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Globale Schwerefeldmodellierung am Beispiel von GOCE

  • Roland Pail
Chapter
Part of the Springer Reference Naturwissenschaften book series (SRN)

Zusammenfassung

Die Satellitenmissionen CHAMP, GRACE und GOCE lieferten neuartige Information über das globale Schwerefeld der Erde. In diesem Beitrag werden die wichtigsten Aspekte der Modellierung des statischen Schwerefeldes aus Satellitendaten und die dabei verwendeten statistisch-numerischen Werkzeuge exemplarisch für die GOCE-Mission diskutiert. Die neue Generation von GOCE-Modellen liefert Genauigkeiten von 2–3 cm in Geoidhöhe und 0,7 mGal in Schwereanomalien bei 100 km räumlicher Wellenlänge. Noch höhere räumliche Auflösung wird durch Kombination mit terrestrischen Schwerefeldbeobachtungen erreicht.

Schlüsselwörter

GOCE Globales Schwerefeldmodell Sphärisch-harmonische Reihenentwicklung Gravitationsgradienten Ausgleichungsrechnung 

Literatur

  1. 1.
    Badura, T.: Gravity Field Analysis from Satellite Orbit Information applying the Energy Integral Approach. Dissertation, 109 S., Graz University of Technology. (2006)Google Scholar
  2. 2.
    Bingham, R.J., Knudsen, P., Andersen, O., Pail, R.: An initial estimate of the North Atlantic steady-state geostrophic circulation from GOCE. Geophys. Res. Lett. 38, EID L01606. Am. Geophys. Union (2011). doi:10.1029/2010GL045633Google Scholar
  3. 3.
    Bock, H., Jäggi, A., Meyer, U., Visser, P., van den IJssel, J., van, T., Helleputte, M., Heinze, Hugentobler, U.: GPS-derived orbits for the GOCE satellite. J. Geod. 85(11), 807–818 (2011). doi:10.1007/s00190-011-0484-9Google Scholar
  4. 4.
    Bouman, J., Rispens, S., Gruber, T., Koop, R., Schrama, E., Visser, P.N.A.M., Tscherning, C.C., Veicherts, M.: Preprocessing of gravity gradients at the GOCE high-level processing facility. J. Geod. 83(7), 659–678 (2009). doi:10.1007/s00190-008-0279-9CrossRefGoogle Scholar
  5. 5.
    Braitenberg, C.: Exploration of tectonic structures with GOCE in Africa and across-continents. Int. J. Appl. Earth Obs. Geoinformation, 01/2014; (2015). doi:10.1016/j.jag.2014.01.013Google Scholar
  6. 6.
    Braitenberg, C., Pivetta, T., Li, Y.: The youngest generation GOCE products in unraveling the mysteries of the crust of North-Central Africa. Geophys. Res. Abs. 14, EGU2012-6022. EGU General Assembly 2012, Vienna (2012)Google Scholar
  7. 7.
    Brockmann, J.M., Zehentner, N., Höck, E., Pail, R., Loth, I., Mayer-Gürr, T., Schuh, W.-D.: (2014) EGM_TIM_RL05: an independent geoid with centimeter accuracy purely based on the GOCE mission. Geophys. Res. Lett., Online 25 Nov 2014. doi:10.1002/2014GL061904Google Scholar
  8. 8.
    Bruinsma, S.L., Doornbos, E., Bowman, B.R.: Validation of GOCE densities and evaluation of thermosphere models. Adv. Sp. Res. 08/2014, (2014a). doi:10.1016/j.asr.2014.04.008Google Scholar
  9. 9.
    Bruinsma, S.L., Foerste, C., Abrikosov, O., Marty, J.C., Rio, M.H., Mulet, S., Bonvalot, S.: The new ESA satellite-only gravity field model via the direct approach. Geophys. Res. Lett. 40, 3607–3612 (2013). doi:10.1002/grl.50716CrossRefGoogle Scholar
  10. 10.
    Bruinsma, S.L., Foerste, C., Abrikosov, O., Lemoine, J.M., Marty, J.C., Mulet, S., Rio, M.H., Bonvalot, S.: ESA’s satellite-only gravity field model via the direct approach based on all GOCE data. Geophys. Res. Lett. 41(21), 7508–7514 (2014b). doi:10.1002/2014GL062045CrossRefGoogle Scholar
  11. 11.
