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Topographische Modellierung des Gravitationsfeldes

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Erdmessung und Satellitengeodäsie

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Zusammenfassung

Topographische Techniken zur Modellierung von Gravitationsfeldern nehmen eine zentrale Rolle in der physikalischen Geodäsie und Geophysik ein. Aus der Topographie gewonnene Schwereinformation ist notwendig für (i) die Reduktion und Interpolation von Schwerefeldbeobachtungen, (ii) die Entwicklung ultra-hochauflösender Schwerefeldmodelle und (iii) die Interpretation von Schwerefeldbeobachtungen. Das vorliegende Kapitel führt in die grundlegenden Methoden der topographischen Modellierung von Gravitationsfeldern ein, wobei eine Unterteilung in numerische Integrations- und Kugelfunktionstechniken erfolgt. Es werden eine Reihe von aktuellen Anwendungsbeispielen gegeben, die von der Erstellung ultra-hochauflösender Schwerefeldmodelle, der Glättung von Schwerefelddaten bis zur Berechnung von Bouguer-Schwerekarten für Erde und Mond reichen. Der Beitrag zeigt zusammenfassend die heutige Relevanz der topographischen Gravitationsfeldmodellierung für erdbezogene und planetare geodätische Anwendungen auf.

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Literatur

  1. Abd-Elmotaal, H., Seitz K., Abd-Elbaky M., Heck, B.: Comparison among three harmonic analysis techniques on the sphere and the ellipsoid. J. Appl. Geodesy 8(1), 1–19 (2014)

    Article  Google Scholar 

  2. Amante, C., Eakins, B.W.: ETOPO1 1 Arc-Minute Global Relief Model: Procedures, Data Sources and Analysis. NOAA Technical Memorandum NESDIS NGDC-24. National Geophysical Data Center, Boulder (2009)

    Google Scholar 

  3. Balmino, G., Vales, N., Bonvalot, S., Briais, A.: Spherical harmonic modelling to ultra-high degree of Bouguer and isostatic anomalies. J. Geodesy 86(7), 499–520 (2012)

    Article  Google Scholar 

  4. Baran I., Kuhn, M., Claessens, S.J., Featherstone, W.E., Holmes, S.A., Vanček, P.: A synthetic Earth gravity model designed specifically for testing regional gravimetric geoid determination algorithms. J. Geodesy 80(1), 1–16 (2006)

    Article  Google Scholar 

  5. Becker, J.J., Sandwell, D.T., Smith, W.H.F., Braud, J., Binder, B., Depner, J., Fabre, D., Factor, J., Ingalls, S., Kim, S.-H., Ladner, R., Marks, K., Nelson, S., Pharaoh, A., Trimmer, R., Von Rosenberg, J., Wallace, G., Weatherall, P.: Global bathymetry and elevation data at 30 arc seconds resolution: SRTM30_PLUS. Marine Geodesy 32(4), 355–371 (2009)

    Article  Google Scholar 

  6. Bezdek, A., Sebera, J.: Matlab script for 3D visualizing geodata on a rotating globe. Comput. Geosci. 56, 127–130 (2013)

    Article  Google Scholar 

  7. Blakeley, R.J.: Potential theory in gravity and magnetic applications. Cambridge University Press, Cambridge (1996)

    Google Scholar 

  8. Bonvalot, S., Balmino, G., Briasis, A., Kuhn, M., Peyrefitte, A., Vales, N., et al.: World Gravtiy Map, 1:50,000,000 map, Eds. BGI-CGMW-CNES-IRD, Paris (2012)

    Google Scholar 

  9. Braitenberg, C.: Exploration of tectonic structures with GOCE in Africa and across-continents. Int. J. Appl. Earth Observ. Geoinf. 35, 88–95 (2015)

    Article  Google Scholar 

  10. Brockmann, J.M., Zehentner, N., Höck, E., Pail, R., Loth, I., Mayer-Gürr, T., Schuh, W.-D.: EGM_TIM_RL05: an independent geoid with centimeter accuracy purely based on the GOCE mission. Geophys. Res. Lett. 41, 8089–8099 (2014)

    Article  Google Scholar 

  11. Bruinsma, S.L., Förste, 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)

    Article  Google Scholar 

  12. Claessens, S.J., Hirt, C.: Ellipsoidal topographic potential – new solutions for spectral forward gravity modelling of topography with respect to a reference ellipsoid. J. Geophys. Res. 118(7), 5991–6002 (2013)

