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...
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References and Reading
Bruns, E. H., 1878. Die Figur der Erde. Publikationen des Königlichen Preussischen Geod ä tischen Instituts. Berlin, P. Stankiewicz Buchdruckerei.
Cui, J. and Freeden, W., 1997. Equidistribution on the sphere. SIAM 18, 595–609.
Freeden, W., 1978. An application of a summation formula to numerical computation of integrals over the sphere. Bulletin Géodésique, 52, 165–175.
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.
Freeden, W., and Gerhards, C., 2012. Geomathematically Oriented Potential Theory. Boca Raton: Chapman & Hall/CRC.
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.
Freeden, W., and Schreiner, M., 2006. Local multiscale modelling of geoid undulations from deflections of the vertical. Journal of Geodesy, 79, 641–651.
Freeden, W., and Wolf, K., 2009. Klassische Erdschwerefeldbestimmung aus der Sicht moderner Geomathematik. Mathematische Semesterberichte, 56, 53–77.
Freeden, W., Gervens, T., and Schreiner, M., 1998. Constructive Approximation on the Sphere (With Applications to Geomathematics). Oxford: Oxford Science Publications/Clarendon Press.
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.
Heiskanen, W. A., and Moritz, H., 1967. Physical Geodesy. San Francisco: W.H. Freeman.
Hofmann-Wellenhof, B., and Moritz, H., 2006. Physical Geodesy, 2nd edn. Wien/New York: Springer.
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.
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).
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.
Stokes, G. G., 1849. On the variation of gravity on the surface of the Earth. Transactions of the Cambridge Philosophical Society, 8, 672–695.
Weyl, H., 1916. Über die Gleichverteilung von Zahlen mod Eins. Mathematische Annalen, 77, 313–352.
Wolf, K., 2009. Multiscale modeling of classical boundary value problems in physical geodesy by locally supported wavelets. PhD thesis, University of Kaiserslautern, Geomathematics Group.
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Augustin, M., Blick, C., Eberle, S., Freeden, W. (2015). Disturbing Potential from Gravity Anomalies: From Globally Reflected Stokes Boundary Value Problem to Locally Oriented Multiscale Modeling. In: Grafarend, E. (eds) Encyclopedia of Geodesy. Springer, Cham. https://doi.org/10.1007/978-3-319-02370-0_124-1
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DOI: https://doi.org/10.1007/978-3-319-02370-0_124-1
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