    Drinkwater, M.R., Floberghagen, R., Haagmans, R., Muzi, D., Popescu, A.: GOCE: ESA’s first earth explorer core mission. In: Beutler, G., Drinkwater, M.R., Rummel, R., von Steiger, R. (Hrsg.) Earth Gravity Field from Space – From Sensors to Earth Sciences. Space Sciences Series of ISSI, Bd. 17, S. 419–432. Kluwer, Dordrecht (2003). ISBN:1-4020-1408-2CrossRefGoogle Scholar
  12. 12.
    Eicker, A.: Gravity field refinements by radial basis functions from in-situ satellite data. Ph.D. thesis, University of Bonn (2008)Google Scholar
  13. 13.
    Fecher, T., Pail, R., Gruber, T.: Global gravity field modeling based on GOCE and complementary gravity data. Int. J. Appl. Earth Obs. Geoinformation. ISSN (Online) 0303-2434 (2013). doi:10.1016/j.jag.2013.10.005Google Scholar
  14. 14.
    Floberghagen, R., Fehringer, M., Lamarre, D., Muzi, D., Frommknecht, B., Steiger, C., Piñeiro, J., da Costa, A.: Mission design, operation and exploitation of the gravity field and steady-state ocean circulation explorer mission. J. Geod. 85(11), 749–758 (2011). doi:10.1007/s00190-011-0498-3CrossRefGoogle Scholar
  15. 15.
    Förste, C., Bruinsma, S.L., Flechtner, F., Marty, J.C., Lemoine, J.M., Dahle, C., Abrikosov, O., Neumayer, K.H., Biancale, R., Barthelmes, F., Balmino, G.: A preliminary update of the Direct approach GOCE Processing and a new release of EIGEN-6C. Presented at the AGU Fall Meeting 2012, San Francisco. Abstract No. G31B-0923. 3–7 Dec 2012Google Scholar
  16. 16.
    Freeden, W., Gervens, T., Schreiner, M.: Constructive Approximation on the Sphere. Clarendon Press, Oxford (1998)Google Scholar
  17. 17.
    Goiginger, H., Pail, R.: Investigation of velocities derived from satellite positions in the framework of the energy integral approach. In: Fletcher K et al. (Hrsg.) Proceedings 3rd International GOCE User Workshop, ESA SP-627, S. 319–324, ESA, (2007). ISBN (Print) 92-9092-938-3, ISSN: 1609-042XGoogle Scholar
  18. 18.
    Goiginger, H. und R. Pail.. Covariance propagation of latitude-dependent orbit errors within the energy integral approach. In: Mertikas SP et al (Hrsg.) Gravity, Geoid and Earth Observation, IAG Symposia, 135, S. 155–161, Springer, (2010) doi: 10.1007/978-3-642-10634-7_21.Google Scholar
  19. 19.
    Gruber, T., Visser, P.N.A.M., Ackermann, C., Hosse, M.: Validation of GOCE gravity fieldmodels by means of orbit residuals and geoid comparisons. J. Geod. 85(11), 845–860. Springer (2011). doi:10.1007/s00190-011-0486-7Google Scholar
  20. 20.
    Hirt, C., Claessens, S., Fecher, T., Kuhn, M., Pail, R., Rexer, M.: New ultra-high resolution picture of Earth’s gravity field. Geophys. Res. Lett. 2013 (2013). doi:10.1002/grl.50838Google Scholar
  21. 21.
    Hosse, M., Pail, R., Horwath, M., Holzrichter, N., Gutknecht, B.D.: Combined regional gravity model of the Andean convergent subduction zone and its application to crustal density modelling in active plate margins. Surv. Geophys. ol. 2014, 6, 1393–1415 (2014). doi:10.1007/s10712-014-9307-xCrossRefGoogle Scholar
  22. 22.
    Ihde, J., Sacher, M.: EUREF Publication 11/I, Bd. 25. Mitteilungen des Bundesamtes für Kartographie und Geodäsie, Frankfurt/Main (2002)Google Scholar
  23. 23.
    Jekeli, C.: The determination of gravitational potential differences from satellite-to-satellite tracking. Celest. Mech. Dyn. Astron. 75, 85–101 (1999)CrossRefGoogle Scholar
  24. 24.
    Kern, M., Preimesberger, T., Allesch, M., Pail, R., Bouman, J., Koop, R.: Outlier detection algorithms and their performance in GOCE gravity field processing. J. Geod. 78(9), 509–519. Springer (2005). doi:10.1007/s00190-004-0419-9Google Scholar
  25. 25.
