Properties of the inverse problem solutions for paleotemperature reconstructions
https://doi.org/10.26583/vestnik.2025.5.5
EDN: LOCBGN
Abstract
The studies of the past temperatures at the Earth surface is important problem for prediction of the climate changes. The systematic instrumental temperature measurements took place no more than two centuries. Thus, indirect estimations of the past temperatures present main information on the past climate. It is considered that the measured temperatures in the boreholes can be used to reconstruct the past surface temperatures at the Earth. The inverse problem on the past surface temperature reconstruction based on the measured borehole temperature in glaciers and rocks is studied. In common case the solution of this problem is not unique and stable. There were many such reconstructions, however, the properties of such solutions have not been derived. We find out that the solution of this problem is not unique and stable. Unfortunately, various previous reconstructions do not take into account these properties. We prove in this paper that the uniqueness and stability properties take place for the inverse problems that assume solution in the form of the finite segments of the Fourier series.
Supporting agencies: The work was supported by the Ministry of Science and Higher Education of the Russian Federation and was carried out under the state assignment FSWU-2023-0031.
About the Authors
O. V. Nagornov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
S. A. Tyuflin
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
V. L. Kamynin
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Russian Federation
Russian Federation
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Review
For citations:
Nagornov O.V., Tyuflin S.A., Kamynin V.L. Properties of the inverse problem solutions for paleotemperature reconstructions. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2025;14(5):424-430. (In Russ.) https://doi.org/10.26583/vestnik.2025.5.5. EDN: LOCBGN
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