    Article  Google Scholar 

  13. Denker, H.: Hochauflösende regionale Schwerefeldbestimmung mit gravimetrischen und topographischen Daten. Wiss. Arb. Fach. Verm. Univ. Hannover 156 (1988)

    Google Scholar 

  14. Denker, H.: Regional gravity field modeling: theory and practical results. In: Xu, G. (Hrsg.) Sciences of Geodesy – II, S. 185–291. Springer, Berlin/Heidelberg (2013)

    Chapter  Google Scholar 

  15. D’Urso, M.G.: Analytical computation of gravity effects for polyhedral bodies. J. Geodesy 88(1), 13–29 (2014)

    Article  Google Scholar 

  16. Elmiger, A.: Studien über Berechnung von Lotabweichungen aus Massen, Interpolation von Lotabweichungen und Geoidbestimmung in der Schweiz. Mitt. Inst. Geod. Phot. ETH Zürich Nr. 12 (1969)

    Google Scholar 

  17. Flury, J.: Schwerefeldfunktionale im Gebirge – Modellierungsgenauigkeit, Messpunktdichte und Darstellungsfehler am Beispiel des Testnetzes Estergebirge. Deutsche Geodätische Kommission C 557, München (2002)

    Google Scholar 

  18. Forsberg, R., Tscherning, C.C.: The use of height data in gravity field approximation by collocation. J. Geophys. Res. 86(B9), 7843–7854 (1981)

    Article  Google Scholar 

  19. Forsberg, R.: A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modelling. OSU Report 355. Department of Geodetic Science and Surveying, Ohio State University, Columbus (1984)

    Google Scholar 

  20. Forsberg, R.: Gravity field terrain effect computations by FFT. Bull. Geodesique 59, 342–360 (1985)

    Article  Google Scholar 

  21. Fretwell, P., Pritchard, H.D., Vaughan, D.G., Bamber, J.L., et al.: Bedmap2: improved ice bed, surface and thickness datasets for Antarctica. The Cryosphere 7, 375–393 (2013)

    Article  Google Scholar 

  22. Göttl, F., Rummel, R.: A geodetic view on isostatic models. Pure Appl. Geophys. 166(8–9), 1247–1260 (2009)

    Article  Google Scholar 

  23. Goossens, S., Matsumoto, K., Liu, Q., Kikuchi, F., Sato, K., Hanada, H., Ishihara, Y., Noda, H., Kawano, N., Namiki, N., Iwata, T., Lemoine, F.G., Rowlands, D.D., Harada, Y., Chen, M.: Lunar gravity field determination using SELENE same-beam differential VLBI tracking data. J. Geodesy 85(4), 205–228 (2011)

    Article  Google Scholar 

  24. Grombein, T., Seitz, K., Heck, B.: Modelling topographic effects in GOCE gravitygradients. GEOTECHNOLOGIEN Science Report 17, 84–93 (2010)

    Google Scholar 

  25. Grombein, T., Seitz, K., Heck, B.: Optimized formulas for the gravitational field of a tesseroid. J. Geodesy 87(7), 645–660 (2013)

    Article  Google Scholar 

  26. Grombein, T., Luo, X., Seitz, K., Heck, B.: A wavelet-based assessment of topographic-isostatic reductions for GOCE gravity gradients. Surv. Geophys. 35(4), 959–982 (2014)

    Article  Google Scholar 

  27. Gruber, C., Novák, P., Flechtner, F., Barthelmes, F.: Derivation of the topographic potential from global DEM models. In: Rizos, C., Willis, P. (Hrsg.) International Association of Geodesy Symposia, Bd. 139, S. 535–542. Springer, Berlin/Heidelberg (2013)

    Google Scholar 

  28. Heck, B., Seitz, K.: A comparison of the tesseroid, prism and point-mass approaches for mass reductions in gravity field modelling. J. Geodesy 81(2), 121–136 (2007)

    Article  Google Scholar 

  29. Hirt, C.: Prediction of vertical deflections from high-degree spherical harmonic synthesis and residual terrain model data. J. Geodesy 84(3), 179–190 (2010)

    Article  Google Scholar 

  30. Hirt, C.: GOCE’s view below the ice of Antarctica: satellite gravimetry confirms improvements in Bedmap2 bedrock knowledge. Geophys. Res. Lett. 41(14), 5021–5028 (2014)

