Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Journal of Geodetic Science

Editor-in-Chief: Eshagh, Mehdi

Open Access
See all formats and pricing
More options …

Artifacts in regional gravity representations with spherical radial basis functions

K. Bentel
  • Corresponding author
  • Norwegian University of Life Sciences, Department of Mathematical Sciences and Technology, IMT, Postboks 5003, 1432 Ås, Norway
  • Email
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
/ M. Schmidt / C. Rolstad Denby
  • Norwegian University of Life Sciences, Department of Mathematical Sciences and Technology, IMT, Postboks 5003, 1432 Ås, Norway
  • Other articles by this author:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2013-10-15 | DOI: https://doi.org/10.2478/jogs-2013-0029


With the increasing number of high-resolution gravity observations, which became available in the recent years, global Earth gravity models can be regionally refined. While global gravity models are usually represented in spherical harmonic basis functions with global support, a very promising option to model the regional refinements is the use of spherical radial basis functions with quasi-compact support. These functions are not necessarily orthogonal on a sphere, and usually, more functions are used in regional modelling than minimally needed from a global point of view. This makes the modelling more difficult. Furthermore, no techniques or choices of radial basis functions and other parameters in the regional modelling approach are established so far, as it is the case for global gravity modelling in spherical harmonics. In this article, a closed-loop simulation is used to investigate the mathematical modelling accuracy of different radial basis functions, which are compared to each other. Furthermore, artificial effects, which occur in the modelling results with very low levels of noise on the observations, are investigated. The whole study is performed on synthetic observations of a residual gravitational potential signal for the Himalaya area with different levels of noise. Spherical radial basis functions are a compromise between spatial and frequency localization, which are mutually exclusive. We show that spatial localization properties are even more important than frequency localization in the regional case, even though a band-limited signal is modeled.

Keywords:: closed-loop simulation; radial basis function; regional gravity field modelling

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

  • ESA, 1999, Gravity field and steady-state ocean circulation mission. Reports for mission selection: The four candidate Earth explorer core missions, ESA SP-1233(1).Google Scholar

  • Schmidt M., Fengler M., Mayer-Gürr T., Eicker A., Kusche J., Sánchez L., and Han S-H., 2007, Regional gravity modeling in terms of spherical base functions. J. Geod., 81(1):17-38.Google Scholar

  • Eicker A., 2008 Gravity Field Refinement by Radial Basis Functions from In-situ Satellite Data. Dissertation, Institut für Geodäsie und Geoinformation, Universität Bonn.Google Scholar

  • Freeden W., Fehlinger T., Klug M., Mathar D., and Wolf K., 2009, Classical globally reflected gravity field determination in modern locally oriented multiscale framework. J. Geod., 83:1171-1191.Web of ScienceGoogle Scholar

  • Wittwer T., 2009, Regional gravity field modeling with radial basis functions. PhD thesis, NCG, Nederlandse Commissie voor Geodesie, Netherlands Geodetic Commission, Publications on Geodesy 72, ISBN 978 90 6132 315 0.Google Scholar

  • Panet I., Kuroishi Y., and Holschneider M., 2010, Wavelet modelling of the gravity field by domain decomposition methods: an example over Japan. Geophys. J. Int., 184(1):203-219.Web of ScienceGoogle Scholar

  • Freeden W., Gervens T., and Schreiner M., 1998, Construc tive Approximation on the Sphere With Applications to Geoscience. Oxford Science Publications, ISBN 019853682.Google Scholar

  • Freeden W. and Michel V., 2004, Multiscale Potential Theory With Applications to Geoscience. Springer Basel AG, ISBN 081764105X.Google Scholar

  • Wolf K., 2009, Multiscale Modeling of Classical Boundary Value Problems in Physical Geodesy by Locally Supported Wavelets. Dissertation, University of Kaiserslautern, Department of Mathematics, Verlag Dr. Hut, ISBN 978-3-86853-249-4.Google Scholar

  • Klees R., Tenzer R., Prutkin I., and Wittwer T., 2008, A data-driven approach to local gravity field modelling using spherical radial basis functions. J. Geod., 82(8):457 - 471.Google Scholar

