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


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.


Gravity field Local covariance function GOCE Least-squares collocation 



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.


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Copyright information

© Akadémiai Kiadó 2017

Authors and Affiliations

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

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