## On the Local Multiscale Determination of the Earth`s Disturbing Potential From Discrete Deflections of the Vertical

• As a first approximation the Earth is a sphere; as a second approximation it may be considered an ellipsoid of revolution. The deviations of the actual Earth's gravity field from the ellipsoidal 'normal' field are so small that they can be understood to be linear. The splitting of the Earth's gravity field into a 'normal' and a remaining small 'disturbing' field considerably simplifies the problem of its determination. Under the assumption of an ellipsoidal Earth model high observational accuracy is achievable only if the deviation (deflection of the vertical) of the physical plumb line, to which measurements refer, from the ellipsoidal normal is not ignored. Hence, the determination of the disturbing potential from known deflections of the vertical is a central problem of physical geodesy. In this paper we propose a new, well-promising method for modelling the disturbing potential locally from the deflections of the vertical. Essential tools are integral formulae on the sphere based on Green's function of the Beltrami operator. The determination of the disturbing potential from deflections of the vertical is formulated as a multiscale procedure involving scale-dependent regularized versions of the surface gradient of the Green function. The modelling process is based on a multiscale framework by use of locally supported surface curl-free vector wavelets.

Author: Willi Freeden, Thomas Fehlinger, Carsten Mayer, Michael Schreiner urn:nbn:de:hbz:386-kluedo-15228 Schriften zur Funktionalanalysis und Geomathematik (32) Preprint English 2007 2007 Technische Universität Kaiserslautern 2008/04/07 Earth's disturbing potential; deflections of the vertical; local multiscale; locally supported (Green's) vector wavelets Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik 42-XX FOURIER ANALYSIS / 42Cxx Nontrigonometric harmonic analysis / 42C40 Wavelets and other special systems 65-XX NUMERICAL ANALYSIS / 65Txx Numerical methods in Fourier analysis / 65T99 None of the above, but in this section 86-XX GEOPHYSICS [See also 76U05, 76V05] / 86Axx Geophysics [See also 76U05, 76V05] / 86A20 Potentials, prospecting 86-XX GEOPHYSICS [See also 76U05, 76V05] / 86Axx Geophysics [See also 76U05, 76V05] / 86A30 Geodesy, mapping problems Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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