進階搜尋


下載電子全文  
系統識別號 U0026-1508201412065900
論文名稱(中文) 以Taylor-Kármán結構張量進行GOCE重力梯度變方-協變方之研究
論文名稱(英文) A study of the Taylor-Kármán structured tensors for variance-covariance of GOCE gravity gradient
校院名稱 成功大學
系所名稱(中) 測量及空間資訊學系
系所名稱(英) Department of Geomatics
學年度 102
學期 2
出版年 103
研究生(中文) 高瑋男
研究生(英文) Wei-Nan Kao
學號 P66011012
學位類別 碩士
語文別 中文
論文頁數 102頁
口試委員 指導教授-尤瑞哲
口試委員-郭重言
口試委員-韓仁毓
中文關鍵字 Taylor-Kármán  GOCE  重力梯度  協變方張量 
英文關鍵字 Taylor-Kármán  GOCE  gravity gradient  covariance tensor 
學科別分類
中文摘要 本研究為藉由四階Taylor-Kármán結構協變方張量做GOCE衛星區域重力梯度擾動之隨機性質分析。Taylor-Kármán結構常用在紊流的統計性質推演上,Taylor與Kármán藉由隨機函數為位能形式之假設與資料具同質性與等向性之假設推導出此數學函式,以表達資料之隨機性質。GOCE衛星全名為重力場及穩態海洋環流探測衛星,搭載靜電重力梯度儀以擷取地球重力場訊號,獲得大量遍布全球之重力梯度觀測值,製作成數個產品以供後續研究使用,例如決定地球重力場。本研究使用測站指北座標系統之重力梯度產品EGG_TRF_2計算台灣地區與冰島地區之經驗協變方張量,藉由經驗協變方張量與四階Taylor-Kármán結構協變方張量之擬合分析重力梯度擾動之隨機性質。在測量實際數值例中,資料往往具有不同之隨機性質。本研究分別依擾動張量具相關性、擾動張量各自獨立與各方向之擾動張量各自獨立等三種方式進行擬合。並依序嘗試不同之隨機模型,估計各種情況下與重力梯度擾動隨機過程最接近之隨機模型。而擬合成果將與由擾動位空間協變方函數推導之理論進行比較。研究成果顯示,重力梯度擾動之各張量分別具有不同之隨機性質,各張量適合之隨機模型不盡相同,但多能以高斯模型與三階馬可夫模型表達。而藉由各方向之擾動張量各自獨立之方式進行擬合,多數協變方張量將符合Taylor-Kármán結構,並且相較於由擾動位空間協變方函數推導之理論,Taylor-Kármán結構可以更好的描述重力梯度擾動之隨機性質。對於後續協變方張量之應用上,Taylor-Kármán理論將可提供更好的成果。
英文摘要 This study analyzed stochastic processes of gravity gradients from Gravity-field and steady-state Ocean Circulation Explorer (GOCE) satellite measurements by the fourth-order Taylor-Kármán structured covariance tensor. The Taylor-Kármán structure is often used in turbulence and is derived based on two assumptions: one is that the random function is of the “potential type”, and the other is that the field is homogenous and isotropic. GOCE carries gravity gradiometers to measure the gravity field signal and provides many different products of Earth's gravity field. In our research, we used EGG_TRF_2 to calculate empirical covariance tensors of Taiwan. We analyzed the stochastic processes of GOCE disturbing gravity gradients by empirical covariance tensors and the fourth-order Taylor-Kármán structured covariance tensors. The disturbing gravity gradient field was produced by subtracting the normal gravity gradient field of GRS80 from the GOCE gravity gradient field.

In our results, we used three different methods to study stochastic process of the disturbing gravity gradient field: 1. The covariance functions for the components of the covariance tensors of the disturbing gradient field are assumed to be the same; 2. The covariance functions of each component of covariance tensor can be individually chosen; 3. The covariance functions are directionally oriented in the second method. In total, six different stochastic models for building the covariance tensor were used. Results show that the disturbing gravity gradient components have different stochastic properties and the Gauss model and the Markov model of third order are the best covariance functions for use. From our analysis, the Taylor-Kármán structured tensors for the stochastic properties are better than the covariance tensors derived from the spatial covariance functions of the anomalous potential.
