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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 19, Issue 2 (Jan 2011)


Characteristic interactions and successive approximations in problems on evaluating coefficients of transport equation and elemental content of a medium

Alfred I. Khisamutdinov
  • Russian Academy of Sciences, Siberian Branch, A. A. Trofimuk Institute of Petroleum Geology and Geophysics, Novosibirsk, Russia.
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Published Online: 2011-05-31 | DOI: https://doi.org/10.1515/jiip.2011.029


Inversion methods are very important components of nuclear-geophysical technologies. Their main aim is to evaluate the set of parameters of a formation, using measurements data. The parameters describe the properties and the elemental content of it, and they enter into coefficients of the transport equation. In this paper we develop and formalize an approach to problems on mathematical interpretation of the data, we state two inverse problems to the equation and construct successive approximations of the “prime” iteration type to solve a corresponding system of parameters evaluation. The approach is based on concepts defined of “characteristic” interactions, elements, and matrix, it uses the superposition principle for transport processes and linear a priori constraints for the unknowns. Earlier a few concrete problems were examined within this approach.

Keywords.: Transport equation; inverse problems; numerical methods; measurement data; nuclear-geophysical logging; evaluation of coefficients parameters and parameters of a medium; iteration methods; convergence

About the article

Received: 2009-12-14

Published Online: 2011-05-31

Published in Print: 2011-06-01

Citation Information: Journal of Inverse and Ill-posed Problems, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip.2011.029. Export Citation

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