    Article  Google Scholar 

  31. Hirt, C., Flury, J.: Astronomical-topographic levelling using high-precision astrogeodetic vertical deflections and digital terrain model data. J. Geodesy 82(4–5), 231–248 (2008)

    Article  Google Scholar 

  32. Hirt, C., Kuhn, M.: Evaluation of high-degree series expansions of the topographic potential to higher-order powers. J. Geophys. Res. Solid Earth 117, B12407 (2012)

    Google Scholar 

  33. Hirt, C., Kuhn, M.: A band-limited topographic mass distribution generates a full-spectrum gravity field – gravity forward modelling in the spectral and spatial domain revisited. J. Geophys. Res. Solid Earth 119(4), 3646–3661 (2014)

    Article  Google Scholar 

  34. Hirt, C., Featherstone, W.E.: A 1.5 km-resolution gravity field model of the Moon. Earth Planet. Sci. Lett. 329–330, 22–30 (2012)

    Google Scholar 

  35. Hirt, C., Featherstone, W.E., Marti, U.: Combining EGM2008 and SRTM/DTM2006.0 residual terrain model data to improve quasigeoid computations in mountainous areas devoid of gravity data. J. Geodesy 84(9), 557–567 (2010)

    Google Scholar 

  36. Hirt, C., Kuhn, M., Featherstone, W.E., Göttl, F.: Topographic/isostatic evaluation of new-generation GOCE gravity field models. J. Geophys. Res. 117, B05407 (2012)

    Google Scholar 

  37. Hirt, C., Claessens, S.J., Kuhn, M., Featherstone, W.: Kilometer-resolution gravity field of Mars: MGM2011. Planet. Space Sci. 67, 147–154 (2012)

    Article  Google Scholar 

  38. Hirt, C., Claessens, S.J., Fecher, T., Kuhn, M., Pail, R., Rexer, M.: New ultra-high resolution picture of Earth’s gravity field. Geophys. Res. Lett. 40(16), 4279–4283 (2013)

    Article  Google Scholar 

  39. Hirt, C., Rexer, M.: Earth2014: 1 arc-min shape, topography, bedrock and ice-sheetmodels – available as gridded data and degree-10,800 spherical harmonics. International Journal of Applied Earth Observation and Geoinformation 39, 103–112 (2015)

    Article  Google Scholar 

  40. Hwang, C., Wang, C.-G., Hsiao, Y.-S.: Terrain correction computation using Gaussian quadrature. Comput. Geosci. 29, 1259–1268 (2003)

    Article  Google Scholar 

  41. Jacoby, W., Smilde, P.L.: Gravity interpretation. Springer, New York (2009)

    Google Scholar 

  42. Laske, G., Masters, G., Ma, Z., Pasyanos, M.: Update on CRUST1.0 – a 1-degree global model of Earth’s crust. Geophys. Res. Abstr. 15, Abstract EGU2013-2658 (2013)

    Google Scholar 

  43. Li, F., Yan, J., Xu, L., Jin, S., Alexis, J., Rodriguez, P., Dohm, J.H.: A 10 km-resolution synthetic Venus gravity field model based on topography. Icarus 247, 103–111 (2015)

    Article  Google Scholar 

  44. Kaban, M.K., Schwintzer, P., Reigber, C.: A new isostatic model of the lithosphere and gravity field. J. Geodesy 78(6), 368–385 (2004)

    Article  Google Scholar 

  45. Kaban, M.K., Mooney, W.D.: Density structure of the lithosphere in the Southwestern United States and its tectonic significance. J. Geophys. Res. 106(B1), 721–739 (2001)

    Article  Google Scholar 

  46. Kuhn, M.: Geoidbestimmung unter Verwendung verschiedener Dichtehypothesen. Deutsche Geodätische Kommission C 520, München (2000)

    Google Scholar 

  47. Kuhn, M.: Geoid determination with density hypotheses from isostatic models and geological information. J. Geodesy 77(1–2), 50–65 (2003)

    Article  Google Scholar 

  48. Kuhn, M., Featherstone, W.E.: On the construction of a synthetic Earth gravity model. In: Tziavos, I. (Hrsg.) Proceed 3rd Meeting of the Intern. Gravity and Geoid Commission, S. 189–194. Thessaloniki: Editions Ziti (2003)

