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Local multi-polar expansions in potential field modeling

Earth, Planets and Space volume 61, pages 1127–1141 (2009)Cite this article

Abstract

The satellite era brings new challenges in the development and the implementation of potential field models. Major aspects are, therefore, the exploitation of existing space- and ground-based gravity and magnetic data for the long-term. Moreover, a continuous and near real-time global monitoring of the Earth system, allows for a consistent integration and assimilation of these data into complex models of the Earth’s gravity and magnetic fields, which have to consider the constantly increasing amount of available data. In this paper we propose how to speed up the computation of the normal equation in potential filed modeling by using local multi-polar approximations of the modeling functions. The basic idea is to take advantage of the rather smooth behavior of the internal fields at the satellite altitude and to replace the full available gravity or magnetic data by a collection of local moments. We also investigate what are the optimal values for the free parameters of our method. Results from numerical experiments with spherical harmonic models based on both scalar gravity potential and magnetic vector data are presented and discussed. The new developed method clearly shows that very large datasets can be used in potential field modeling in a fast and more economic manner.

References

  • Bettadpur, S., Level 2 gravity field product user handbook GRACE 327–734, http://podaac.jpl.nasa.gov/grace, 2007.

    Google Scholar 

  • Bettadpur, S., Release notes for CSR RL04 GRACE L2 products, http://podaac.jpl.nasa.gov/grace, 2008.

    Google Scholar 

  • Biancale et al., Five years of gravity variations from GRACE and LAGEOS data at 10-day interval over the period from July 29th 2002 to September 10th 2007, http://bgi.cnes.fr:8110/geoid-variations/README.html, 2007.

    Google Scholar 

  • Chambodut, A., J. Schwarte, B. Langlais, H. Lühr, and M. Mandea, The selection of data in field modelling, OIST-4 Proceedings, Danish Meteorological Institute Scientific Report 03-09, 31–34, 2003.

    Google Scholar 

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

    Article  Google Scholar 

  • Colombo, O. L., Numerical methods for harmonic analysis on the sphere, Reports of the Department of Geodetic Science, 310, Ohio State University, Columbus, 1981.

  • Colombo, O. L., The global mapping of gravity with two satellites, The Netherlands Geodetic Commission. Publications on Geodesy, 7, Delft, 1984.

  • Ditmar, P., R. Klees, and F. Kostenko, Fast and accurate computation of spherical harmonics coefficients from satellite gravity gradiometry data, J. Geod., 76, 690–705, 2003.

    Article  Google Scholar 

  • Döll, P. F., F. Kaspar, and B. Kaspar, A global hydrological model for deriving water availability indicators: model tuning and validation, J. Hydrol., 270, 105–134, 2003.

    Article  Google Scholar 

  • Epton, M. and B. Dembart, Multipole translation theory for the three-dimensional Laplace and Helmholtz equations, SIAM J. Sci. Comput., 16, 865–897, 1995.

    Article  Google Scholar 

  • Han, S.-C., Efficient determination of global gravity field from satellite-to-satellite tracking mission, Celestial Mech. Dyn. Astron., 88, 69–102, 2004.

    Article  Google Scholar 

  • Han, S.-C., C. Jekeli, and C. K. Shum, Static and temporal gravity field recovery using GRACE potential difference observables, Adv. Geosci., 1, 19–26, 2003.

    Article  Google Scholar 

  • Holschneider, M., A. Chambodut, and M. Mandea, From global to regional analysis of the magnetic field on the sphere using wavelet frames, Phys. Earth Planet. Inter., 135, 107–124, 2003.

    Article  Google Scholar 

  • Jekeli, C., The determination of gravitational potential differences from satellite-to-satellite tracking, Celestial Mech. Dyn. Astron., 75, 85–101, 1999.

    Article  Google Scholar 

  • Katanforoush, A. and M. Shahshahani, Distributing points on the sphere, I Exp. Math., 12, 199–209, 2003.

    Article  Google Scholar 

  • Keller, W., A wavelet approach for the construction of multi-grid solvers for large linear systems, in Proc. AG 2001 Scientific Assembly, 2–7 September 2001, Budapest, 2001.

    Google Scholar 

  • Klees, R., R. Koop, R. Visser, and J. van der Ijssel, Efficient gravity field recovery from GOCE gravity gradient observations, J. Geod., 74, 561–571, 2000.

    Article  Google Scholar 

  • Kusche, J., Implementation of multigrid solvers for satellite gravity anomaly recovery, J. Geod., 74, 773–782, 2000.

    Article  Google Scholar 

  • Langel, R. A. and W. J. Hinze, The Magnetic Field of the Earth s Lithosphere: The Satellite Perspective, Cambridge Univ. Press, New York, 1998.

    Book  Google Scholar 

  • Lemoine, F. G., S. C. Kenyon, J. K. Factor, R. G. Trimmer, N. K. Pavlis, D. S. Chinn, C. Cox, S. M. Klosko, S. B. Luthcke, M. H. Torrence, Y. M. Wang, R. G. Williamson, E. C. Pavlis, R. H. Rapp, and T. R. Olson, The development of the joint NASA GSFC and the National Imagery and Mapping Agency (NIMA) geopotential model EGM96, NASA Technical Paper, 1998-206861, Greenbelt, Maryland, 1998.

