 881-887. DOI: 10.13485/j.cnki.11-2089.2014.0160. LIU Xiaogang, LI Yingchun, XIAO Yun, et al. Optimal Regularization Parameter Determination Method in Downward Continuation of Gravimetric and Geomagnetic Data[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(9): 881-887. DOI: 10.13485/j.cnki.11-2089.2014.0160.
[27] 黄谟涛, 欧阳永忠, 刘敏, 等. 海域航空重力测量数据向下延拓的实用方法[J]. 武汉大学学报(信息科学版), 2014, 39(10): 1147-1152. HUANG Motao, OUYANG Yongzhong, LIU Min, et al. Practical Methods for Downward Continuation of Airborne Gravity Data in the Sea Area[J]. Geomatics and Information Science of Wuhan University, 2014, 39(10): 1147-1152.
[28] 黄谟涛, 宁津生, 欧阳永忠, 等. 联合使用位模型和地形信息的陆区航空重力向下延拓方法[J]. 测绘学报, 2015, 44(4): 355-362. DOI: 10.11947/j.AGCS.2015.20130751. HUANG Motao, NING Jinsheng, OUYANG Yongzhong, et al. Downward Continuation of Airborne Gravimetry on Land Using Geopotential Model and Terrain Information[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(4): 355-362. DOI: 10.11947/j.AGCS.2015.20130751.
[29] NOVÁK P, HECK B. Downward Continuation and Geoid Determination Based on Band-limited Airborne Gravity Data[J]. Journal of Geodesy, 2002, 76(5): 269-278.
[30] MORITZ H. Advanced Physical Geodesy[M]. Karlsruhe: Herbert Wichmann Verlag, 1980.
[31] HWANG C, HSIAO Y S, SHIH H C, et al. Geodetic and Geophysical Results from a Taiwan Airborne Gravity Survey: Data Reduction and Accuracy Assessment[J]. Journal Geophysical Research, 2007, 112(B4): 93-101.
[32] FORSBERG R, OLESEN A V. Airborne Gravity Field Determination[M]//XU Guochang. Sciences of Geodesy-I. Berlin: Springer-Verlag, 2010: 83-103.
[33] 黄谟涛, 欧阳永忠, 翟国君, 等. 融合多源重力数据的Tikhonov正则化配置法[J]. 海洋测绘, 2013, 33(3): 6-12. HUANG Motao, OUYANG Yongzhong, ZHAI Guojun, et al. Tikhonov Regularization Collocation for Multi-source Gravity Data Fusion Processing[J]. Hydrographic Surveying and Charting, 2013, 33(3): 6-12.
[34] 黄谟涛, 欧阳永忠, 刘敏, 等. 融合海域多源重力数据的正则化点质量方法[J]. 武汉大学学报(信息科学版), 2015, 40(2): 170-175. HUANG Motao, OUYANG Yongzhong, LIU Min, et al. Regularization of Point-mass Model for Multi-source Gravity Data Fusion Processing[J]. Geomatics and Information Science of Wuhan University, 2015, 40(2): 170-175.
[35] NOVÁK P, KERN M, SCHWARZ K P, et al. On Geoid Determination from Airborne Gravity[J]. Journal of Geodesy, 2003, 76(9-10): 510-522.
[36] PAUL M K. A Method of Evaluating the Truncation Error Coefficients for Geoidal Height[J]. Bulletin Géodésique, 1973, 110(1): 413-425.
[37] 陆仲连. 球谐函数[R]. 郑州: 测绘学院, 1984. LU Zhonglian. Spherical Harmonic Function[R]. Zhengzhou: Surveying and Mapping Institute, 1984.
[38] OLESEN A V. Improved Airborne Scalar Gravimetry for Regional Gravity Field Mapping and Geoid Determination[D]. Copenhagen: University of Copenhagen, 2002.
[39] 孙中苗. 航空重力测量理论、方法及应用研究[D]. 郑州:信息工程大学, 2004. SUN Zhongmiao. Theory, Methods and Applications of Airborne Gravimetry[D]. Zhengzhou: Information Engineering University, 2004.
[40] PAVLIS N K, HOLMES S A, KENYON S C, et al. The Development and Evaluation of the Earth Gravitational Model 2008(EGM 2008)[J]. Journal Geophysical Research, 2012, 117(B4): 531-535.
[41] 章传银, 郭春喜, 陈俊勇, 等. EGM 2008地球重力场模型在中国大陆适用性分析[J]. 测绘学报, 2009, 38(4): 283-289. ZHANG Chuanyin, GUO Chunxi, CHEN Junyong, et al. EGM 2008 and Its Application Analysis in Chinese Mainland[J]. Acta Geodaetica et Cartographica Sinica, 2009, 38(4): 283-289.
[42] 欧阳永忠, 邓凯亮, 陆秀平, 等. 多型航空重力仪同机测试及其数据分析[J]. 海洋测绘, 2013, 33(4): 6-11. OUYANG Yongzhong, DENG Kailiang, LU Xiuping, et al. Tests of Multi-type Airborne Gravimeters and Data Analysis[J]. Hydrographic Surveying and Charting, 2013, 33(4): 6-11.
[43] MORITZ H. The Computation of the External Gravity Field and the Geodetic Boundary-Value Problem[C]//Proceedings of the Symposium on the Extension of Gravity Anomalies to Unsurveyed Areas. Geophysical Monograph Series Number 9.[S.l.]: American Geophysical Union of the National Academy of Sciences, 1966: 127-136.
[44] ARGESEANU V S. Upward Continuation of Surface Gravity Anomaly Data[C]//Proceedings of the IAG Symposium on Airborne Gravity Field Determination. Boulder:[s.n.], 1995: 95-102.

