The New Method of Tsunami Source Reconstruction With r-Solution Inversion Method

  • T. A. VoroninaEmail author
  • A. A. Romanenko
Part of the Pageoph Topical Volumes book series (PTV)


Application of the \(r-\)solution method to reconstructing the initial tsunami waveform is discussed. This methodology is based on the inversion of remote measurements of water-level data. The wave propagation is considered within the scope of a linear shallow-water theory. The ill-posed inverse problem in question is regularized by means of a least square inversion using the truncated Singular Value Decomposition method. As a result of the numerical process, an r-solution is obtained. The method proposed allows one to control the instability of a numerical solution and to obtain an acceptable result in spite of ill posedness of the problem. Implementation of this methodology to reconstructing of the initial waveform to 2013 Solomon Islands tsunami validates the theoretical conclusion for synthetic data and a model tsunami source: the inversion result strongly depends on data noisiness, the azimuthal and temporal coverage of recording stations with respect to the source area. Furthermore, it is possible to make a preliminary selection of the most informative set of the available recording stations used in the inversion process.


Tsunami numerical modeling ill-posed inverse problem  regularization singular value decomposition r-solution 


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© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Institute of Computational Mathematics and Mathematical Geophysics of SB RASNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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