A Direct Approach to Determine the External Disturbing Gravity Field by Applying Green Integral with the Ground Boundary Value

doi:10.11947/j.AGCS.2015.20140516

Abstract

Abstract: By using the ground as the boundary, Molodensky problem usually gets the solution in form of series. Higher order terms reflect the correction between a smooth surface and the ground boundary. Application difficulties arise from not only computational complexity and stability maintenance, but also data-intensiveness. Therefore, in this paper, starting from the application of external gravity disturbance, Green formula is used on digital terrain surface. In the case of ignoring the influence of horizontal component of the integral, the expression formula of external disturbance potential determined by boundary value consisted of ground gravity anomalies and height anomaly difference are obtained, whose kernel function is reciprocal of distance and Poisson core respectively. With this method, there is no need of continuation of ground data. And kernel function is concise, and suitable for the stochastic computation of external disturbing gravity field.

Key words: Green formula, Stokes formula, disturbing gravity, gravity anomaly, boundary value problem

CLC Number:

P223

TIAN Jialei, WU Xiaoping, LI Shanshan. A Direct Approach to Determine the External Disturbing Gravity Field by Applying Green Integral with the Ground Boundary Value[J]. Acta Geodaetica et Cartographica Sinica, 2015, 44(11): 1189-1195.

References

[1] SJÖBERG L E. On the Discrete Boundary Value Problem of Physical Geodesy with Harmonic Reduction to an Internal Sphere[R]. Stockholm:Royal Institute of Technology, 1975.
[2] WANG Zhengtao, DANG Yamin, CHAO Dingbo.Theory and Methodology of Ultra-high-degree Geopotential Model Determination[M]. Beijing:Surveying and Mapping Press, 2011.(王正涛, 党亚民, 晁定波. 超高阶地球重力位模型的确定的理论与方法[M]. 北京:测绘出版社, 2011.)
[3] CHENG Luying. General Kernel Functions Based on Integral Transformation among Different Disturbing Potential Elements[J]. Acta Geodaetica et Cartographica Sinica, 2013, 42(2):203-210.(程芦颖. 不同扰动位泛函间的积分变换广义核函数[J]. 测绘学报, 2013, 42(2):203-210.)
[4] SEEBER G. Satellite Geodesy[M]. 2nd ed. Berlin:Walter de Gruyter, 2003.
[5] LIN Miao, DENKER H, MüLLER J. Regional Gravity Field Modeling Using Free-positional Point Masses[J]. Studia Geophysica et Geodaetica, 2014, 58(2):206-227.
[6] XU Houze,LU Zhonglian. Earth's Gravity Feld and Geoid in China[M]. Beijing:The People's Liberation Army Press, 1997.(许厚泽, 陆仲连. 中国地球重力场与大地水准面[M]. 北京:解放军出版社, 1997.)
[7] STOKES G G. On the Variation of Gravity on the Surface of the Earth[J]. Transactions of the Cambridge Philosophical Society, 1849, 8(5):672-695.
[8] DENKER H,Regional Gravity Field Modeling:Theory and Practical Results[M]//XU Guochang. Sciences of Geodesy-Ⅱ. Berlin Heidelbreg:Springer Verlag, 2013:185-291.
[9] HEISKANEN W A, MORITZ H. Physical Geodesy[M]. LU Fukang, HU Guoli trans. Beijing:Surveying and Mapping Press, 1979.(海斯卡涅W A, 莫里斯H. 物理大地测量学[M]. 卢福康, 胡国理, 译. 北京:测绘出版社, 1979.)
[10] MORITZ H. Advance Physical Geodesy[M]. London:Abacus Press, 1980.
[11] HOFMANN-WELLENHOF B, MORIZE H. Physical Geodesy[M]. Heidelberg:Springer, 2005.
[12] MOLODENSKY M S, EREMEEV V F, YOURKINA M I. Methods for Study of the External Gravitational Field and Figure of the Earth. Works of Central Research Institute of Geodesy. Aerial Photography and Cartography[M]. Moscow:Geodetic Literature Press, 1960.
[13] MOLODENSKY M S, EREMEEV V F, YOURKINA M I. An Evaluation of Accuracy of Stokes' Series and of Some Attempts to Improve His Theory[J]. Bulletin Géodésique, 1962, 63(1):19-37.
[14] SUNKEL H. Point Mass Models and the Anomalous Gravitational Field of the Earth:Report No.328[R]. Columbus:Ohio State University, 1981.
[15] KATSAMBALOS K E. Simulation Studies on the Computation of the Gravity Vector in Space from Surface Data Considering the Topography of the Earth:Report No.323[R]. Columbus:Ohio State University, 1981.
[16] BJERHAMMAR A. A New Theroy of Geodetic Gravity[M]. Stockholm:Tekniska Hogskolan, 1964.
[17] FORSBERG R. A Study of Terrain Reductions, Density Anomalies, and Geophysical Inversion Methods in Gravity Field Modelling:Report No.355[R]. Columbus:Ohio State University, 1984.
[18] JIANG Tao, LI Jiancheng, DANG Yamin, et al. Regional Gravity Field Modeling Based on Rectangular Harmonic Analysis[J]. Science China:Earth Sciences, 2014, 57(7):1637-1644.
[19] LU Zhonglian. Theory and Method of Earth's Gravity[M]. Beijing:The People's Liberation Army Press, 1996.(陆仲连. 地球重力场理论与方法[M]. 北京:解放军出版社, 1996.)
[20] LU Zhonglian, WU Xiaoping, DING Xingbin, et al. Ballistic Missile Gravity[M]. Beijing:The Ba Yi Press, 1993.(陆仲连, 吴晓平, 丁行斌, 等. 弹道导弹重力学[M]. 北京:八一出版社, 1993.)