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J. Sib. Fed. Univ. Math. Phys., 2014, Volume 7, Issue 2, Pages 224–234 (Mi jsfu365)  

This article is cited in 4 scientific papers (total in 4 papers)

Numerical evaluation of the truncated singular value decomposition within the seismic traveltimes tomography framework

Alexandr S. Serdyukova, Andrey V. Patutinb, Tatiana V. Shilovab

a Novosibirsk State University, Pirogova, 2, Novosibirsk, 630090 Russia
b Institute of Mining, Krasny, 54, Novosibirsk, 630091 Russia

Abstract: The method of truncated singular value decomposition is a powerful tool of regularization and solution of inverse problems. Application of this method is limited by the memory requirements for the calculation of singular value decomposition of matrices. The solution is a usage of iterative procedures, that provide the possibility to evaluate only the largest singular values and corresponding vectors. For the practical application of this methodology one should answer the questions: what part of the spectrum can be determined numerically and whether the number of singular vectors is enough for the solution. These problems are considered in the present paper within the seismic traveltimes inversion framework.

Keywords: inverse problems, numerical methods, truncated singular value decomposition, geophysics, seismic traveltimes.

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UDC: 512.54
Received: 20.08.2013
Received in revised form: 25.12.2013
Accepted: 20.02.2014

Citation: Alexandr S. Serdyukov, Andrey V. Patutin, Tatiana V. Shilova, “Numerical evaluation of the truncated singular value decomposition within the seismic traveltimes tomography framework”, J. Sib. Fed. Univ. Math. Phys., 7:2 (2014), 224–234

Citation in format AMSBIB
\by Alexandr~S.~Serdyukov, Andrey~V.~Patutin, Tatiana~V.~Shilova
\paper Numerical evaluation of the truncated singular value decomposition within the seismic traveltimes tomography framework
\jour J. Sib. Fed. Univ. Math. Phys.
\yr 2014
\vol 7
\issue 2
\pages 224--234

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    This publication is cited in the following articles:
    1. Nikitin A.A., Serdyukov A.S., Duchkov A.A., Azarov A.V., Yablokov A.V., “Parallel Implementation of Seismic Traveltime Computations For 3D Tomography”, Science and Technologies in Geology, Exploration and Mining, Sgem 2014, Vol III, International Multidisciplinary Scientific Geoconference-Sgem, Stef92 Technology Ltd, 2015, 919–924  isi
    2. M. V. Kurlenya, G. S. Chernyshov, A. S. Serdyukov, A. A. Duchkov, A. V. Yablokov, “Procedure and results of seismic investigations into causes of landslides in permafrost rocks”, J. Min. Sci., 52:5 (2016), 835–841  crossref  isi  scopus
    3. A. S. Serdyukov, A. V. Yablokov, G. S. Chernyshov, A. V. Azarov, “The surface waves-based seismic exploration of soil and ground water”, All-Russian Conference on Challenges For Development in Mining Science and Mining Industry Devoted to the 85Th Anniversary of Academician Mikhail Kurlenya, IOP Conf. Ser. Earth Envir. Sci., IOP Conference Series-Earth and Environmental Science, 53, ed. M. Kurlenya, IOP Publishing Ltd, 2017, UNSP 012010  crossref  isi  scopus
    4. L. Lu, G. Tong, G. Guo, Sh. Liu, “Split Bregman iteration based reconstruction algorithm for electrical capacitance tomography”, Trans. Inst. Meas. Control, 41:9 (2019), 2389–2399  crossref  isi  scopus
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