## On Mathematical Aspects of a Combined Inversion of Gravity and Normal Mode Variations by a Spline Method

• This paper provides a brief overview of two linear inverse problems concerned with the determination of the Earth’s interior: inverse gravimetry and normal mode tomography. Moreover, a vector spline method is proposed for a combined solution of both problems. This method uses localised basis functions, which are based on reproducing kernels, and is related to approaches which have been successfully applied to the inverse gravimetric problem and the seismic traveltime tomography separately.

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Verfasserangaben: Paula Berkel, Volker Michel urn:nbn:de:hbz:386-kluedo-15800 Schriften zur Funktionalanalysis und Geomathematik (41) Preprint Englisch 2008 2008 Technische Universität Kaiserslautern 03.11.2008 Wellengeschwindigkeit; harmonische Dichte ; reproduzierender Kern ; schlecht gestellt body wave velocity ; harmonic density ; normal mode ; reproducing kernel; splitting function Eigenschwingung; Gravimetrie ; Harmonische Funktion ; Inverses Problem ; Massendichte ; Newtonsches Potenzial ; Regularisierung ; Spline Fachbereich Mathematik 5 Naturwissenschaften und Mathematik / 510 Mathematik 45-XX INTEGRAL EQUATIONS / 45Bxx Fredholm integral equations / 45B05 Fredholm integral equations 45-XX INTEGRAL EQUATIONS / 45Qxx Inverse problems / 45Q05 Inverse problems 46-XX FUNCTIONAL ANALYSIS (For manifolds modeled on topological linear spaces, see 57Nxx, 58Bxx) / 46Exx Linear function spaces and their duals [See also 30H05, 32A38, 46F05] (For function algebras, see 46J10) / 46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32] 65-XX NUMERICAL ANALYSIS / 65Dxx Numerical approximation and computational geometry (primarily algorithms) (For theory, see 41-XX and 68Uxx) / 65D07 Splines 65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F22 Ill-posedness, regularization 86-XX GEOPHYSICS [See also 76U05, 76V05] / 86Axx Geophysics [See also 76U05, 76V05] / 86A22 Inverse problems [See also 35R30] Standard gemäß KLUEDO-Leitlinien vor dem 27.05.2011

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