Abstract
This chapter studies locally supported surface mollifier decorrelation of the Earth’s gravitational potential model (EGM), the gravity disturbances and anomalies for the Galapagos, the deflections of the vertical of the hotspots of Hawaii and Iceland, as well as the resulting geological specifics.
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Augustin, M.A., Bauer, M., Blick, C., Eberle, S., Freeden, W., Gerhards C., Ilyasov M., Kahnt R., Klug M., Möhringer, S., Neu, T., Nutz, H., Michel, I. née Ostermann, Punzi, A.: Modeling deep geothermal reservoirs: recent advances and future perspectives. In: Freeden, W., Nashed, M.Z., Sonar, T. (eds.) Handbook of Geomathematics (2), 2nd edn., pp. 1547–1629. Springer, New York (2015)
Cui, J., Freeden, W.: Equidistribution on the sphere. SIAM J. Sci. Stat. Comput. 18, 595–609 (1997)
Cui, J., Freeden, W., Witte, B.: Gleichmäßige Approximation mittels sphärischer Finite Elemente und ihre Anwendung in der Geodäsie. Z. Vermessungswesen 5, 266–278 (1992)
Fehlinger, T.: Multiscale formulations for the disturbing potential and the deflections of the vertical in locally reflected Physical Geodesy. Ph.D. thesis, University of Kaiserslautern, Geomathematics Group (2009)
Foulger, G., Natland, J., Presnall, D., Anderson, D.: Plates, Plumes, and Paradigms. Geological Society of America, Boulder (2005)
Freeden, W.: Stokes boundary value problem of Physical Geodesy and its numerical computation. Mitt. Inst. Theor. Geod. Bonn 56, 1–26 (1978a)
Freeden, W.: An application of a summation formula to numerical computation of integrals over the sphere. Bull. Géod. 52, 165–175 (1978b)
Freeden, W.: Über eine Klasse von Integralformeln der Mathematischen Geodäsie. Veröff. Geod. Inst. RWTH Aachen, Report 27 (1979a)
Freeden, W.: Über ein Verfahren zur Bestimmung des Gravitationspotentials im Äußeren der Kugel. ZAMM 59, T57–T59 (1979b)
Freeden, W.: On the approximation of the external gravitational potential with closed systems of (trial) functions. Bull. Geod. 54, 1–20 (1980a)
Freeden, W.: On spherical spline interpolation and approximation. Math. Meth. Appl. Sci. 3, 551–575 (1981a)
Freeden, W.: Spherical spline approximation and its application in physical geodesy. In: Vogel, A., Ofeagbu, C.O., Gorenflo, R., Ursin, B. (eds.) Geophysical Data Inversion Methods and Applications, pp. 79–104. Vieweg Publication, Leipzig (1990a)
Freeden, W.: Multiscale Modeling of Spaceborne Geodata. Teubner, Stuttgart (1999)
Freeden, W.: Geomathematics: its role, its aim, and its potential. In: Freeden, W., Nashed, Z., Sonar, T. (eds.) Handbook of Geomathematics, vol. 1, 2nd edn., pp. 3–78. Springer, Heidelberg, New York, Dordrecht, London (2015)
Freeden, W., Gerhards, C.: Geomathematically Oriented Potential Theory. CRC Press/Taylor & Francis, Boca Raton (2013)
Freeden, W., Gutting, M.: Integration and Cubature Methods. Chapman and Hall, CRC Press, Boca Raton, London, New York (2018)
Freeden, W., Hesse, K.: On the multiscale solution of satellite problems by use of locally supported kernel functions corresponding to equidistributed data on spherical orbits. Stud. Sci. Math. Hung. 39, 37–74 (2002)
Freeden, W., Maier, T.: On multiscale denoising of spherical functions: basic theory and numerical aspects. Electron. Trans. Numer. Anal. 14, 40–62 (2002)
Freeden, W., Mason, J.C.: Uniform piecewise approximation on the sphere. In: Cox, M.G., Mason, J.C. (eds.) Algorithms for Approximation II. Chapman and Hall Mathematics, pp. 320–333. Chapman & Hall, London (1990)
Freeden, W., Michel V.: Multiscale Potential Theory (With Applications to Geoscience). Birkhäuser, Boston (2004)
Freeden, W., Nutz, H.: Satellite gravity gradiometry as tensorial inverse problem. GEM Int. J. Gemath. 2, 177–218 (2011)
