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From Tensor to Vector of Gravitation Cover

From Tensor to Vector of Gravitation

By: Mehdi Eshagh  
Open Access
|Jun 2014

References

  1. Bobojć A. and Drożyner A. (2003) Satellite orbit determination using satellite gravity gradiometry observations in GOCE mission perspective, Advances in Geosciences, 1, 109-112.10.5194/adgeo-1-109-2003
  2. Bouman J. and Koop R. (2003) Error assessment of GOCE SGG data using along track interpolation, Advances in Geosciences, 1, 27-32.10.5194/adgeo-1-27-2003
  3. Bouman J., Koop R., Haagmans R., Mueller J., Sneeuw N. Tscherning C.C., and Visser P. (2003) Calibration and validation of GOCE gravity gradients, Paper presented at IUGG meeting, pp. 1-6.
  4. Bouman J., Koop R., Tscherning C. C. and Visser P. (2004) Calibration of GOCE SGG data using high-low STT, terrestrial gravity data and global gravity field models, Journal of Geodesy, 78, 124-137.10.1007/s00190-004-0382-5
  5. Bouman J., Fiorot S., Fuchs M., Gruber T., Schrama E., Tscherning C., Veicherts M., Visser P. (2011) GOCE gravitational gradients along the orbit, Journal of Geodesy, 85, 791-805. 10.1007/s00190-011-0464-0
  6. de Min E. (1994) On the numerical evaluation of Stokes’s integral, International Geoid Service Bulletin, 3, 41-46.
  7. ESA (1999) Gravity Field and Steady-State Ocean Circulation Mission, ESA SP-1233(1), Report for mission selection of the four candidate earth explorer missions. ESA Publications Division, pp. 217, July 1999.
  8. Eshagh M. (2003) Precise orbit determination of a low Earth orbiting satellite, MSc thesis, K. N. Toosi University of Technology, Tehran, Iran.
  9. Eshagh M. (2005) Step-variable numerical orbit integration of a low Earth orbiting satellite, Journal of the Earth & Space Physics, 31, 1, 1-12.
  10. Eshagh M. (2008) Non-singular expression for the vector and gradient tensor of gravitation in a geocentric spherical frame, Computers & Geosciences, 34, 1762-1768.10.1016/j.cageo.2008.02.022
  11. Eshagh M. (2009a) Orbit integration in non-inertial frames, Journal of the Earth & Space Physics, 35, 1, 1-8.
  12. Eshagh M. (2009b) Alternative expressions for gravity gradients in local-north oriented frame and tensor spherical harmonics, Acta Geophysica, 58, 215-243.10.2478/s11600-009-0048-z
  13. Eshagh M. (2010a) Least-squares modification of extended Stokes’ formula and its secondorder radial derivative for validation of satellite gravity gradiometry data, Journal of Geodynamics, 49, 92-104.10.1016/j.jog.2009.11.003
  14. Eshagh M. (2010b) Towards validation of satellite gradiometric data using modified version of 2nd order partial derivatives of extended Stokes’ formula, Artificial Satellites, 44, 4, 103-129.10.2478/v10018-009-0024-5
  15. Eshagh M. (2011a) Semi-stochastic modification of second-order radial derivative of Abel- Poisson's formula for validating satellite gravity gradiometry data, Advances in Space Research, 47, 2, 757-767.10.1016/j.asr.2010.10.003
  16. Eshagh M. (2011b) The effect of spatial truncation error on integral inversion of satellite gravity gradiometry data, Advances in Space Research, 47, 1238-1247.10.1016/j.asr.2010.11.035
  17. Eshagh M. and Abdollahzadeh M. (2010) Semi-vectorization: an efficient technique for synthesis and analysis of gravity gradiometry data, Earth Science Informatics, 3,149-158.10.1007/s12145-010-0062-3
  18. Eshagh M. and Abdollahzadeh M. (2011) Software for generating gravity gradients using a geopotential model based on irregular semi-vectorization algorithm, Computers & Geosciences, 32, 152-160.10.1016/j.cageo.2011.06.003
  19. Eshagh M. and Najafi-Alamdari M. (2006) Comparison of different numerical integration methods of orbit integration, Journal of the Earth & Space Physics, 33, 1, 41-57. (in Persian)
  20. Eshagh M. and Najafi-Alamdari M. (2007) Perturbations in orbital elements of a low Earth orbiting satellite, Journal of the Earth & Space Physics, 33, 1, 1-12.