    Google Scholar 

  • Lesur, V., I. Wardinski, M. Rother, and M. Mandea, GRIMM—The GFZ Reference Internal Magnetic Model besed on vector satellite and observatory data, Geophys. J. Int., 2007 (in press).

    Google Scholar 

  • Maus, S., M. Rother, C. Stolle, W. Mai, S. Choi, H. Lühr, D. Cooke, and C. Roth, Third generation of the Potsdam Magnetic Model of the Earth (POMME), Geochem. Geophys. Geosyst., 7, Q07008, 2006.

  • Maus, S., T. Sazonova, K. Hemant, J. D. Fairhead, and D. Ravat, National Geophysical Data Center candidate for the World Digital Magnetic Anomaly Map, Geochem. Geophys. Geosyst., 8, Q06017, doi:10.1029/2007GC001643, 2007.

  • Migliaccio, F., M. Reguzzoni, and F. Sanso, Space-wise approach to satellite gravity field determination in the presence of coloured noise, J. Geod., 78, 304–313, 2004.

    Article  Google Scholar 

  • Migliaccio, F., M. Reguzzoni, F. Sanso, and N. Tselfes, On the use of gridded data to estimate potential fields coefficients, Proceedings of the 3rd International GOCE USsers Workshop, Frascati, Italy, 6–8 November 2006, 2006.

    Google Scholar 

  • Moritz, H., Advanced Physical Geodesy, Herbert Wichmann, Karlsruhe, Germany, 1980.

    Google Scholar 

  • Nakajima, K., Parallel multilevel iterative linear solvers with unstructured adaptive grids for simulations in Earth science, ACES 2001 Special Issue of Concurrency and Computation: Practice and Experience, 2001.

    Google Scholar 

  • Panet, I., A. Chambodut, M. Diament, M. Holschneider, and O. Jamet, New insights on intraplate volcanism in French Polynesia from wavelet analysis of GRACE, CHAMP and sea-surface data, J. Geophys. Res., 111(B9), B09403, doi10.1029/2005JB004141, 2006.

    Google Scholar 

  • Reubelt, T., M. Gotzelmann, and W. Grafarend, A new CHAMP gravitational field model based on the GIS acceleration approach and two years of kinematic CHAMP data, Paper presented at the Joint CHAMPGRACE Science Team meeting, GFZ Potsdam, Germany, 5–8 July 2004, 2004.

    Google Scholar 

  • Rowlands, D. D., R. D. Ray, D. S. Chinn, and F. G. Lemoine, Short-arc analysis of intersatellite tracking data in a gravity mapping mission, J. Geod., 76, 307–316, 2002.

    Article  Google Scholar 

  • Sanso, F. and C. C. Tscherning, Fast spherical collocation: theory and examples, J. Geod., 77, 101–112, 2003.

    Article  Google Scholar 

  • Schuh, W.-D., Scientific data processing algorithms, in From Eotvos to milligal, final report, ESA report study, ESA/ESTEC contract 13392/98/LN/GD, edited by Sunkel, H., 2000.

    Google Scholar 

  • Shum, C. K., S. C. Han, A. Braun, F. Schwartz, and M. Schmidt, Quantification of GRACE continental hydrology observations: aliasing and high-frequency signal recovery, GRACE-Hydrology workshop, UCIrvine, March 22nd, 2004.

    Google Scholar 

  • Strykowski, G., Outline of a new space-domain method for forward modelling, in Gravity Field of the Earth, Proceedings of the 1st International Symposium of the International Gravity Field Service (IGFS), 28th August–1st Sptember 2006, Istanbul, Turkey, 2006 (accepted).

    Google Scholar 

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Author notes

  1. B. Minchev

    Present address: Global Life, Allianz SE, 70178, Stuttgart, Germany

  2. M. Mandea

    Present address: Institut de Physique du Globe de Paris Géophysique spatiale et planétaire, Université Paris Diderot, Paris, France

  3. G. Ramillien

    Present address: Géodésie Spatiale, CNRS DTP UMR 5562, OMP, Toulouse, France

Authors and Affiliations

  1. Department of Applied and Industrial Mathematics, University of Potsdam, Potsdam, Germany

    B. Minchev & M. Holschneider

  2. Institut de Physique du Globe de Strasbourg, UMR 7516 CNRS, Université de Strasbourg/EOST, Strasbourg, France

    A. Chambodut

  3. Institut de Physique du Globe de Paris, CNRS, Paris, France

    I. Panet

  4. Space Geodesy Research Division, Geographical Survey Institute, Tsukuba, Ibaraki, Japan

    I. Panet

  5. Institut Géographique National, Laboratoire LAREG, Marne-la-Vallée, France

    I. Panet

  6. Institute of Theoretical Physics, Berlin University of Technology, Germany

    E. Schöll

  7. Helmholtz-Zentrum Potsdam, Deutsches GeoForschungsZentrum—GFZ, Potsdam, Germany

    M. Mandea

  8. Laboratoire d’Etudes en Géophysique et Océanographie Spatiales, Observatoire 048 Midi-Pyrénées, Toulouse, France

    G. Ramillien

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  1. B. Minchev
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Correspondence to B. Minchev.

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Minchev, B., Chambodut, A., Holschneider, M. et al. Local multi-polar expansions in potential field modeling. Earth Planet Sp 61, 1127–1141 (2009). https://doi.org/10.1186/BF03352965

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