Freeden, W., Nutz, H.: Geodetic observables and their mathematical treatment in multiscale framework. In: Freeden, W., Nashed, M.Z. (eds.) Handbook of Mathematical Geodesy. Geosystems Mathematics, pp. 315–458. Springer International Publishing, Birkhäuser, Basel, New York, Heidelberg (2018a)
Freeden, W., Schneider, F.: An integrated wavelet concept of physical geodesy. Inverse Problems J. Geod. 72, 259–281 (1998b)
Freeden, W., Schreiner, M.: Non-orthogonal expansions on the sphere. Math. Meth. Appl. Sci. 18, 83–120 (1995)
Freeden, W., Schreiner, M.: Orthogonal and non-orthogonal multiresolution analysis, scale discrete and exact fully discrete wavelet transform on the sphere. Constr. Approx. 14, 493–515 (1997)
Freeden, W., Schreiner, M.: Local multiscale modeling of geoid undulations from deflections of the vertical. J. Geodesy 79, 641–651 (2006)
Freeden, W., Schreiner, M.: Spherical Functions of Mathematical Geosciences: A Scalar, Vectorial, and Tensorial Setup. Springer, Heidelberg (2009)
Freeden, W., Windheuser, U.: Spherical wavelet transform and its discretization. Adv. Comput. Math. 5, 51–94 (1996)
Freeden, W., Windheuser, U.: Combined spherical harmonic and wavelet expansion. Appl. Comput. Harm. Anal. 4, 1–37 (1997)
Freeden, W., Witte, B.: From Gaussian least squares approximation to today’s operator-theoretic regularization of ill-posed problems. In: Freeden, W. (Bd. Hrsg.), Freeden, W., Rummel, R. (Hrsg.) Handbuch der Geodäsie, Mathematische Geodäsie/Mathematical Geodesy, vol. 2, pp. 827–930. Springer Spektrum, Heidelberg (2020)
Freeden, W., Wolf, K.: Klassische Erdschwerefeldbestimmung aus der Sicht moderner Geomathematik. Math. Semesterber. 56, 53–77 (2009)
Freeden, W., Schreiner, M., Franke, R.: A survey on spherical spline approximation. Surv. Math. Ind. 7, 29–85 (1996)
Freeden, W., Gervens, T., Schreiner, M.: Constructive Approximation on the Sphere (with Applications to Geomathematics). Oxford Science Publications, Clarendon Press, Oxford, Oxford (1998)
Freeden, W., Nashed, M.Z., Schreiner, M.: Spherical Sampling. Geosystems Mathematics. Springer International Publishing, Basel, New York, Heidelberg (2018)
Freeden, W., Sonar, T., Witte, B.: Gauss as mediator between Mathematics and Geodesy from the past to the present. In: Freeden, W., Nashed, M.Z. (eds.) Handbook of Mathematical Geodesy. Geosystems Mathematics, pp. 1–163. Springer International Publishing, Birkhäuser, Basel, New York, Heidelberg (2018)
Freeden W., Nutz H., Rummel R., Schreiner M.: Satellite gravity gradiometry (SGG): methodological foundation and geomathematical advances. In: Freeden, W. (Bd. Hrsg.), Freeden, W., Rummel, R. (Hrsg.) Handbuch der Geodäsie, Mathematische Geodäsie/Mathematical Geodesy, vol. 2, pp. 1185–1256. Springer Spektrum, Heidelberg (2020)
Gauss, C.F.: Allgemeine Theorie des Erdmagnetismus. Resultate aus den Beobachtungen des magnetischen Vereins, Göttingen (1838)
Georgsson, L.S., Friedleifsson, I.B.: Geothermal energy in the world from energy perspective. Short Course IV on Exploration for Geothermal Resources 1–22 (2009)
Gerhards, C.: Spherical multiscale methods in terms of locally supported wavelets: Theory and application to geomagnetic modeling. Ph.D. thesis, University of Kaiserslautern, Geomathematics Group (2011)
Groten, E.: Geodesy and the Earth’s Gravity Field I + II. Dümmler, Bonn (1979)
Heiskanen, W.A., Moritz, H.: Physical Geodesy. Freeman, San Francisco (1967)
Kious, W.J., Tilling, R.I.: This Dynamic Earth: The Story of Plate Tectonics. DIANE Publishing, Washington (1996)
Laplace, P.S. de: Theorie des attractions des sphéroides et de la figure des planètes. Mèm. de l’Acad., Paris (1785)
Legendre, A.M.: Recherches sur l’attraction des sphèroides homogènes. Mèm. math. phys. près. à l’Acad. Aci. par. divers savantes 10, 411–434 (1785)
