Abstract
With the aid of classical results of potential theory, the limit- and jump-relations, a multiscale framework on geodetically relevant regular surfaces is established corresponding to oblique derivative data. By the oblique distance to the regular surface a scale factor in the kernel functions of the limit- and jump-operators is introduced, which connects these intergral kernels with the theory of scaling functions and wavelets.
As applications of the wavelet approach some numerical examples are presented on an ellipsoid of revolution. At the end we discuss a fast multiscale representation of the solution of the (exterior) oblique derivative (boundary—value) problem corresponding to geoscientifically relevant surfaces. A local as well as global reconstruction of the gravitational potential model EGM96 on the reference ellipsoid will illustrate the power of this appoach.
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References
Freeden W. (1980). On the Approximation of External Gravitational Potential With Closed Systems of (Trial) Functions, Bull. Géod., 54, 1–20.
Freeden W., H. Kersten (1980). The Geodetic Boundary Value Problem Using the Known Surface of the Earth, Report No. 29, Geod. Inst. RWTH Aachen.
W. Freeden, H. Kersten (1981). A Constructive Approximation Theorem for the Oblique Derivative Problem in Potential Theory, Math. Meth. Appl. Sci., 3, 104–114.
Freeden W., M. Schreiner, R. Franke (1996). A Survey on Spherical Spline Approximation, Surv. Math., 7, 29–85.
Freeden W., U. Windheuser, Spherical Wavelet Transform and Its Discretization, Adv. Comput. Math., 5, 51–94.
Freeden W., T. Gervens, M. Schreiner (1998). Constructive Approximation on the Sphere (With Applications to Geomathematics). Oxford Science Publications, Clarendon.
Freeden W., C. Mayer (2001). Wavelets Generated by Layer Potentials, Apllied Computational Harmonic Analysis (accepted for publication).
Glockner O. (2001). On Numerical Aspects of Gravitational Field Modeling from SST and SGG by Harmonic Splines and Wavelets (With Application to CHAMP Data). Doctoral Thesis, Geomathematics Group, Shaker Verlag.
Kellogg O.D. (1929). Foundations of Potential Theory. Frederick Ungar Publishing Company.
Kersten H. (1980). Grenz-und Sprungrelationen für Potentiale mit quadratsummierbarer Flächenbelegung, Resultate der Mathematik, 3, 17–24.
Mayer C. (2001). Potential Operators, Jump Relations and Wavelets. Diploma Thesis, Department of Mathematics, Geomathematics Group, University of Kaiserslautern.
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Freeden, W., Mayer, C. (2004). Multiscale Solution of Oblique Boundary-Value Problems by Layer Potentials. In: Sansò, F. (eds) V Hotine-Marussi Symposium on Mathematical Geodesy. International Association of Geodesy Symposia, vol 127. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10735-5_12
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DOI: https://doi.org/10.1007/978-3-662-10735-5_12
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