  • Antoni M., Keller W., and Weigelt M., 2009, Representation of regional gravity fields by radial base functions. In Michael G Sideris, editor, Observing our Changing Earth, volume 133 of International Association of Geodesy Symposia, pages 293-299. Springer, Berlin Heidelberg.Google Scholar

  • Fischer D., 2011, Sparse Regularization of a Joint Inversion of Gravitational Data and Normal Mode Anomalies. Dissertation, University of Siegen.Google Scholar

  • Bentel K., Schmidt M., and Gerlach Ch., 2013, Different radial basis functions and their applicability for regional gravity field representation on the sphere. International Journal on Geomathematics, 4:67-96.Google Scholar

  • Tenzer R. and Klees R., 2008, The choice of the spherical radial basis functions in local gravity field modeling. Studia Geophysica et Geodaetica, 52:287-304.Web of ScienceGoogle Scholar

  • Pavlis N. K., Holmes S. A., Kenyon S. C., and Factor J. K., 2012, The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). Journal of Geophysical Research (Solid Earth), 117(B16):4406.Google Scholar

  • Lemoine F.G., Kenyon S.C., Factor J.K., Trimmer R.G., Pavlis N.K., Chinn D.S., Cox C.M., Klosko S.M., Luthcke S.B., Torrence M.H., Wang Y.M., Williamson R.G., Pavlis E.C., Rapp R.H., and Olson T.R., 1998, The development of the joint NASA GSFC and the National IMagery and Mapping Agency (NIMA) geopotential model EGM96. Technical report, NASA Technical Paper NASA/TP1998206861, Goddard Space Flight Center, Greenbelt, USA.Google Scholar

  • Koch K.-R. and Kusche J., 2002, Regularization of geopotential determination from satellite data by variance components. J. Geod., 76:259-268.Google Scholar

  • Schmidt M., Han S-C., Kusche J., Sanchez L., and Shum C. K., 2006, Regional high-resolution spatiotemporal gravity modeling from GRACE data using spherical wavelets. Geophys. Res. Lett., 33:1-4.Google Scholar

  • Holschneider M., Chambodut A., and Mandea M., 2003, From global to regional analysis of the magnetic field on the sphere using wavelet frames. Physics of the Earth and Planetary Interiors, 135(2-3):107-124.Google Scholar

  • Chambodut A., Panet I., Mandea M., Diament M., Holschneider M., and Jamet O., 2005 Wavelet frames: an alternative to spherical harmonic representation of potential fields. Geophys. J. Int., 163(3):875-899.Google Scholar

  • Panet I., Jamet O., Diament M., and Chambodut A., 2005, Modelling the Earth’s gravity field using wavelet frames. In Christopher Jekeli, Luisa Bastos, Joana Fernandes, and Fernando Sansò, editors, Gravity, Geoid and Space Missions, volume 129 of International Association of Geodesy Symposia, pages 48-53. Springer Berlin Heidelberg.Google Scholar

  • Naeimi M., 2013, Inversion of satellite gravity data using spherical radial base functions. Phd thesis, Institute of Geodesy, University of Hanover. Google Scholar

About the article

Published Online: 2013-10-15

Published in Print: 2013-09-01

Citation Information: Journal of Geodetic Science, Volume 3, Issue 3, Pages 173–187, ISSN (Online) 2081-9943, ISSN (Print) 2081-9919, DOI: https://doi.org/10.2478/jogs-2013-0029.

Export Citation

This content is open access.

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Yihao Wu, Zhicai Luo, Bo Zhong, and Chuang Xu
Geoscientific Model Development, 2018, Volume 11, Number 12, Page 4797
Majid Naeimi, Jakob Flury, and Phillip Brieden
Geophysical Journal International, 2015, Volume 202, Number 2, Page 1041
Blažej Bucha, Juraj Janák, Juraj Papčo, and Aleš Bezděk
Geophysical Journal International, 2016, Volume 207, Number 2, Page 949
Verena Lieb, Michael Schmidt, Denise Dettmering, and Klaus Börger
Journal of Geophysical Research: Solid Earth, 2016, Volume 121, Number 5, Page 3825

Comments (0)

Please log in or register to comment.
Log in