Abstract
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.
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Baba T. and Cummins Phil R., Contiguous rupture areas of two Nankai Trough earthquakes revealed by high-resolution tsunami waveform inversion, Geophysical Research Letters, VOL. 32, L08305, doi:10.1029/2004GL022320, (2005).
Cheverda,V.A., Kostin,V.I., r-pseudoinverse for compact operator, Siberian Electronic Mathematical Reports, V. 7, 258–282 (2010).
Lavrentiev, M.M, Romanenko,A.A., Lysakov K.F.: Modern Computer Architecture to Speed-Up Calculation of Tsunami Wave Propagation, Proc. of the Eleventh Pacific/Asia Offshore Mech. Symp. Shanghai,China, October 12-16, ISSN 1946-004X, 186–191 (2014).
Percival, D. B., Denbo, D. W., Eble, M. C., Gica, E., Mofjeld, H. O., Spillane, M. C., Tang, L., and Titov, V. V., Extraction of tsunami source coefficients via inversion of DARTr buoy data, Nat. Hazards, V. 58, 567–590 (2011).
Piatanesi, A., Tinti, S., and Pagnoni, G., Tsunami waveform inversion by numerical finite-elements Green’s functions, Nat. Hazards Earth Syst. Sci.,V. 1, 187-194, (2001).
Pires, C. and Miranda, P. M. A., Tsunami waveform inversion by adjoint methods, J. Geophys. Res., V. 106, 19773–19796 (2001).
Satake, K., Inversion of tsunami waveforms for the estimation of a fault heterogeneity: method and numerical experiments, J. Phys. Earth, 35, 241–254 (1987).
Titov, V.V., F.I. Gonzlez, E.N. Bernard, M.C. Eble, H.O. Mofjeld, J.C. Newman, and A.J. Venturato, Real-time tsunami forecasting: Challenges and solutions. Nat. Hazards, 35(1), Special Issue, U.S. National Tsunami Hazard Mitigation Program, 41–58 (2005).
Voronina, T. A. and Tcheverda, V. A., Reconstruction of tsunami initial form via level oscillation, Bull. Nov. Comp. Center, Math. Model. Geoph., V. 4, 127–136 (1998).
Voronina, T. A., Determination of spatial distribution of oscillation sources by remote measurements on a finite set of points, Sib. J. Calc. Math., V. 3, 203–211 (2004).
Voronina, T. A., Reconstruction of Initial Tsunami Waveforms by a Truncated SVD Method, J. Inverse and Ill-posed Problems, V. 19, 615–629 (2012).
Voronina, T. A., Tcheverda, V. A., and Voronin, V. V., Some properties of the inverse operator for a tsunami source recovery, Siberian Electronic Mathematical Reports, V. 11, 532–547 (2014).
Voronin,V.V., Voronina,T.A., and Tcheverda,V.A., Inversion method for initial tsunami waveform reconstruction, Nat. Hazards Earth Syst. Sci., V. 15, 1251–1263 (2015).
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Voronina, T.A., Romanenko, A.A. (2016). The New Method of Tsunami Source Reconstruction With r-Solution Inversion Method. In: Geist, E.L., Fritz, H.M., Rabinovich, A.B., Tanioka, Y. (eds) Global Tsunami Science: Past and Future, Volume I. Pageoph Topical Volumes. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-55480-8_21
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DOI: https://doi.org/10.1007/978-3-319-55480-8_21
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