The Application of Reproducing Kernel Based Spline Approximation to Seismic Surface and Body Wave Tomography: Theoretical Aspects and Numerical Results

  • The main aim of this work was to obtain an approximate solution of the seismic traveltime tomography problems with the help of splines based on reproducing kernel Sobolev spaces. In order to be able to apply the spline approximation concept to surface wave as well as to body wave tomography problems, the spherical spline approximation concept was extended for the case where the domain of the function to be approximated is an arbitrary compact set in R^n and a finite number of discontinuity points is allowed. We present applications of such spline method to seismic surface wave as well as body wave tomography, and discuss the theoretical and numerical aspects of such applications. Moreover, we run numerous numerical tests that justify the theoretical considerations.

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Author:Abel Amirbekyan
URN (permanent link):urn:nbn:de:hbz:386-kluedo-21039
Advisor:Michel Volker
Document Type:Doctoral Thesis
Language of publication:English
Year of Completion:2007
Year of Publication:2007
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2007/04/16
Tag:Sobolev spaces; inverse problem; localizing basis; seismic tomography; splines
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:510 Mathematik
MSC-Classification (mathematics):41A15 Spline approximation
45Q05 Inverse problems
86A15 Seismology

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