Lemoine, F.G., Kenyon, S.C., Factor, J.K., Trimmer, R.G., Pavlis, N.K., Shinn, D.S., Cox, C.M., Klosko, S.M., Luthcke, S.B., Torrence, M.H., Wang, Y.M., Williamson, R.G., Pavlis, E.C., Rapp, R.H., Olson, T.R.: The Development of the Joint NASA GSFC and NIMA geopotential Model EGM96. NASA/TP-1998-206861, NASA Goddard Space Flight Center, Greenbelt MD (1998)
Listing, J.B.: Über unsere jetzige Kenntnis der Gestalt und Größe der Erde. Dietrichsche Verlagsbuchhandlung, Göttingen (1873)
Molodensky, M.S., Eremeev, V.F., Yurkina, M.I.: Methods for Study of the External Gravitational Field and Figure of the Earth. Trudy TSNIIGAiK, p. 131. Geodezizdat, Moscow (1960). English translat.: Israel Program for Scientific Translation, Jerusalem, 1962
Morgan, W.J.: Convective plumes in the lower mantle. Nature 230, 42–43 (1971)
Moritz, H.: Classical physical geodesy. In: Freeden, W., Nashed, Z., Sonar, T. (eds.) Handbook of Geomathematics, 1st edn., vol. 1, pp. 253–289. Springer, Reference, Heidelberg (2015)
Neumann, F.: Vorlesungen über die Theorie des Potentials und der Kugelfunktionen, pp. 135–154. Teubner, Leipzig (1887)
Nutz, H.: A unified setup of gravitational field observables. Shaker, Aachen (2002)
Pavlis, N.K., Holmes, S.A., Kenyon, S.C., John, K., Factor, J.K.: The development and evaluation of the Earth Gravitational Model 2008 (EGM2008). J. Geophys. Res. Solid Earth (1978–2012) 117(B4) (2012) Induced microearthquake patterns in hydrocarbon and geothermal reservoirs: six case studies. Pure Appl. Geophys. 159, 345–369 (2002)
Pizzetti, P.: Geodesia - sulla espressione della gravita alla super cie del geoide, supposto ellissoidico. Att. R. Acad. Lincei 3, 331–350 (1894)
Pizzetti, P.: Corpi equivalenti rispetto alla attrazione newtoniana esterna. Rom. Acc. L. Rend. 18, 211–215 (1909)
Ritter, J.R.R., Christensen, U.R.: Mantle Plumes, a Multidisciplinary Approach. Springer, Berlin (2007)
Rummel, R.: Spherical spectral properties of the Earth’s gravitational potential and its first and second derivatives. In: Sanso, S., Rummel, R. (eds.) Geodetic Boundary Value Problems in View of the One Centimeter Geoid, vol. 65. Lecture Notes in Earth Science, pp. 359–404. Springer, Berlin (1997)
Rummel, R., van Gelderen, M.: Spectral analysis of the full gravity tensor. Geophys. J. 111, 159–169 (1992)
Saemundsson, K.: Geothermal systems in global perspective. In: Short Course IV on Exploration for Geothermal Resources, Lake Naivasha, UNU-GTP, KenGen and GDC, 2009
Schubert, G., Turcotte, T.L., Olson, P.: Mantle Convection in the Earth and Planets. Cambridge University Press, Cambridge (2001)
Stokes, G.G.: On the variation of gravity at the surface of the Earth. Trans. Camb. Philos. Soc. 148, 672–712 (1849)
Tilling, R.I., Heliker, C., Swanson, D.A.: Eruptions of Hawaiian Volcanoes: Past, Present, and Future. U.S. Geol. Surv. General Inf. Prod. 117, 1–63 (2010)
Torge, W.: Geodäsie. Walter de Gruyter, Berlin (2003)
Torge, W., Müller, J.: Geodesy, 4th edn. Walter de Gruyter, Berlin (2012)
Vanicek, P., Krakiwsky, E.J.: Geodesy. Elsevier Science, Amsterdam (1986)
Vening Meinesz, F.A.: A formula expressing the deflection of the plumb-line in the gravity anomalies and some formulae for the gravity field and the gravity potential outside the geoid. In: Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen, vol. 31, pp. 315–331 (1928)
Weyl, H.: Über die Gleichverteilung von Zahlen mod. Eins. Math. Ann. 77, 313–352 (1916)
Wilson, J.T.: A possible origin of the Hawaiian Island. Canad. J. Phys. 41, 863–868 (1963)
Wolf, K.: Multiscale modeling of classical boundary value problems in physical geodesy by locally supported wavelets. Ph.D. thesis, University of Kaiserslautern, Geomathematics Group (2009)
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Freeden, W. (2021). Surface Applications. In: Decorrelative Mollifier Gravimetry. Geosystems Mathematics. Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-69909-3_8
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