    Knudsen, P., Bingham, R., Andersen, O., Rio, M.-H.: A global mean dynamic topography and ocean circulation estimation using a preliminary GOCE gravity model. J. Geod. 85(11), 861–879 (2011). doi:10.1007/s00190-011-0485-8CrossRefGoogle Scholar
  26. 26.
    Koch, K.H., Kusche, J.: Regularization of geopotential determination from satellite data by variance components. J. Geod. 76, 259–268. Springer (2002). doi:10.1007/s00190-002-0245-xGoogle Scholar
  27. 27.
    Krarup, T.: A Contribution to the Mathematical Foundation of Physical Geodesy, Bd. 44. Geodætisk Instituts Meddelelse, Copenhagen (1969)Google Scholar
  28. 28.
    Lemoine, F., Luthcke, S., Rowlands, D., Chinn, D., Klosko, S., Cox, C.: The use of mascons to resolve time-variable gravity from GRACE. In: Tregoning, P., et al. (Hrsg.) Dynamic Planet, S. 231–236. Springer, Berlin (2007)CrossRefGoogle Scholar
  29. 29.
    Mayer-Gürr, T.: Gravitationsfeldbestimmung aus der Analyse kurzer Bahnbögen am Beispiel der Satellitenmissionen CHAMP und GRACE. Dissertation, University of Bonn (2006)Google Scholar
  30. 30.
    Mayer-Gürr, T., Eicker, A., Kurtenbach, E., Ilk, K.-H.: ITG-GRACE: global static and temporal gravity field models from GRACE data. In: Flechtner, F., Gruber, T., Güntner, A., Mandea, M., Rothacher, M., Schöne, T., Wickert, J. (Hrsg.) System Earth via Geodetic-Geophysical Space Techniques, S. 159–168 (2010). doi:10.1007/978-3-642-10228-8_13Google Scholar
  31. 31.
    Metzler, B.: Spherical cap regularization – a spatially restricted regularization method tailored to the polar gap problem. Dissertation, TU Graz (2007)Google Scholar
  32. 32.
    Metzler, B., Pail, R.: GOCE data processing: the spherical cap regularization approach. Stud. Geophys. Geod. 49, 441–462 (2005). doi:10.1007/s11200-005-0021-5CrossRefGoogle Scholar
  33. 33.
    Migliaccio, F., Reguzzoni, M., Sansò, F., Tscherning, C.C., Veicherts, M.: GOCE data analysis: the space-wise approach and the first space-wise gravity field model. In: Lacoste-Francis, H. (Hrsg.) Proceedings of the ESA Living Planet Symposium, ESA Publication SP-686, ESA/ESTEC, Noordwijk (2010)Google Scholar
  34. 34.
    Moritz, H.: Advanced least-squares methods. Reports of the Department of Geodetic Science, no. 175, The Ohio State University (1972)Google Scholar
  35. 35.
    Moritz, H.: Least-squares collocation. Rev. Geophys. Space Phys. 16(3), 421–430 (1978)CrossRefGoogle Scholar
  36. 36.
    Pail, R.: A parametric study on the impact of satellite attitude errors on GOCE gravity field recovery. J. Geod. 79, 231–241. Springer (2005). doi:10.1007/s00190-005-0464-zGoogle Scholar
  37. 37.
    Pail, R., Bingham, R., Braitenberg, C., Dobslaw, H., Eicker, A., Güntner, A., Horwath, M., Ivins, E., Longuevergne, L., Panet, I., Wouters, B.: Science and User Needs for Observing Global Mass Transport to Understand Global Change and to Benefit Society. Surv. in Geophys. 36(6), 743-772 (2015). doi: 10.1007/s10712-015-9348-9CrossRefGoogle Scholar
  38. 38.
    Pail, R., Bruinsma, S., Migliaccio, F., Förste, C., Goiginger, H., Schuh, W.-D., Höck, E., Reguzzoni, M., Brockmann, J.M., Abrikosov, O., Veicherts, M., Fecher, T., Mayrhofer, R., Krasbutter, I., Sansó, F., Tscherning, C.C.: First GOCE gravity field models derived by three different approaches. J. Geod. 85(11), 819–843. Springer (2011). doi:10.1007/s00190-011-0467-xGoogle Scholar
  39. 39.
