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An efficient regularization method for a large scale ill-posed geothermal problem
Linköping University, Department of Mathematics, Computational Mathematics. Linköping University, Faculty of Science & Engineering.ORCID iD: 0000-0002-2681-8965
State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China.
State Key Laboratory of Lithospheric Evolution, Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China; CAS Center for Excellence in Tibetan Plateau Earth Sciences, Beijing, China.
Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering. Department of Mathematics, Makerere University, Kampala, Uganda.
2017 (English)In: Computers & Geosciences, ISSN 0098-3004, E-ISSN 1873-7803, Vol. 105, 1-9 p.Article in journal (Refereed) Published
Abstract [en]

The inverse geothermal problem consists of estimating the temperature distribution below the earth's surface using measurements on the surface. The problem is important since temperature governs a variety of geologic processes, including the generation of magmas and the deformation style of rocks. Since the thermal properties of rocks depend strongly on temperature the problem is non-linear.

The problem is formulated as an ill-posed operator equation, where the righthand side is the heat-flux at the surface level. Since the problem is ill-posed regularization is needed. In this study we demonstrate that Tikhonov regularization can be implemented efficiently for solving the operator equation. The algorithm is based on having a code for solving a well-posed problem related to the above mentioned operator. The algorithm is designed in such a way that it can deal with both 2D and 3D calculations.

Numerical results, for 2D domains, show that the algorithm works well and the inverse problem can be solved accurately with a realistic noise level in the surface data.

Place, publisher, year, edition, pages
Elsevier, 2017. Vol. 105, 1-9 p.
National Category
Earth and Related Environmental Sciences Mathematics
Identifiers
URN: urn:nbn:se:liu:diva-139052DOI: 10.1016/j.cageo.2017.04.010ISI: 000404697000001OAI: oai:DiVA.org:liu-139052DiVA: diva2:1117637
Available from: 2017-06-29 Created: 2017-06-29 Last updated: 2017-08-14Bibliographically approved

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The full text will be freely available from 2019-04-27 10:29
Available from 2019-04-27 10:29

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
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