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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Author:Paula Berkel, Volker Michel
URN (permanent link):urn:nbn:de:hbz:386-kluedo-15800
Serie (Series number):Schriften zur Funktionalanalysis und Geomathematik (41)
Document Type:Preprint
Language of publication:English
Year of Completion:2008
Year of Publication:2008
Publishing Institute:Technische Universität Kaiserslautern
Tag:Wellengeschwindigkeit; harmonische Dichte ; reproduzierender Kern ; schlecht gestellt
body wave velocity ; harmonic density ; normal mode ; reproducing kernel; splitting function
GND-Keyword:Eigenschwingung; Gravimetrie ; Harmonische Funktion ; Inverses Problem ; Massendichte ; Newtonsches Potenzial ; Regularisierung ; Spline
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik
MSC-Classification (mathematics):45B05 Fredholm integral equations
45Q05 Inverse problems
46E22 Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32]
65D07 Splines
65F22 Ill-posedness, regularization
86A22 Inverse problems [See also 35R30]

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