論文目次 摘要 I
EXTENDED ABSTRACT II
致謝 VI
目錄 VII
表目錄 X
圖目錄 XI
第一章 介紹 1
1.1 研究背景與動機 1
1.2文獻回顧 4
1.3 研究方法 6
1.4 論文架構 8
第二章 地球重力場 9
2.1 地球重力場理論 9
2.2 地球重力場模型 12
2.2.1 EGM96 13
2.2.2 EGM2008 14
2.2.3 EIGEN-5C 15
2.2.4 GO_CONS_GCF_2_SPW_R2 16
2.2.5 各模型精度及比較 17
第三章 GOCE衛星觀測原理 19
3.1 GOCE衛星簡介 19
3.2 儀器性能與目的 21
3.2.1 靜電重力梯度儀 22
3.2.2 GPS接收儀 24
3.2.3 恆星感測器 25
3.3 地球重力場反演方式 26
3.3.1 重力梯度計算 26
3.3.2 重力梯度前處理 28
3.3.3 座標轉換 31
3.3.4 衛星定軌 33
3.3.5 重力場求解 34
第四章 GOCE資料結構 36
4.1 地面設施 36
4.2 資料產品 37
4.3 GOCE座標參考框架 43
4.3.1 梯度儀參考座標系統(Gradiometer Reference Frame, GRF) 43
4.3.2 測站指北座標系統(Local North Oriented Frame, LNOF) 44
4.3.3 協議慣性座標系統(Inertial Reference Frame, IRF) 44
4.3.4 地心地固座標系統(Earth-Fixed Reference Frame, EFRF) 44
4.3.5 時間系統 45
第五章 Taylor-Kármán結構變方-協變方張量 46
5.1 Taylor-Kármán變方-協變方張量介紹 46
5.2 理論推導 48
5.3 函數模型 51
第六章 試驗分析 52
6.1 擾動張量計算 52
6.2 實驗設計 56
6.3實驗區域 57
6.4 資料分群與擬合 61
6.5 台灣區域成果分析 62
6.6 冰島區域成果分析 83
第七章 結論與建議 96
參考文獻 98
參考文獻 Álvarez, O., M. Gimenez, C. Braitenberg and A. Folguera, 2012. GOCE satellite derived gravity and gravity gradient corrected for topographic effect in the South Central Andes region. Geophysical Journal International, 190, pp. 941-959.
Batchelor, G. K. and A. A. Townsend, 1948. Decay of Turbulence in the Final Period. Proceedings of the Royal Society, A-194, pp. 527-543
Bock, H., A. Jäggi, D. Svehla, G. Beutler, U. Hugentobler and P. Visser, 2007. Precise orbit determination for the GOCE satellite using GPS. Advances in Space Research, 39, pp. 1638-1647.
Bock, H., A. Jäggi, U. Meyer, P. Visser, J. van den IJssel, T. van Helleputte, M. Heinze and U. Hugentobler, 2011. GPS-derived orbits for the GOCE satellite. Journal of Geodesy, 85(11), pp. 807-818.
Bouman, J., 2007. Alternative method for rotation to TRF. GO-TN-HPF-GS-0193, issue 1.0. European Space Agency, Noordwijk, 16 May 2007.
Bouman, J., S. Fiorot, M. Fuchs, T. Gruber, E. Schrama, C. C. Tscherning, M. Veicherts and P. Visser, 2011. GOCE gravitational gradients along the orbit. Journal of Geodesy, 85(11), pp. 791-805.
Bouman, J., S. Rispens, P. Visser, M. Veicherts, C. C. Tscherning, R. Pail, R. Mayrhofer, T. Gruber, E. Schrama and M. Fuchs, 2010. Gravity Gradient Analysis at the GOCE HPF. Session G7, EGU Vienna, 7 May 2010.