    Google Scholar 

  49. Kuhn, M., Featherstone, W.E., Kirby, J.F.: Complete spherical Bouguer gravity anomalies over Australia. Aust. J. Earth Sci. 56(2), 213–223 (2009)

    Article  Google Scholar 

  50. Kuhn, M.; Hirt, C.: Topographic gravitational potential up to second-order derivatives: an examination of approximation errors caused by Rock-Equivalent-Topography (RET), unter Begutachtung (2016)

    Google Scholar 

  51. Lemoine, F.G., Goossens, S., Sabaka, T.J., Nicholas, J.B., Mazarico, E., Rowlands, D.D., Loomis, B.D., Chinn, D.S., Neumann, G.A., Smith, D.E., Zuber, M.T.: GRGM900C: a degree-900 lunar gravity model from GRAIL primary and extended mission data. Geophys. Res. Lett. 41(6), 3382–3389 (2014)

    Article  Google Scholar 

  52. Makhloof, A.A.: The use of topographic-isostatic mass information in geodetic applications. Dissertation D98, Institut für Geodäsie und Geoinformation der Universität Bonn (2007)

    Google Scholar 

  53. Marti, U.: Geoid der Schweiz 1997. Geodätisch-geophysikalische Arbeiten in der Schweiz Nr. 56. Schweizerische Geodätische Kommission (1997)

    Google Scholar 

  54. Nagy, D., Papp, G., Benedek, J.: The gravitational potential and its derivatives for the Prism. J. Geodesy 74(7–8), 552–560 (2000); Erratum in J. Geodesy 76(8), 475

    Google Scholar 

  55. Novák, P., Tenzer, R.: Gravitational gradients at satellite altitudes in global geophysical studies. Surv. Geophys. 34(5), 653–673 (2013)

    Article  Google Scholar 

  56. 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., Sansò, F., Tscherning, C.C.: First GOCE gravity field models derived by three different approaches. J. Geodesy 85(7), 819–843 (2011)

    Article  Google Scholar 

  57. Papp, G.: Gravity field approximation based on volume element model of the density distribution. Acta Geod. Geoph. Hung. 91, 339–358 (1996)

    Google Scholar 

  58. Pavlis, N.K., Factor, J.K., Holmes, S.A.: Terrain-related gravimetric quantities computed for the next EGM. In: Proceedings of the 1st International Symposium of the IGFS, S. 318–323. Harita Dergisi, Istanbul (2007)

    Google Scholar 

  59. 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(B4), B04406 (2012)

    Article  Google Scholar 

  60. Rabus, B., Eineder, M., Roth, A., Bamler, R.: The shuttle radar topography mission – a new class of digital elevation models acquired by Spaceborne Radar. ISPRS J. Photogramm. Remote Sens. 57, 241–262 (2003)

    Article  Google Scholar 

  61. Reuter H.I., Nelson, A., Jarvis, A.: An evaluation of void filling interpolation methods for SRTM data. Int. J. Geograph. Inf. Sci. 21(9), 983–1008 (2007)

    Article  Google Scholar 

  62. Rexer, M., Hirt, C.: Spectral analysis of the Earth’s topographic potential via 2D-DFT -a new data-based degree variance model to degree 90,000. J. Geodesy 89(9), 887–909 (2015)

    Article  Google Scholar 

  63. Rummel, R., Rapp, R.H., Sünkel, H., Tscherning, C.C.: Comparisons of global topographic/isostatic models to the Earth’s observed gravity field. OSU Report 388. Department of Geodetic Science and Surveying, Ohio State University, Columbus (1988)

    Google Scholar 

  64. Rummel, R., van Gelderen, M.: Meissl scheme – spectral characteristics of physical geodesy. Manuscr. Geodetica 20, 379–385 (1995)

    Google Scholar 

  65. Sneeuw, N.: Global spherical harmonic analysis by least-squares and numerical quadrature methods in historical perspective. Geophys. J. Int. 118(3), 707–716 (1994)

    Article  Google Scholar 

  66. Smith, D.A.: The gravitational attraction of any polygonally shaped vertical prism with inclined top and bottom faces. J. Geodesy 74(5), 414–420 (2000)

    Article  Google Scholar 

  67. Strang van Hees, G.L.: Some elementary relations between mass distributions inside the Earth and the geoid and gravity field. J. Geodyn. 29(1–2), 111–123 (2000)

