IGFS 2014 pp 53-61 | Cite as

Wavelet Multi-Resolution Analysis of Recent GOCE/GRACE GGMs

  • A. C. Peidou
  • G. S. VergosEmail author
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 144)


The realization of the GRACE/GOCE missions offer new opportunities for gravity field approximation with higher accuracy at the medium wavebands, while wavelets (WL) provide powerful gravity field analysis tools in the space/frequency domain. This work focuses on the spectral analysis of GOCE, GOCE/GRACE and combined Global Geopotential Models (GGMs) through wavelet decomposition, filtering and reconstruction to improve their performance in the higher bands of the spectrum. The GGMs evaluated refer to the latest DIR-R4/R5, TIM-R4/R5 and GOCO03s models, which are compared with local GPS/Leveling geoid heights and gravity anomalies, while EGM2008 is used as a reference. Through a WL-based multi-resolution analysis, gravity anomalies and geoid heights are analyzed to derive their approximation and detail coefficients for various levels of decomposition, which correspond to different spatial scales. The content and signal power of each level of decomposition is analyzed to conclude on the amount and quality of signal power that GOCE/GRACE GGMs represent compared to EGM2008, especially up to the targeted waveband of 100–150 km. Filtering is investigated as well to remove high-frequency information from the low resolution GOCE models and adjust the WL reconstruction. The model synthesis that follows, through WL coefficient reconstruction, aims at the generation of new synthesized GGMs, where both GOCE and EGM2008 information is used, the latter serving to model the omission error in the GOCE GGMs. The synthesized GOCE GGMs offer an improvement of more than 30 cm compared to the original GOCE GGMs, while they provide a 1–2 cm improvement compared to EGM2008. In terms of the validation with gravity anomalies, a 5 mGal improvement was found, w.r.t. to the original GOCE GGMs, while w.r.t. EGM2008 there was no improvement. Finally, it was concluded that the GOCE GGMs show improved, between 5–22%, correlation with the land topography compared to EGM2008 for spatial scales between 176–704 km.


Correlation Filtering Gravity field Multi-resolution analysis Spectrum coherency Validation Wavelets 


  1. Amante C, Eakins BW (2009) ETOPO1 1 arc-minute global relief model: procedures, data sources and analysis. NOAA Technical Memorandum NESDIS NGDC-24. National Geophysical Data Center, NOAA. doi:10.7289/V5C8276M. Accessed Feb 2014Google Scholar
  2. Balmino G, Vales N, Bonvalot S, Briais A (2012) Spherical harmonic modeling to ultra-high degree of Bouguer and isostatic anomalies. J Geod 86(7):499–520. doi: 10.1007/s00190-011-0533-4CrossRefGoogle Scholar
  3. Bendat JS, Piersol AG (2010) Random data: analysis and measurement procedures, 4th edn. Wiley, New York. ISBN 978-0-470-24877-5CrossRefGoogle Scholar
  4. Bruinsma SL et al (2010) GOCE gravity field recovery by means of the direct numerical method. Presented at the ESA Living Planet Symposium, Bergen, Norway, 27 June – 2 JulyGoogle Scholar
  5. Bruinsma SL et al (2013) The new ESA satellite-only gravity field model via the direct approach. Geophys Res Lett 40(14):3607–3612. doi: 10.1002/grl.50716CrossRefGoogle Scholar
  6. Chui C (1992) An Introduction to Wavelets, 1st edn. Academic Press, San Diego. ISBN: 978–0121745844Google Scholar
  7. ESA (1999) Gravity field and steady-state ocean circulation mission. ESA Publication Division, ESTEC, Noordwijk, Netherlands, SP-1223Google Scholar
  8. Fuchs MJ, Bouman J, Broerse T, Visser P, Vermeersen B (2013) Observing coseismic gravity change from the Japan Tohoku-Oki 2011 earthquake with GOCE gravity gradiometry. J Geophys Res 118(10):5712–5721CrossRefGoogle Scholar
  9. Grebenitcharsky R, Moore P (2014) Application of wavelets for along-tracking multi-resolution analysis of GOCE SGG data. In: Marti U (ed) Gravity, geoid and height systems, International association of geodesy symposia, vol 141, Springer, Switzerland, pp 41–50. doi: 10.1007/978-3-319-10837-7_6
  10. Grebenitcharsky RS, Sideris MG (2005) The compatibility conditions in altimetry–gravimetry boundary value problems. J Geod 78(10):626–636. doi: 10.1007/s00190-004-0429-7CrossRefGoogle Scholar
  11. Gruber TH, Visser PNAM, Ackermann CH, Hosse M (2011) Validation of GOCE gravity field models by means of orbit residuals and geoid comparisons. J Geod 85(11):845–860CrossRefGoogle Scholar
  12. Hayn M, Panet I, Diamen M, Holschneider M, Mandea M, Davaille A (2012) Wavelet-based directional analysis of the gravity field: evidence for large-scale undulations. Geophys J Int 189(3):1430–1456. doi: 10.1111/j.1365-246X.2012.05455.xCrossRefGoogle Scholar
  13. Hirt C, Gruber T, Featherstone WE (2011) Evaluation of the first GOCE static gravity field models using terrestrial gravity, vertical deflections and EGM2008 quasigeoid heights. J Geod 85(10):723–740CrossRefGoogle Scholar
  14. Knudsen P, Bingham R, Andersen OB, Rio M-H (2011) A global mean dynamic topography and ocean circulation estimation using a preliminary GOCE gravity model. J Geod 85(11):861–879CrossRefGoogle Scholar
  15. Mallat SG (1989) A theory for multiresolution signal decomposition: the wavelet representation. IEEE Trans Pattern Anal Mach Intel 11:674–693. doi: 10.1109/34.192463CrossRefGoogle Scholar
  16. Mallat S (1999) A wavelet tour of signal processing, 3rd edn. Academic Press, San Diego. ISBN: 978-0-12-374370-1Google Scholar
  17. Mayer-Gurr T et al (2012) The new combined satellite only model GOCO03s. Presentation at GGHS 2012 IAG Symposia, Venice, October 2012Google Scholar
  18. Menna M, Poulain P-M, Mauri E, Samppietro D, Panzetta F, Reguzzoni M, Sansò F (2014) Mean surface geostrophic circulation of the Mediterranean Sea estimated from GOCE geoid models and altimetric mean sea surface: initial validation and accuracy assessment. Boll Geofis Teor Appl 54(4):347–365. doi: 10.4430/bgta0104Google Scholar
  19. Pail R et al (2011) First GOCE gravity field models derived by three different approaches. J Geod 85(11):819–843CrossRefGoogle Scholar
  20. Panet I, Kuroishi Y, Holschneider M (2011) Wavelet modelling of the gravity field by domain decomposition methods: an example over Japan. Geophys J Int 184(1):203–219. doi: 10.1111/j.1365-246X.2010.04840.xCrossRefGoogle Scholar
  21. Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development and evaluation of the earth gravitational model 2008 (EGM2008). J Geophys Res 117:B04406. doi: 10.1029/2011JB008916CrossRefGoogle Scholar
  22. Vergos GS, Grigoriadis VN, Tziavos IN, Kotsakis C (2014) Evaluation of GOCE/GRACE global geopotential models over Greece with collocated GPS/Levelling observations and local gravity data. In: Marti U (ed) Gravity, geoid and height systems, International association of geodesy symposia, vol 141. Springer, Switzerland, pp 85–92. doi: 10.1007/978-3-319-10837-7_11Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Department of Geodesy and SurveyingAristotle University ofThessalonikiThessalonikiGreece

Personalised recommendations