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

doi:10.11947/j.AGCS.2022.20210222

Abstract

Abstract: 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.

Key words: horizontal component of band-limited airborne vector gravity data, geoid, two-step integral method, generalized band-limited horizon boundary value problem, band-limited Dirichlet boundary value problem

CLC Number:

P223

HUANG Motao, DENG Kailiang, WU Taiqi, WANG Weiping, OUYANG Yongzhong, CHEN Xin, WANG Xu. A two-step integral method for geoid determination using generalized band-limited airborne vector gravity data[J]. Acta Geodaetica et Cartographica Sinica, 2022, 51(11): 2245-2254.

References

[1] 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.
[2] FEATHERSTONE W E. GNSS-based heighting in Australia: current, emerging and future issues[J]. Journal of Spatial Science, 2008, 53(2):115-133. DOI:10.1080/14498596.2008.9635153.
[3] 蒋涛. 利用航空重力测量数据确定区域大地水准面[D]. 武汉:武汉大学, 2011. JIANG Tao. Regional geoid determination using airborne gravimetry data[D]. Wuhan:Wuhan University, 2011.
[4] 李建成. 最新中国陆地数字高程基准模型:重力似大地水准面CNGG2011[J]. 测绘学报, 2012, 41(5): 651-660. LI Jiancheng. The recent Chinese terrestrial digital height datum model: gravimetric quasi-geoid CNGG2011[J]. Acta Geodaetica et Cartographica Sinica, 2012, 41(5): 651-660.
[5] MA Jian, WEI Ziqing, REN Hongfei.The spectral analysis and application of low-degree modified spheroidal Hotine kernel[J].Journal of Geodesy and Geoinformation Science,2020,3(3):104-114.DOI:10.11947/j.JGGS.2020.0310.
[6] HUANG Motao,DENG Kailiang,WU Taiqi,et al.Research and evaluation on key technological indicators for airborne and shipborne gravimetry[J].Journal of Geodesy and Geoinformation Science,2019,2(3):44-54.
[7] 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.
[8] FERGUSON S, ELIEFF S, BELL R, et al. Measuring the gravity vector with an airborne gravimeter [C]//Proceedings of the 2nd International Gravity Field Symposium. Fairbanks, Alaska, USA:[s.n.], 2010.
[9] 欧阳永忠. 海空重力测量数据处理关键技术研究[D]. 武汉: 武汉大学, 2013. OUYANG Yongzhong. On key technologies of data processing for air-sea gravity surveys[D]. Wuhan: Wuhan University, 2013.
[10] CAI Shaokun, ZHANG Kaidong, WU Meiping. Improving airborne strapdown vector gravimetry using stabilized horizontal components[J]. Journal of Applied Geophysics, 2013, 98:79-89.
[11] SANDER L, FERGUSON S. Advances in SGL AIRGrav acquisition and processing [C]//Proceedings of 2010 Australian Society of Exploration Geophysicists Conference. Sydney, Australia:[s.n.], 2010.
[12] 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.
[13] NOVÁK P, KERN M, SCHWARZ K P, et al. On geoid determination from airborne gravity[J]. Journal of Geodesy, 2003, 76(9):510-522.
[14] 孙中苗, 夏哲仁, 王兴涛. 利用航空重力确定局部大地水准面的精度分析[J]. 武汉大学学报(信息科学版), 2007, 32(8): 692-695. SUN Zhongmiao, XIA Zheren, WANG Xingtao. Detemining accuracy of local geoid determined from airborne gravity data[J]. Geomatics and Information Science of Wuhan University, 2007, 32(8): 692-695.
[15] 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. SUN Zhongmiao,ZHAI Zhenhe,XIAO Yun,et al. Airborne gravimetry in Bohai bay and its role on the refining of the regional marine geoid[J]. Acta Geodaetica et Cartographica Sinica, 2014, 43(11):1101-1108.
[16] JEKELI C, KWON J H. Geoid profile determination by direct integration of GPS inertial navigation system vetor gravimetry[J]. Journal of Geophysical Research:Solid Earth, 2002, 107(B10): 2156-2202.
[17] SERPAS J G, JEKELI C. Local geoid determination from airborne vector gravimetry[J].Journal of Geodesy, 2005, 78(10):577-587.
[18] DENG Kailiang, CHANG Guobin, HUANG Motao, et al. Geoid determination using band limited airborne horizontal gravimetric data[J]. Journal of Spatial Science, 2020. DOI.org/10.1080/14498596.2020.1746703.
[19] HEISKANEN W A, MORITZ H. Physical geodesy[M]. San Francisco: Freeman and Company,1967.
[20] 程芦颖, 许厚泽. 广义逆Stokes公式、广义逆Vening-Meinesz公式以及广义Molodensky公式[J]. 中国科学(D辑地球科学), 2006, 36(4):370-374. CHENG Luying, XU Houze. General inverse of Stokes, Vening-Meinesz and Molodensky formulae[J]. Science in China Series D Earth Sciences, 2006, 36(4):370-374.
[21] HWANG C. Inverse Vening-Meinesz formula and deflection-geoid formula: applications to the predictions of gravity and geoid over the South China Sea[J]. Journal of Geodesy, 1998, 72(5): 304-312.
[22] ŠPRLÁK M, TANGDAMRONGSUB N. Vertical and horizontal spheroidal boundary-value problems[J]. Journal of Geodesy, 2018, 92(7):811-826.
[23] 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.
[24] ALBERTS B, KLEES R. A comparison of methods for the inversion of airborne gravity data [J]. Journal of Geodesy, 2004, 78(1):55-65.
[25] 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.
[26] TZIAVOS I N, ANDRITSANOS V D, FORSBERG R, et al. Numerical investigation of downward continuation methods for airborne gravity data [C]//Proceedings of 2005 IAG Symposia: Gravity, Geoid and Space Missions. Berlin, Germany: Springer, 2005:119-124.
[27] 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 regulation based on signal-to-noise in airborne gravity downward to the earth surface[J]. Acta Geodaetica et Cartographica Sinica, 2010,39(5):458-464.
[28] 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.
[29] 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.
[30] 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. 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.
[31] KERN M. An analysis of the combination and downward continuation of satellite, airborne and terrestrial gravity data[D]. Calgary:University of Calgary, 2003.
[32] GRAFAREND E W. The spherical horizontal and spherical vertical boundary value problem-vertical deflections and geoidal undulations the completed Meissl diagram[J]. Journal of Geodesy, 2001, 75(7): 363-390. DOI:10.1007/s001900100186.
[33] PAUL M. A method of evaluation the truncation error coefficients for geoidal heights[J]. Bulletin Geodesique, 1973(110):413-425.
[34] VANICEK P, NOVAK P, MARTINEC Z. Geoid, topography and the Bouguer plate or shell[J]. Journal of Geodesy, 2001, 75(4): 210-215.
[35] 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.
[36] JIANG Tao,WANG Yanming. On the spectral combination of satellite gravity model, terrestrial and airborne gravity data for local gravimetric geoid computation[J]. Journal of Geodesy, 2016, 90(12):1405-1418. DOI:10.1007/s00190-016-0932-7.
[37] PAVLIS N K, HOLMES S A, KENYON S C, et al. The development and evaluation of the Earth gravitational model 2008 (EGM2008)[J]. Journal Geophysical Research, 2012, 117(B10). DOI: 10.1029/2011JB008916.
[38] 章传银, 郭春喜, 陈俊勇,等. EGM2008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. EGM2008 and its application analysis in Chinese mainland[J]. Acta Geodaetica et Cartographica Sinica, 2009, 38(4): 283-289.