  21. Eshagh M. and Romeshkani M., (2011). Generation of vertical-horizontal and horizontalhorizontal gravity gradients using stochastically modified integral estimators, Advances in Space Research, 48, 1341−1358.10.1016/j.asr.2011.06.018
  22. Eshagh M. and Romeshkani M., (2013). Quality assessment for terrestrial gravity anomalies by variance component estimation using GOCE gradiometric data and Earth’s gravity models. Studia Geophysica et Geodaetica, 57, 67−83.10.1007/s11200-012-0820-4
  23. Eshagh M., Abdollahzadeh M., and Alamdari-Najafi M. (2009) Simplification of geopotential perturbing force acting on a satellite, Artificial Satellites, 43, 2, 45-64.10.2478/v10018-009-0006-7
  24. Haagmans R. Prijatna K. and Omang O. (2002) An alternative concept for validation of GOCE gradiometry results based on regional gravity, In Proc. Gravity and Geoid 2002, GG2002, August 26-30, Thessaloniki, Greece.
  25. Heiskanen W. and Moritz H. (1967) Physical Geodesy. W.H Freeman and company, San Francisco and London.10.1007/BF02525647
  26. Hirt C., Featherstone W.E. and Claessens S. J. (2011) On the accurate numerical evaluation of gedetic convolution integrals, Journal of Geodesy, 85, 519-538. 10.1007/s00190-011-0451-5
  27. Hwang C. and Lin J.M. (1998) Fast integration of low orbiter’s trajectory perturbed by the earth’s non-sphericity, Journal of Geodesy, 72, 578-585.10.1007/s001900050196
  28. IERS Conventions (2010). Gérard Petit and Brian Luzum (eds.). (IERS Technical Note ; 36) Frankfurt am Main: Verlag des Bundesamts für Kartographie und Geodäsie, 2010. 179 pp., ISBN 3-89888-989-6.
  29. Kaula W. (1966) Theory of satellite geodesy, Blaisdell, Waltheim Keller W. and Sharifi M. A. (2005) Satellite gradiometry using a satellite pair, Journal of Geodesy, , 78, 544-557.
  30. Kern M. and Haagmans R. (2004) Determination of gravity gradients from terrestrial gravity data for calibration and validation of gradiometric GOCE data, In Proc. Gravity, Geoid and Space missions, GGSM 2004, IAG International symposium, Portugal, August 30- September 3, pp. 95-100.
  31. Kern M., Preimesberger T., Allesch M., Pail. R., Bouman J. and Koop R. (2005) Outlier detection algorithms and their performance in GOCE gravity field processing, Journal of Geodesy, 78, 509-519.10.1007/s00190-004-0419-9
  32. Martinec Z. (1998) Boundary-Value Problems for Gravimetric Determination of a Precise Geoid, Springer Verlag, 240 p.
  33. Martinec Z. (2003) Green’s function solution to spherical gradiometric boundary-value problems, Journal of Geodesy, 77, 41-49.10.1007/s00190-002-0288-z
  34. Moritz H. (1980) Geodetic Reference System 1980, Bulletin Géodésique, 54:3.10.1007/BF02521480
  35. Moritz, H. (2000) Geodetic Reference System 1980, Journal of Geodesy, 74, 1, 128-162.10.1007/s001900050278
  36. Mueller J., Denker H., Jarecki F. and Wolf K.I. (2004) Computation of calibration gradients and methods for in-orbit validation of gradiometric GOCE data, In Proc. Second international GOCE user workshop “Goce, The Geoid and Oceanography”, ESA-ESRIN, Frascati, Italy, 8-10 March 2004.
  37. Novak P., Vanicek P., Veronneau M., Holmes SA. Featherstone WE. (2001) On the accuracy of modified Stokes’s integration in high-frequency gravimetric geoid determination, Journal of Geodesy, 74, 9, 644-654.10.1007/s001900000126
  38. Parrot D. (1989) Short arc orbit improvement for GPS satellites, MSc thesis, Department of Surveying Engineering, University of New Brunswick, Canada.
  39. Pail R. (2003) Local gravity field continuation for the purpose of in-orbit calibration of GOCE SGG observations, Advances in Geosciences, 1, 11-1810.5194/adgeo-1-11-2003
  40. Pavlis N., Holmes SA., Kenyon SC. and Factor JK. (2008) An Earth Gravitational model to degree 2160: EGM08. Presented at the 2008 General Assembly of the European Geosciences Union, Vienna, Austria, April 13-18, 2008.
  41. Petrovskaya P. and Vershkov A.N. (2006) Non-singular expressions for the gravity gradients in the local north-oriented and orbital frames. Journal of Geodesy, 80, 117-127.10.1007/s00190-006-0031-2
  42. Reed GB. (1973) Application of kinematical geodesy for determining the short wave length components of the gravity field by satellite gradiometer, The Ohio State University, Dept. of Geod. Sciences, Rep. No. 201, Columbus, Ohio.
  43. Reigber C., Schwintzer P. and Lühr H. (1999) The CHAMP geopotential mission, Boll. Geof. Teor. Appl. 40, 285-289.
  44. Reigber Ch., Jochmann H., Wünsch J., Petrovic S., Schwintzer P., Barthelmes F., Neumayer K.-H., König R., Förste Ch., Balmino G., Biancale R., Lemoine J.-M., Loyer S. and Perosanz F. (2004) Earth Gravity Field and Seasonal Variability from CHAMP. In: Reigber, Ch., Lühr, H., Schwintzer, P., Wickert, J. (eds.), Earth Observation with CHAMP - Results from Three Years in Orbit, Springer, Berlin, 25-30.