Bouman, J., S. Rispens, T. Gruber, R. Koop, E. Schrama, P. Visser, C. C. Tscherning and M. Veicherts, 2009. Preprocessing of gravity gradients at the GOCE high-level processing facility. Journal of Geodesy, 83(7), pp. 659-678.
Darbeheshti, N. and W. E. Featherstone, 2009. Non-stationary covariance function modelling in 2D least-squares Collocation. Journal of Geodesy, 83(6), pp. 495-508.
European Space Agency, 2006. GOCE Level 1b Product User Handbook. GOCE-GSEG-EOPG-TN-06-0137, issue 1.0. European Space Agency, Noordwijk, 2 October 2006.
Förste, C., F. Flechtner , R. Schmid, R. Stubenvoll, M. Rothacher, J. Kusche,,H. Ne umayer, R. Biancale, J.-M. Lemoine, F. Barthelmes, S. Bruinsma, R. König and U. Meyer, 2008. EIGEN-GL05C- a new global combined high-resolution GRACE-based gravity field model of the GFZ-GRGS cooperation. General Assembly European Geosciences Union (Vienna, Austria 2008), Geophys Res Abstr 10, Abstract No. EGU2008-A-06944
Fuchs, M. J. and J. Bouman, 2011. Rotation of GOCE gravity gradients to local frames. Geophysical Journal International, 187(2), pp. 743-753.
Grafarend, E. and Bonn, 1971. Isotropietests von Lotabweichungsverteilungen in Westdeutschland I. Zeitschrift für Geophysik, 37, pp. 719-733.
Grafarend, E. and Bonn, 1972. Isotropietests von Lotabweichungsverteilungen in Westdeutschland Ⅱ. Zeitschrift für Geophysik, 38, pp. 243-255.
Gruber, T., R. Rummel and R. Koop, 2007. How to use GOCE level 2 products. Proceedings of the 3rd international GOCE user workshop, 6-8 November 2006, Frascati, Italy(ESA SP-627, January 2007), pp. 205-211
Gruber, T., R. Rummel, O. Abrikosov and R. van Hees, 2010. GOCE level 2 product data handbook. GO-MA-HPF-GS-0110, issue 4.3. European Space Agency, Noordwijk, 9 December 2010.
Kármán, T. and Howarth, L., 1938. On the statistical theory of turbulence. Proceedings of the Royal Society, A-164, pp. 192-215.
Kaula, W. M., 1963. Determination of the earth’s gravitational field. Reviews of Geophysics, 1(4), pp. 507-551.
Lemoine, F. G., S. C. Kenyon, J. K. Factor, R. G. Trimmer, N. K. Pavlis, D. S. Chinn, C. M. Cox, S. M. Klosko, S. B. Luthcke, M. H. Torrence, Y. M. Wang, R. G. Williamson, E. C. Pavlis, R. H. Rapp and T. R. Olsen, 1998. The development of the joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) geopotential model EGM96. NASA technical paper NASA/TP-1998-206861. Goddard Space Flight Center, Greenbelt
Maggi, A., F. Migliaccio, M. Reguzzoni and N. Tselfes, 2007. Combination of Ground Gravimetry and GOCE Data for Local Geoid Determination: a Simulation Study. Proceedings of the 1st International Symposium of the International Gravity Field Service, August 28 – September 01, 2006, Istanbul, Turkey.
Marinkovic, P., E. Grafarend and T. Reubelt, 2003. Space gravity spectroscopy: the benefits of Taylor-Kármán structured criterion matrices. Advances in Geosciences, 1, pp. 113-120.
Meier, S., 1981. Planar geodetic covariance functions. Review of Geophysics and Space Physics, 19(4), pp. 673-686.
Meier, S., 1987. Two-point statistics of vertical crustal movements of the pannonian basin. Journal of Geodynamics, 8, pp. 321-335.
