Advertisement

Acta Geodaetica et Geophysica

, Volume 53, Issue 1, pp 125–138 | Cite as

Analysis of local covariance functions applied to GOCE satellite gravity gradiometry data

  • Branislav HábelEmail author
  • Juraj Janák
Original Study
  • 105 Downloads

Abstract

GOCE Level 2 products of corrected gravity gradients in Local North-Oriented Frame were used in this study. We analyzed four accurately measured elements of the gravity tensor, which were transformed to disturbing gravitational gradients. The investigation was carried out in the restricted region of dimension 20° × 20° covering the south part of Europe. We applied several types of analytical covariance functions in a local approximation, which have the best fit to the empirical covariances calculated from the disturbing gravitational gradients in particular sub-regions. At first, we have investigated four different types of the 1-dimensional covariance function. Obtained results show that the Gaussian covariance function approximates the empirical covariances the best from tested functions. Moreover, a time stability of calculated parameters of the covariance functions was studied by assuming GOCE data from different time periods. In the second experiment, we have compared two types of the 2-dimensional covariance function, which also enables a spatial stochastic modeling. The second study revealed that the least-squares collocation using the 2-dimensional local covariance function can produce the local grid of GOCE disturbing gravitational gradients directly from GOCE Level 2 products right below GOCE orbit, which in general fits well with the recent Earth’s global gravity field models and might have some advantages. Such local grids can be useful for specific tasks, e.g. mutual comparing of GOCE data collected during particular time periods.

Keywords

Gravity field Local covariance function GOCE Least-squares collocation 

Notes

Acknowledgements

We gratefully acknowledge the reviewers comments and suggestions, which improved the paper essentially. This study is based on research carried out within the Slovak National Project VEGA 1/0954/15: Analysis of Global Data Sources and Possibilities of Their Application in the Refinement and Testing of Earth Gravity Field Models. Thanks also to the HPC center at the Slovak University of Technology in Bratislava, which is a part of the Slovak Infrastructure of High Performance Computing (SIVVP project, ITMS code 26230120002, funded by the European region development funds, ERDF), for the computational time and resources made available.

References

  1. Bouman J, Ebbing J, Fuchs M, Sebera J, Lieb V, Szwillus W, Haagmans R, Novak P (2016) Satellite gravity gradient grids for geophysics. Nat Sci Rep. doi: 10.1038/srep21050 Google Scholar
  2. Brockmann JM, Zehentner N, Höck E, Pail R, Loth I, Mayer-Gürr T, Schuh WD (2014) EGM_TIM_RL05: an independent geoid with centimeter accuracy purely based on the GOCE mission. Geophys Res Lett 41:8089–8099. doi: 10.1002/2014GL061904 CrossRefGoogle Scholar
  3. Bucha B, Janák J (2013) A MATLAB-based graphical user interface program for computing functionals of the geopotential up to ultra-high degrees and orders. Comput Geosci 56:186–196CrossRefGoogle Scholar
  4. ESA (1999) Gravity field and steady-state ocean circulation mission, report for mission selection of the four candidate Earth explorer missions. Technical report ESA SP-1233(1), European Space Agency, ESA Publication DivisionGoogle Scholar
  5. Förste C, Bruinsma S, Abrikosov O, Lemoine JM, Marty JC, Flechtner F, Balmino G, Barthelmes F, Biancale R (2014) EIGEN-6C4 the latest combined global gravity field model including GOCE data up to degree and order 2190 of GFZ Potsdam and GRGS Toulouse. doi:10.5880/icgem.2015.1. Accessed 12 Feb 2014Google Scholar
  6. Gatti A, Migliaccio F, Reguzzoni M, Sansò F (2013) Space-wise global grids of GOCE gravity gradients at satellite altitude. In: Geophysical research abstracts. Abstracts of the earth, planetary and space sciences, vol 15. Copernicus Publications, GöttingenGoogle Scholar
  7. Gruber T, Rummel R, Abrikosov O, Van Hess R (2010) GOCE level 2 product data handbook. Technical report GO-MA-HPF-GS-0110, The European GOCE Gravity Consortium EGG-CGoogle Scholar
  8. Heiskanen WA, Moritz H (1967) Physical Geodesy. W. H, Freeman and Company, San FranciscoGoogle Scholar
  9. Jekeli C (2010) Correlation modeling of the gravity field in classical geodesy. Springer, Berlin, pp 833–863. doi: 10.1007/978-3-642-01546-5_28 Google Scholar
  10. Moritz H (1980) Advanced physical geodesy. Wichmann, KarlsruheGoogle Scholar
  11. Moritz H, Sünkel H (1978) Approximation methods in geodesy. Wichmann, KarlsruheGoogle Scholar
  12. Pail R, Bruinsma S, Migliaccio F, Förste C, Goiginger H, Schuh WD, Höck E, Reguzzoni M, Brockmann JM, Abrikosov O, Veicherts M, Fecher T, Mayrhofer R, Krasbutter I, Sansò F, Tscherning CC (2011) First GOCE gravity field models derived by three different approaches. J Geodesy 85:819–843. doi: 10.1007/s00190-011-0467-x CrossRefGoogle Scholar
  13. Pavlis NK, Holmes SA, Kenyon SC, Factor JK (2012) The development and evaluation of the earth gravitational model 2008 (EGM2008). J Geophys Res. doi: 10.1029/2011JB008916 Google Scholar
  14. Rapp R (1978) Results of the application of least-squares collocation to selected geodetic problems. In: Moritz H, Sünkel H (eds) Approximation methods in geodesy. Wichmann, Karlsruhe, pp 117–156Google Scholar
  15. Rousseeuw PJ, Leroy AM (1987) Robust regression and outlier detection. Wiley, New YorkCrossRefGoogle Scholar
  16. Šprlák M (2012) A graphical user interface application for evaluation of the gravitational tensor components generated by a level ellipsoid of revolution. Comput Geosci 46:77–83CrossRefGoogle Scholar
  17. Tscherning CC (1976) Covariance expressions for second and lower order derivatives of the anomalous potential. Technical report 225, Department of Geodetic Science, The Ohio State UniversityGoogle Scholar
  18. Tscherning CC (2010) The use of least-squares collocation for the processing of GOCE data. Vermess Geoinf 1:21–26Google Scholar
  19. Wessel P, Smith WHF, Scharroo R, Luis J, Wobbe F (2013) Generic mapping tools: improved version released. Eos Trans Am Geophys Union 94(45):409–410. doi: 10.1002/2013EO450001 CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó 2017

Authors and Affiliations

  1. 1.Department of Theoretical Geodesy, Faculty of Civil EngineeringSlovak University of Technology in BratislavaBratislavaSlovakia

Personalised recommendations