  45. Rim H. J. and Schutz B. E. (2001) Precision orbit determination (POD), Geoscience laser and altimeter satellite system, University of Texas, United States of America.
  46. Romeshkani M., (2011). Validation of GOCE Gravity Gradiometry Data Using Terrestrial Gravity Data. M.Sc. Thesis, K.N.Toosi University of Technology, Tehran, Iran.
  47. Rummel R., Sanso F., Gelderen M., Koop R., Schrama E., Brovelli M., Migiliaccio F., and Sacerdote F. (1993) Spherical harmonic analysis of satellite gradiometry. Publications in Geodesy, New Series, No. 39 Netherlands Geodetic Commission, Delft 10.54419/kmqa4w
  48. Santos M. C. (1994) On real time orbit improvement for GPS satellites, Ph.D thesis, Department of Geodesy and Geomatics Engineering, University of New Brunswick, Canada.
  49. Schwartz K-P., Sideris M.G. and Forsberg R. (1990) The use of FFT techniques in Physical Geodesy, Geophysical Journal International, 100, 3, 485-514.10.1111/j.1365-246X.1990.tb00701.x
  50. Sharifi M.A. (2006) Satellite to satellite tracking in the space-wise approach, PhD dissertation, Geodätisches Institut der Universität Stuttgart.
  51. Sneeuw N. (1992) Representation coefficients and their use in satellite geodesy, Manuscripta Geodaetica, 17, 117-123.
  52. Somodi B. and Földvary L. (2011) Application of numerical integration techniques for orbit determination of state-of-the-art LEO satellites, Per. Pol. Civil Eng., 55, 2, 99-106, 2011.
  53. Su H. (2000) Orbit determination of IGSO, GEO and MEO satellites, Ph.D thesis, Department of Geodesy, University of Bundeswehr, Munchen, Germany
  54. Tapley B., Ries J. Bettadpur S., Chambers D., Cheng M., Condi F., Gunter B., Kang Z., Nagel P., Pastor R., Pekker T., Poole S. and Wang F. (2005) GGM02-An improved Earth gravity field model from GRACE. Journal of Geodesy, 79, 467-478.10.1007/s00190-005-0480-z
  55. Toth G., Földvary L., Tziavos I. and Adam J. (2004) Upward/downward continuation of gravity gradients for precise geoid determination, Proc. Second International GOCE user workshop “GOCE, The Geoid and Oceanography”, ESA-ESRIN, Frascati, Italy, 8-10 March 2004.
  56. Toth G. and Földvary L. (2005) Effect of geopotential model errors in the projection of GOCE gradiometer observables, In: Gavity, Geoid and Space missions, IAG symposia, 129. (Eds.Jekeli C., Bastos J. and Fernandes L.), Spriner verlag, Berlin Heidelberg, p. 72-76.
  57. Tscherning C. C., Veicherts M. and Arabelos D. (2006) Calibration of GOCE gravity gradient data using smooth ground gravity, In Proc. GOCINA workshop, Cahiers de center European de Geodynamique et de seismilogie, 25, 63-67, Luxenburg.
  58. Vermeer M. (1990) Observable quantities in satellite gradiometry, Bulletin Geodaesique, 64, 347-36110.1007/BF02538408
  59. Visser P. (1992) The use of satellites in gravity field determination and adjustment, PhD dissertation, University of Delft Visser P. (2009) GOCE gradiometer: estimation of biases and scale factors of all six individual accelerometers by precise orbit determination, Journal of Geodesy, 83, 1, 69-85.
  60. Wolf R. (2000) Satellite orbit and ephemeris determination using inter satellite links, Ph.D thesis, Department of Geodesy, University of Bundeswehr, Munchen, Germany.
  61. Wolf K. I. (2007) Kombination globaler potentialmodelle mit terresrischen schweredaten fur die berechnung der zweiten ableitungen des gravitationspotentials in satellitenbahnhohe, PhD thesis, University of Hannover, Germany.
  62. Zielinski J.B. and Petrovskaya M.S. (2003) The possibility of the calibration/validation of the GOCE data with the balloon-borne gradiometer, Advances in Geosciences, 1, 149-153. 10.5194/adgeo-1-149-2003
DOI: https://doi.org/10.2478/arsa-2014-0006 | Journal eISSN: 2083-6104 | Journal ISSN: 1509-3859
Language: English
Page range: 63 - 80
Submitted on: Feb 28, 2014
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Accepted on: Mar 21, 2014
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Published on: Jun 6, 2014
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2014 Mehdi Eshagh, published by Polish Academy of Sciences, Space Research Centre
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.