    Pail, R., Fecher, T., Murböck, M., Rexer, M., Stetter, M., Gruber, T., Stummer, C.: Impact of GOCE Level 1b data reprocessing on GOCE-only and combined gravity field models. Studia Geophys. Geod. 57, 155–173 (2013). doi:10.1007/s11200-012-1149-8CrossRefGoogle Scholar
  40. 40.
    Pail, R., Goiginger, H., Schuh, W.-D., Höck, E., Brockmann, J.M., Fecher, T., Gruber, T., Mayer-Gürr, T., Kusche, J., Jäggi, A., Rieser, D.: Combined satellite gravity field model GOCO01S derived from GOCE and GRACE. Geophys. Res. Lett. 37, EID L20314. American Geophysical Union (2010b). doi:10.1029/2010GL044906Google Scholar
  41. 41.
    Pail, R., Plank, G.: Assessment of three numerical solution strategies for gravity field recovery from GOCE satellite gravity gradiometry implemented on a parallel platform. J. Geod. 76, 462–474. Springer (2002). doi:10.1007/s00190-002-0277-2Google Scholar
  42. 42.
    Pail, R., Wermuth, M.: GOCE SGG and SST quick-look gravity field analysis. Adv. Geosci. 1, 5–9 (2003)CrossRefGoogle Scholar
  43. 43.
    Panet, I., Chambodut, A., Diament, M., Holschneider, M., Jamet, O.: New insights on intra-plate volcanism in French Polynesia from wavelet analysis of GRACE, CHAMP and sea-surface data. J. Geophys. Res. 111(B9), B09403 (2006). doi:10.1029/2005JB00 4141Google Scholar
  44. 44.
    Pavlis, N.K., Holmes, S.A., Kenyon, S.C., Factor, J.K.: The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). J. Geophys. Res. 117(B04406), 38 (2012). doi:10.1029/2011JB008916Google Scholar
  45. 45.
    Rapp, R.H., Basic, T.: Oceanwide gravity anomalies from GEOS-3, SEASAT and GEOSAT altimeter data. J. Geophys. Res. Lett. 19(19), 1979–1982 (1992)CrossRefGoogle Scholar
  46. 46.
    Reigber, C., Balmino, G., Schwintzer, P., Biancale, R., Bode, A., Lemoine, J.-M., Koenig, R., Loyer, S., Neumayer, H., Marty, J.C., Barthelmes, F., Perossanz, F.: A high quality global gravity field model from CHAMP GPS tracking data and accelerometry (EIGEN-1S). Geophys. Res. Lett. 29, 14 (2002). http://dx.doi.org/10.1029/2002GL015064 CrossRefGoogle Scholar
  47. 47.
    Rudenko, S., Dettmering, D., Esselborn, S., Schoene, T., Foerste, C., Lemoine, J.-M., Ablain, M., Alexandre, D., Neumayer, K.-H.: Influence of time variable geopotential models on precise orbits of altimetry satellites, global and regional mean sea level trends. Adv. Space Res. (2014). doi:10.1016/j.asr.2014.03.010Google Scholar
  48. 48.
    Rummel, R.: GOCE: gravitational gradiometry in a satellite. In: Freeden, W., Nashed, M.Z., Sonar, T. (Hrsg.) Handbook of Geomathematics, Bd. 2, S. 93–103. Springer (2010). doi:10.1007/978-3-642-01546-5_4Google Scholar
  49. 49.
    Rummel, R.: Height unification using GOCE. J. Geod. Sci. 2012, 2(Heft 4), 355–362 (2013). Versita. doi:10.2478/v10156-011-0047-2Google Scholar
  50. 50.
    Rummel, R., Gruber, T., Koop, R.: High level processing facility for GOCE: products and processing strategy. In: Lacoste, H. (Hrsg.) Proceedings 2nd International GOCE User Workshop „GOCE, The Geoid and Oceanography“, ESA SP-569, ESA, Noordwijk (2004)Google Scholar
  51. 51.
    Rummel, R., Yi, W., Stummer, C.: GOCE gravitational gradiometry. J. Geod. 85(11), 777–790. Springer (2011). doi:10.1007/s00190-011-0500-0Google Scholar
  52. 52.
    Sampietro, D., Reguzzoni, M., Braitenberg, C.: The GOCE estimated Moho Beneath the Tibetan Plateau and Himalaya. In: Rizos, C., Willis, P. (Hrsg.) Earth on the Edge: Science for a Sustainable Planet. International Association of Geodesy Symposia, Bd. 139, S. 391–397 (2014). doi:10.1007/978-3-642-37222-3_52CrossRefGoogle Scholar
  53. 53.