Mikhail, E. M. and F. Ackermann, 1976. Observations and Least Squares. Thomas Y. Crowell Company, Inc, NY.
Moritz, H., 1989. Advanced Physical Geodesy(2nded). Herbert Wichman, Karlsruhe, Germany.
Moritz, H., 2000. Geodetic Reference System 1980. Journal of Geodesy, 74, pp. 128-133.
Moritz, H., 2006. Physical Geodesy(2nd ed). SpringerWienNewYork, Austria.
Pail, R., S. Bruinsma, F. Migliaccio, C. Förste, H. Goiginger, W.-D. Schuh, E. Höck, M. Reguzzoni, J. M. Brockmann, O. Abrikosov, M. Veicherts, T. Fecher, R. Mayrhofer, I. Krasbutter, F. Sansò and C. C. Tscherning, 2011. First GOCE gravity field models derived by three different approaches. Journal of Geodesy, 85(11), pp. 819-843.
Pavlis, N. K., S. A. Holmes, S. C. Kenyon and J. K. Factor, 2012. The development and evaluation of the Earth Gravitational Model 2008(EGM2008). Journal of Geophysical Research, 117(B4), B04406
Rapp, R. H., Y. Wang and N. Pavlis, 1991. The Ohio State 1991 geopotenial and sea surface topography harmonic coefficient models, Rep 410, Department of Geodetic Science and Surveying, The Ohio State University, Columbus.
Rieser, D., R. Pail and A. I. Sharov, 2010. Refining regional gravity field solutions with GOCE gravity gradients for cryospheric investigationa. In Proceedings of the ESA Living Planet Symposium, 28 June-2 July 2010, Bergen, Norway.
Rummel, R. and T. Gruber, 2012. Product Acceptance Review (PAR)-Level 2 Product Report, GO-TN-HPF-GS-0296, issue 1.0. European Space Agency, Noordwijk, 13 February 2012.
Rummel, R., W. Yi and C. Stummer, 2011. GOCE gravitational gradiometry. Journal of Geodesy, 85(11), pp. 777-790.
Seeber, G., 2003. Satellite Geodesy(2nd ed). Walter de Gruyter, Berlin, New York.
Siemes, C., 2012. GOCE gradiometer calibration and Level 1b data processing. ESA Working Paper EWP-2384, 6 January 2012, Noordwijk, Netherlands.
Taylor, G. I., 1938. The spectrum of turbulence. Proceedings of the Royal Society, A-164, pp. 476-490.
Visser, P., J. van den IJssel, T. van Helleputte, H. Bock, A. Jaeggi, G. Beutler and M. Heinze, 2010. Rapid and precise orbit determination for the GOCE satellite. In Proceedings of the ESA Living Planet Symposium, 28 June-2 July 2010, Bergen, Norway.
Wermuth, M. K., 2009. Gravity field analysis from the satellite misson CHAMP and GOCE. Doktor-Ingenieurs Dissertation, Fakultät für Bauingenieur- und Vermessungswesen, TU München.
Yildiz, H., 2012. A study of regional gravity field recovery from GOCE vertical gravity gradient data in the Auvergne test area using collocation. Studia Geophysica et Geodaetica, 56(1), pp. 171-184.
You, R. J. and E. W. Grafarend, 2014. The Taylor-Kármán Structured Covariance Tensor of Fourth Order for Gravity Gradient Predictions by means of the Hankel Transformation. Journal of Geodesy(in review).
You, R. J. and H. W. Hwang, 2006. Coordinate Transformation between Two Geodetic Datums of Taiwan by Least-Squares Collocation. Journal of Surverying Engineering, 132(2), pp. 64-70.
論文全文使用權限
  • 同意授權校內瀏覽/列印電子全文服務,於2014-08-27起公開。
  • 同意授權校外瀏覽/列印電子全文服務,於2016-09-01起公開。


  • 如您有疑問,請聯絡圖書館
    聯絡電話:(06)2757575#65773
    聯絡E-mail:etds@email.ncku.edu.tw