Encyclopedia of Geodesy

Living Edition
| Editors: Erik Grafarend

Disturbing Potential from Gravity Anomalies: From Globally Reflected Stokes Boundary Value Problem to Locally Oriented Multiscale Modeling

  • Matthias AugustinEmail author
  • Christian Blick
  • Sarah Eberle
  • Willi FreedenEmail author
Living reference work entry
DOI: https://doi.org/10.1007/978-3-319-02370-0_124-1

Definition

Stokes problem, Fourier series expansion in terms of outer harmonics, classical global solution by convolving gravity anomalies against the Stokes kernel , regularization of the Stokes kernel, local multiscale approximation.

Introduction

The traditional approach of physical geodesy (cf., e.g., Heiskanen and Moritz, 1967; Moritz, 2015) starts from the assumption that scalar gravity intensity is available over the whole Earth’s surface. The gravitational part of the gravity potential can then be regarded as a harmonic function outside the Earth’s surface. A classical approach to gravity field modeling was conceived by G.G. Stokes (1849). He proposed reducing the given gravity accelerations from the Earth’s surface to the geoid (see, e.g., Listing, 1878), where the geoid is a level surface, e.g., its potential value is constant. The difference between the reduced gravity disturbing potential, i.e., the difference between the actual and the reference potential, can be obtained...

Keywords

Gravity Anomaly Local Support Cubature Formula Gravity Disturbance Spherical Approximation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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References and Reading

  1. Bruns, E. H., 1878. Die Figur der Erde. Publikationen des Königlichen Preussischen Geod ä tischen Instituts. Berlin, P. Stankiewicz Buchdruckerei.Google Scholar
  2. Cui, J. and Freeden, W., 1997. Equidistribution on the sphere. SIAM 18, 595–609.Google Scholar
  3. Freeden, W., 1978. An application of a summation formula to numerical computation of integrals over the sphere. Bulletin Géodésique, 52, 165–175.CrossRefGoogle Scholar
  4. 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 pp. 3–78. Heidelberg: Springer.Google Scholar
  5. Freeden, W., and Gerhards, C., 2012. Geomathematically Oriented Potential Theory. Boca Raton: Chapman & Hall/CRC.CrossRefGoogle Scholar
  6. Freeden, W., and Maier, T., 2002. On multiscale denoising of spherical functions: basic theory and numerical aspects. Electronic Transactions on Numerical Analysis (ETNA), 14, 56–78.Google Scholar
  7. Freeden, W., and Schreiner, M., 2006. Local multiscale modelling of geoid undulations from deflections of the vertical. Journal of Geodesy, 79, 641–651.CrossRefGoogle Scholar
  8. Freeden, W., and Wolf, K., 2009. Klassische Erdschwerefeldbestimmung aus der Sicht moderner Geomathematik. Mathematische Semesterberichte, 56, 53–77.CrossRefGoogle Scholar
  9. 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
  10. Grafarend, E. W., Klapp, M., and Martinec, Z., 2015. Spacetime modelling of the Earth’s gravity field by ellipsoidal harmonics. In Freeden, W., Nashed, Z., and Sonar, T. (eds.), Handbook of Geomathematics, 2nd edn, pp. 381–496, Heidelberg: Springer.Google Scholar
  11. Heiskanen, W. A., and Moritz, H., 1967. Physical Geodesy. San Francisco: W.H. Freeman.Google Scholar
  12. Hofmann-Wellenhof, B., and Moritz, H., 2006. Physical Geodesy, 2nd edn. Wien/New York: Springer.Google Scholar
  13. Listing, J. B., 1878. Neue geometrische und dynamische Constanten des Erdkörpers. Nachrichten von der Königlichen Gesellschaft der Wissenschaften und der Georg-Augusts-Universität zu Göttingen, pp. 749–815.Google Scholar
  14. Molodensky, M. S., Eremeev, V. F., and Yurkina, M. I., 1960. Methods for study of the external gravitational field and figure of the Earth. Trudy TsNIIGAiK, Geodezizdat, Moscow, p. 131 (English translat.: Israel Program for Scientific Translation, Jerusalem, 1962).Google Scholar
  15. Moritz, H., 2015. Classical physical geodesy. In Freeden, W., Nashed, Z., and Sonar, T. (eds.), Handbook of Geomathematics. 2nd edn, pp. 253–290, Heidelberg: Springer.Google Scholar
  16. Stokes, G. G., 1849. On the variation of gravity on the surface of the Earth. Transactions of the Cambridge Philosophical Society, 8, 672–695.Google Scholar
  17. Weyl, H., 1916. Über die Gleichverteilung von Zahlen mod Eins. Mathematische Annalen, 77, 313–352.CrossRefGoogle Scholar
  18. Wolf, K., 2009. Multiscale modeling of classical boundary value problems in physical geodesy by locally supported wavelets. PhD thesis, University of Kaiserslautern, Geomathematics Group.Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Mathematical Image Analysis GroupSaarland UniversitySaarbrückenGermany
  2. 2.Geomathematics GroupUniversity of KaiserslauternKaiserslauternGermany
  3. 3.Numerical Analysis GroupUniversity of TübingenTübingenGermany