    Schall, J., Eicker, A., Kusche, J.: The ITG-Goce02 gravity field model from GOCE orbit and gradiometer data based on the short arc approach. J. Geod. 88(4), 403–409 (2014). doi:10.1007/s00190-014-0691-2CrossRefGoogle Scholar
  54. 54.
    Schmidt, M., Fengler, M., Mayer-Gürr, T., Eicker, A., Kusche, J., Sanchez, L., Han, S.-C.: Regional gravity modelling in terms of spherical base functions. J. Geod. 81, 17–38 (2007). doi:10.1007/s00190-006-0101-5CrossRefGoogle Scholar
  55. 55.
    Schneider, M.: A general method of orbit determination. Library Translation, Band 1279, Royal Aircraft Establishment, Ministry of Technology, Farnborough (1968)Google Scholar
  56. 56.
    Schuh, W.-D.: Tailored numerical solution strategies for the global determination of the Earth’s gravity field. Mitteil. Geod. Inst. TU Graz, 81, 156. Graz. (1996)Google Scholar
  57. 57.
    Schwarz, K.P., Sideris, M.G., Forsberg, R.: The use of FFT techniques in physical geodesy. Geophys. J. Int. 100, 485–514 (1990)CrossRefGoogle Scholar
  58. 58.
    Siemes, C.: Digital filtering algorithms for decorrelation within large least squares problems. Dissertation, University of Bonn, Germany (2008)Google Scholar
  59. 59.
    Sneeuw, N.: A semi-analytical approach to gravity field analysis from satellite observations. Dissertation, DGK, Reihe C, no. 527, Bayerische Akademie Wissenschaften, Munich (2000)Google Scholar
  60. 60.
    Sneeuw, N., van Gelderen, M.: The polar gap. In: Geodetic Boundary Value Problems in View of the One Centimeter Geoid. Lecture Notes in Earth Sciences, Bd. 65, S. 559–568. Springer, Berlin (1997). doi:10.1007/BFb0011699Google Scholar
  61. 61.
    Stetter, M.: Stochastische Modellierung von GOCE-Gradiometerbeobachtungen mittels digitaler Filter. Master Thesis, no. D240, TU München (2012)Google Scholar
  62. 62.
    Stummer, C., Fecher, T., Pail, R.: Alternative method for angular rate determination within the GOCE gradiometer processing. J. Geod. 85(11), 585–596. Springer (2011). doi:10.1007/s00190-011-0461-3Google Scholar
  63. 63.
    Stummer, C., Siemes, C., Pail, R., Frommknecht, B., Floberghagen, R.: Upgrade of the GOCE level 1b gradiometer processor. Adv. Space. Res. 49(4), 739–752 (2012). doi:10.1016/j.asr.2011.11.027CrossRefGoogle Scholar
  64. 64.
    Tapley, B.D., Bettadpur, S., Watkins, M., Reigber, C.: The gravity recovery and climate experiment: mission overview and early results. Geophys. Res. Lett. 31(9), L09607, AmericanGeophysical Union (2004). http://dx.doi.org/10.1029/2004GL019920
  65. 65.
    van der Meijde, M., Julià, J., Assumpção, M.: Gravity derived Moho for South America. Tectonophysics 609, 456–467 (2013). doi:10.1016/j.tecto.2013.03.023CrossRefGoogle Scholar
  66. 66.
    Vanícek, P., Wells, D., Derenyi, E., Kleusberg, A., Yazdani, R., Arsenault, T., Christou, N., Mantha, J., Pagiatakis, S.: Satellite altimetry applications for marine gravity. Technical report No.128, Dept. of Surveying Engineering, University of New Brunswick, Fredericton (1987)Google Scholar
  67. 67.
    Yi, W., Rummel, R., Gruber, T.: Gravity field contribution analysis of GOCE gravitational gradient components. Studia Geophysica et Geodaetica 57(2), 174–202 (2013). ISSN (Online) 1573–1626. doi:10.1007/s11200-011-1178-8Google Scholar
  68. 68.
    Yoder, C.F., Williams, J.G., Dickey, J.O., Schutz, B.E., Eanes, R.J., Tapley, B.D.: Secular variation of Earth’s gravitational harmonic J2 coefficient from Lageos and non-tidal acceleration of Earth rotation. Nature 303, 757–762 (1983)CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Institut für Astronomische und Physikalische GeodäsieTechnische Universität MünchenMünchenDeutschland

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