Incorporating Topographic-Isostatic Information into GOCE Gravity Gradient Processing

  • Thomas Grombein
  • Kurt Seitz
  • Bernhard Heck
Part of the Advanced Technologies in Earth Sciences book series (ATES)


Global high-resolution digital terrain models provide precise information on the Earth’s topography, which can be used to determine the high- and mid-frequency constituents of the gravity field (topographic-isostatic signals). By using a Remove-Compute-Restore concept these signals can be incorporated into many methods of gravity field modelling. Due to the smoothing of observation signals such a procedure benefits from an improved numerical stability in the calculation process. In this paper the Rock-Water-Ice topographic-isostatic gravity field model is presented that we developed in order to generate topographic-isostatic signals which are suitable to smooth gravity gradients observed by the satellite mission GOCE. In contrast to previous approaches, this model is more sophisticated due to a three-layer decomposition of the topography and a modified Airy-Heiskanen isostatic concept. By using measured GOCE gravity gradients, the degree of smoothing is analyzed, showing a significant reduction of the standard deviation (about 30 %) and the range (about 20–40 %). Furthermore, we validate the performance of the generated topographic-isostatic signals by means of a wavelet analysis.


Gravity Field Digital Terrain Model Gravity Gradient Spherical Harmonic Coefficient Spherical Harmonic Degree 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



This research was funded by the German Federal Ministry of Education and Research under grant number 03G0726F within the REAL GOCE project of the GEOTECHNOLOGIEN Programme. N.K. Pavlis (NGA) is acknowledged for providing the topographic data base DTM2006.0. Furthermore, the authors would like to thank X. Luo (KIT) sincerely for his great support in performing the wavelet transform and producing the wavelet spectrograms.


  1. Bassin C, Laske G, Masters G (2000) The current limits of resolution for surface wave tomography in North America. EOS Trans AGU, 81. F897Google Scholar
  2. Forsberg R (1984) A study of terrain reductions, density anomalies and geophysical inversion methods in gravity field modelling. Rep 355, Department of geodetic science, The Ohio State University, Columbus, USAGoogle Scholar
  3. Forsberg R, Tscherning C (1997) Topographic effects in gravity field modelling for BVP. In: Sansò F, Rummel R (eds) Geodetic boundary value problems in view of the one centimeter geoid, lecture notes in earth Sciences, vol 65, Springer, pp 239–272. doi: 10.1007/BFb0011707
  4. Grombein T, Seitz K, Heck B (2010a) Modelling topographic effects in GOCE gravity gradients. GEOTECHNOLOGIEN Sci Rep 17:84–93. doi: 10.2312/ Google Scholar
  5. Grombein T, Seitz K, Heck B (2010b) Untersuchung zur effizienten Berechnung topographischer Effekte auf den Gradiententensor am Fallbeispiel der Satellitengradiometriemission GOCE. KIT Scientific Reports, 7547, KIT Scientific Publishing, Karlsruhe, Germany. doi: 10.5445/KSP/1000017531
  6. Grombein T, Seitz K, Heck B (2011) Smoothing GOCE gravity gradients by means of topographic-isostatic reductions. In: Ouwehand L (ed) Proceedings of the 4th International GOCE User Workshop, ESA Publication SP-696, ESA/ESTECGoogle Scholar
  7. Grombein T, Seitz K, Heck B (2013a) Optimized formulas for the gravitational field of a tesseroid. J Geod. Doi: 10.1007/s00190-013-0636-1
  8. Grombein T, Seitz K, Heck B (2013b) Topographic-isostatic reduction of GOCE gravity gradients. In: Proceedings of the XXV IUGG, 2011, IAG Symposia, vol 139, Springer, Melbourne, Australia (in print)Google Scholar
  9. Heck B, Seitz K (2007) A comparison of the tesseroid, prism and point-mass approaches for mass reductions in gravity field modelling. J Geod 81:121–136. doi: 10.1007/s00190-006-0094-0 Google Scholar
  10. Heiskanen WA, Moritz H (1967) Physical geodesy. W. H. Freeman & Co., USAGoogle Scholar
  11. Janák J, Wild-Pfeiffer F (2010) Comparison of various topographic-isostatic effects in terms of smoothing gradiometric observations. In: Sansò F, Mertikas SPP (eds) IAG symposia, vol 135, Springer, pp 377–381. doi: 10.1007/978-3-642-10634-7_50
  12. Janák J, Wild-Pfeiffer F, Heck B (2012) Smoothing the gradiometric observations using different topographic-isostatic models: a regional case study. In: Sneeuw et al. (eds) Proceedings of VII Hotine-Marussi Symposium, Rome, Italy, 2009, IAG Symposia, vol 137, Springer, pp 245–250. doi: 10.1007/978-3-642-22078-4_37
  13. Moritz H (1980) Geodetic reference system 1980. Bull Géod 54:395–405. doi: 10.1007/BF02521480
  14. Pavlis NK, Factor J, Holmes S (2007) Terrain-related gravimetric quantities computed for the next EGM. In: Kiliçoğlu A, Forsberg R (eds) Proceedings of 1st International Symposium IGFS: Gravity field of the earth, Istanbul, Turkey, 2006. Harita Dergisi, Special Issue 18, pp 318–323Google Scholar
  15. Torrence C, Compo GP (1998) A practical guide to wavelet analysis. Bull Am Meteorol Soc 79(1):61–78. doi: 10.1175/1520-0477(1998)079 Google Scholar
  16. Wild-Pfeiffer F (2008) A comparison of different mass elements for use in gravity gradiometry. J Geod 82:637–653. doi: 10.1007/s00190-008-0219-8 Google Scholar
  17. Wittwer T, Klees R, Seitz K, Heck B (2008) Ultra-high degree spherical harmonic analysis and synthesis using extended-range arithmetic. J Geod 82:223–229. doi: 10.1007/s00190-007-0172-y Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Geodetic InstituteKarlsruhe Institute of Technology (KIT)KarlsruheGermany

Personalised recommendations