顾及地形效应的重力向下延拓模型分析与检验

Test and Analysis of Downward Continuation Models for Airborne Gravity Data with Regard to the Effect of Topographic Height

PDF

可视化

被引次数

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价

[1]	黄谟涛, 邓凯亮, 吴太旗, 欧阳永忠, 陈欣, 刘敏, 王许. 重力异常向上延拓严密改化模型及向下延拓应用[J]. 测绘学报, 2022, 51(1): 41-52.
[2]	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.
[3]	赵启龙, 李建成, 徐新禹, 赵永奇, 于男. 航空重力向下延拓的误差影响分析[J]. 测绘学报, 2017, 46(6): 689-697.
[4]	郑凯, 刘站科, 肖学年, 张小红. 航空重力GPS测速多粗差探测方法[J]. 测绘学报, 2016, 45(6): 663-669.
[5]	黄谟涛, 宁津生, 欧阳永忠, 邓凯亮, 翟国君, 陆秀平, 吴太旗. 联合使用位模型和地形信息的陆区航空重力向下延拓方法[J]. 测绘学报, 2015, 44(4): 355-362.
[6]	陈强, 罗容, 杨莹辉, 雍琦. 利用SAR影像配准偏移量提取地表形变的方法与误差分析[J]. 测绘学报, 2015, 44(3): 301-308.
[7]	翟振和, 孙中苗, 李迎春, 肖云. 航空重力测量在近海区域的精度评估与分析[J]. 测绘学报, 2015, 44(1): 1-5.
[8]	黄谟涛, 宁津生, 欧阳永忠, 陆秀平, 翟国君, 邓凯亮, 吴太旗. 航空重力测量厄特弗斯改正公式注记[J]. 测绘学报, 2015, 44(1): 6-12.
[9]	刘晓刚李迎春肖云翟振和. 重力与磁力测量数据向下延拓中最优正则化参数确定方法研究[J]. 测绘学报, 2014, 43(9): 881-887.
[10]	孙文吴晓平王庆宾刘晓刚王凯. 航空重力数据向下延拓的波数域迭代Tikhonov正则化方法[J]. 测绘学报, 2014, 43(6): 566-574.
[11]	欧阳永忠. 海空重力测量数据处理关键技术研究[J]. 测绘学报, 2014, 43(4): 435-435.
[12]	孙中苗翟振和肖云. 渤海湾航空重力及其在海域大地水准面精化中的应用[J]. 测绘学报, 2014, 43(11): 1101-1108.
[13]	卞光浪翟国君高金耀朱丹李连登方建勋李研. 基于改进泰勒级数法的总强度磁异常稳健向下延拓[J]. 测绘学报, 2014, 43(1): 30-36.
[14]	曾小牛刘代志牛超齐玮. 基于改进高斯-牛顿法的位场向下延拓[J]. 测绘学报, 2014, 43(1): 37-44.
[15]	梁星辉柳林涛吴鹏飞何建刚. 顾及误差频谱特性的CHZ重力仪航空应用研究[J]. , 2013, 42(5): 633-639.