Harmonic Continuation and Gravimetric Inversion of Gravity in Areas of Negative Geodetic Heights

  • P. VajdaEmail author
  • A. Ellmann
  • B. Meurers
  • P. Vaníček
  • P. Novák
  • R. Tenzer
Conference paper
Part of the International Association of Geodesy Symposia book series (IAG SYMPOSIA, volume 135)


By the decomposition of the real earth’s gravity potential it can be shown that the attraction of the anomalous mass density, which is sought as the unknown in gravimetric inversion (gravity data interpretation), matches exactly the gravity disturbance corrected for the attraction of topography and bathymetry (the BT disturbance), and eventually also for attractions of other known density contrasts, such as sediments, lakes, glaciers, isostatic roots, etc (the stripped BT disturbance). The involved (global) topographic correction requires the use of reference ellipsoid (RE) as the bottom interface of topographic masses. Topographic correction based on the RE introduces the attraction of “liquid topography” offshore, which is the attraction of sea water between the RE and sea level (geoid). The topo-correction onshore requires the use of reference (such as constant average crustal) topographic density for the “solid topography”. The ultimate knowledge of real topo-density is avoided, since anomalous density relative to the reference topo-density is part of the interpretation (is sought). In areas of negative geodetic heights, both onshore (e.g., Dead Sea region) and offshore (negative geoidal heights), we run into the problem of evaluating the normal gravity and the problem of the legitimacy of the upward harmonic continuation of the gravity data to be interpreted (inverted). We propose to overcome these problems by a new approach based on the concept of the reference quasi-ellipsoid (RQE). The gravimetric inverse problem is first reformulated based on the RQE that replaces the RE in the decomposition of actual potential. The RQE approach enables for stations of negative heights the use of the international gravity formula (IGF) for computing normal gravity at the station, and facilitates the legitimacy of the harmonic continuation in regions of negative heights. Second, the gravity data (the RQE-based BT disturbances) are continued onto or above the RE. Third, the inverse problem is transformed back to be formulated with respect to the RE, and solved using classical known techniques.


BT gravity disturbance Reference quasi-ellipsoid Topographic correction Bathymetric correction Normal gravity Harmonic upward continuation Gravimetric inversion 



Peter Vajda acknowledges the support of the VEGA grant agency projects No. 2/3004/23 and 2/6019/26. Pavel Novak was supported by the Grant 205/08/1103 of the Czech Science Foundation.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • P. Vajda
    • 1
    Email author
  • A. Ellmann
    • 2
  • B. Meurers
    • 3
  • P. Vaníček
    • 4
  • P. Novák
    • 5
    • 6
  • R. Tenzer
    • 7
  1. 1.Geophysical Institute, Slovak Academy of SciencesBratislavaSlovak Republic
  2. 2.Department of Civil EngineeringTallinn University of TechnologyTallinnEstonia
  3. 3.Institute of Meteorology and Geophysics, University of ViennaViennaAustria
  4. 4.Department of Geodesy and Geomatics EngineeringUniversity of New BrunswickFrederictonCanada
  5. 5.Research Institute of Geodesy, Topography and CartographyPilsenCzech Republic
  6. 6.Department of MathematicsUniversity of West BohemiaZdibyCzech Republic
  7. 7.Delft Institute of Earth Observation and Space Systems (DEOS)Delft University of TechnologyDelftThe Netherlands

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