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Disturbing Potential from Deflections of the Vertical: From Globally Reflected Surface Gradient Equation to Locally Oriented Multiscale Modeling

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Encyclopedia of Geodesy

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Definition

Deflection of the Vertical :

Difference between the direction of the normal vector associated with the reference potential and the normal vector associated with the (actual) gravity potential.

Disturbing Potential :

Difference between the normal potential and the true (measured) potential.

Introduction

The force of gravity, i.e., the resultant of gravitational and centrifugal force, provides a directional structure to the space above the Earth’s surface. It is tangential to the vertical plumb lines and perpendicular to all (level) equipotential surfaces. Any water surface at rest is part of a level surface. Level (equipotential) surfaces are ideal reference surfaces, for example, for heights. The geoid is defined as that level surface of the gravity field which best fits the mean sea level. Gravity vectors can be measured by absolute or relative gravimeters. The highest accuracy relative gravity...

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References and Reading

  • Bruns, E. H., 1878. Die Figur der Erde. Berlin: P. Stankiewicz Buchdruckerei.

    Google Scholar 

  • Fehlinger, T., 2009. Multiscale Formulations for the Disturbing Potential and the Deflections of the Vertical in Locally Reflected Physical Geodesy. PhD thesis, University of Kaiserslautern, Geomathematics Group.

    Google Scholar 

  • Freeden, W., 1979. Über eine Klasse von Integralformeln der Mathematischen Geodäsie. Veröff Geod Inst RWTH Aachen, 27. Habilitation Thesis.

    Google Scholar 

  • Freeden, W., 2015. Geomathematics: its role, its aim, and its potential. In Freeden, W., Nashed, Z., and Sonar, T. (eds.), Handbook of Geomathematics, 2nd edn, p 3–78. Heidelberg: Springer.

    Google Scholar 

  • Freeden, W., and Gerhards, C., 2012. Geomathematically Oriented Potential Theory. Boca Raton: Chapman & Hall/CRC Press.

    Book  Google Scholar 

  • Freeden, W., and Maier, T., 2003. Spectral and multiscale signal-to-noise thresholding of spherical vector fields. Computational Geosciences, 7, 215–250.

    Article  Google Scholar 

  • Freeden, W., and Schreiner, M., 2006. Local multiscale modelling of geoid undulations from deflections of the vertical. Journal of Geodesy, 79, 641–651.

    Article  Google Scholar 

  • Freeden, W., and Schreiner, M., 2009. Spherical Functions of Mathematical Geosciences – A Scalar, Vectorial and Tensorial Setup. Berlin/Heidelberg: Springer.

    Google Scholar 

  • Freeden, W., Gervens, T., and Schreiner, M., 1998. Constructive Approximation on the Sphere (With Applications to Geomathematics). Oxford: Oxford Science Publications/Clarendon Press.

    Google Scholar 

  • Grafarend, E. W., Klapp, M., and Martinec, Z., 2015. Spacetime modeling of the Earth’s gravity field by ellipsoidal harmonics. In Freeden, W., Nashed, Z., and Sonar, T. (eds.), Handbook of Geomathematics, 2nd edn, p 381–496. Heidelberg: Springer.

    Google Scholar 

  • Heiskanen, W. A., and Moritz, H., 1967. Physical Geodesy. San Francisco: W.H. Freeman.

    Google Scholar 

  • Hofmann-Wellenhof, B., and Moritz, H., 2006. Physical Geodesy, 2nd edn, p 253–290 Wien/New York: Springer.

    Google Scholar 

  • Jekeli, C., 1999. An analysis of deflections of the vertical derived from high-degree spherical harmonic models. Journal of Geodesy, 73, 10–22.

    Article  Google Scholar 

  • Pick, M., Pícha, J., and Vyskočil, V., 1973. Theory of the Earth’s Gravity Field. Amsterdam: Elsevier Scientific.

    Google Scholar 

  • Torge, W., 1991. Geodesy, 2nd edn. Berlin: de Gruyter.

    Book  Google Scholar 

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Author information

Authors and Affiliations

  1. Geomathematics Group, University of Kaiserslautern, Kaiserslautern, Germany

    Willi Freeden & Helga Nutz

  2. Computational Science Center, University of Vienna, Vienna, Austria

    Christian Gerhards

  3. Institute for Computational Engineering ICE, University of Buchs, Buchs, Switzerland

    Michael Schreiner

Authors
  1. Willi Freeden
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  2. Christian Gerhards
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  3. Helga Nutz
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  4. Michael Schreiner
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Corresponding author

Correspondence to Willi Freeden .

Editor information

Editors and Affiliations

  1. Geodetic Institute, University of Stuttgart, Stuttgart, Germany

    Erik Grafarend

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Freeden, W., Gerhards, C., Nutz, H., Schreiner, M. (2016). Disturbing Potential from Deflections of the Vertical: From Globally Reflected Surface Gradient Equation to Locally Oriented Multiscale Modeling. In: Grafarend, E. (eds) Encyclopedia of Geodesy. Springer, Cham. https://doi.org/10.1007/978-3-319-02370-0_126-2

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  • DOI: https://doi.org/10.1007/978-3-319-02370-0_126-2

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  • Publisher Name: Springer, Cham

  • Online ISBN: 978-3-319-02370-0

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