    Google Scholar 

  68. Tapley, B.D., Bettadpur, S., Watkins, M., Reigber, C.: The gravity recovery and climate experiment: Mission overview and early results. Geophys. Res. Lett. 31, L09607 (2004)

    Article  Google Scholar 

  69. Tenzer, R., Novák, P., Gladkikh, V.: On the accuracy of the bathymetry-generated gravitational field quantities for a depth-dependent seawater density distribution. Studia Geophys. et Geodaetica 55(4), 609–626 (2011)

    Article  Google Scholar 

  70. Tenzer, R., Chen, W., Tsoulis, D., Bagherbandi, M., Sjöberg, L.E., Novák, P., Jin, S.: Analysis of the refined CRUST1.0 crustal model and its gravity field. Surv. Geophys. online first (2014)

    Google Scholar 

  71. Torge, W., Müller, J.: Geodesy, 4. Aufl. W. de Gruyter, Berlin/New York (2012)

    Book  Google Scholar 

  72. Tsoulis, D.: A comparison between the Airy/Heiskanen and the Pratt/Hayford isostatic models for the computation of potential harmonic coefficients. J. Geodesy 74(9), 637–643 (2001)

    Article  Google Scholar 

  73. Tsoulis, D., Novák, P., Kadlec, M.: Evaluation of precise terrain effects using high-resolution digital elevation models. J. Geophys. Res. 114, B02404 (2009)

    Article  Google Scholar 

  74. Tziavos, I.N., Vergos, G.S., Grigoriadis, V.N.: Investigation of topographic reductions and aliasing effects to gravity and the geoid over Greece based on various digital terrain models. Surv. Geophy. 31(1), 23–67 (2010)

    Article  Google Scholar 

  75. Tziavos, I.N., Sideris, M.G.: Topographic reductions in gravity and geoid modeling. In: Sansò, F., Sideris, M.G. (Hrsg.) Lecture notes in earth system sciences, Bd. 110, S. 337–400. Springer, Berlin/Heidelberg (2013)

    Google Scholar 

  76. Watts, A.B.: Isostasy. In: Gupta, H.K. (Hrsg.) Encyclopedia of solid earth geophysics, Bd. 1, S. 647–662. Springer, Berlin/Heidelberg (2011)

    Chapter  Google Scholar 

  77. Wieczorek, M.A.: Gravity and topography of the terrestrial planets. In: Schubert, G. (Hrsg.) Treatise on geophysics, Bd. 10, S. 165–206. Elsevier-Pergamon, Oxford (2007)

    Chapter  Google Scholar 

  78. Wieczorek, M.A., Phillips, R.J.: Potential anomalies on the sphere: applications to the thickness of the lunar crust. J. Geophys. Res. 103(E1), 1715–1724 (1998)

    Article  Google Scholar 

  79. Wild, F., Heck, B.: A comparison of different isostatic models applied to satellite gravity gradiometry. In: Jekeli, C., Bastos, L., Fernandes, L. (Hrsg.) International Association of Geodesy Symposia, Bd. 129, S. 230–235. Springer, Berlin/Heidelberg (2005)

    Google Scholar 

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Danksagung

Der Autor wurde vom Australian Research Council und Institute for Advanced Study der Technischen Universität München unterstützt. Dank gilt allen Entwicklern von Schwerefeld- und Topographiemodellen, und allen Wissenschaftlern, die mit ihren Beiträgen das Forschungsfeld der topographischen Modellierung weiterentwickelt haben. Ein besonderer Dank geht an Michael Kuhn und Sten Claessens für eine sehr erfolgreiche Zusammenarbeit.

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  1. Institut für Astronomische und Physikalische Geodäsie, Institute for Advanced Study, Technische Universität München, 80333, München, Deutschland

    Christian Hirt

  2. Department of Spatial Sciences, Western Australian Geodesy Group, The Institute for Geoscience Research, Curtin University Perth, Bentley, Australien

    Christian Hirt

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  1. Institut für Astronomische und Physikalische Geodäsie, Technische Universität München, München, Germany

    Reiner Rummel

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Hirt, C. (2017). Topographische Modellierung des Gravitationsfeldes. In: Rummel, R. (eds) Erdmessung und Satellitengeodäsie. Springer Reference Naturwissenschaften . Springer Spektrum, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47100-5_9

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