Abstract:
This study deals with the application of the r-solution method to recover the initial tsunami waveform in a tsunami source area by inverting the remote water-level measurements for a real event. The inverse problem in question is regarded as the so-called ill-posed problem and it is regularized by means of the least square inversion using the truncated Singular Value Decomposition method. The method presented allows one to control the instability of the numerical solution and to obtain an acceptable result in spite of the ill-posedness of the problem. Moreover, it is possible to make a preliminary prediction of the quality of the inversion with a given set of observational stations and to estimate further changes in the inversion result after modifying the monitoring system.
Key words:
tsunami numerical modeling, ill-posed inverse problem, regularization, singular value decomposition and r-solution.
Citation:
T. A. Voronina, “Recovering a tsunami source and designing an observational system based on the r-solution method”, Sib. Zh. Vychisl. Mat., 19:4 (2016), 343–356; Num. Anal. Appl., 9:4 (2016), 267–276
\Bibitem{Vor16}
\by T.~A.~Voronina
\paper Recovering a~tsunami source and designing an observational system based on the $r$-solution method
\jour Sib. Zh. Vychisl. Mat.
\yr 2016
\vol 19
\issue 4
\pages 343--356
\mathnet{http://mi.mathnet.ru/sjvm622}
\crossref{https://doi.org/10.15372/SJNM20160401}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3600773}
\elib{https://elibrary.ru/item.asp?id=27298002}
\transl
\jour Num. Anal. Appl.
\yr 2016
\vol 9
\issue 4
\pages 267--276
\crossref{https://doi.org/10.1134/S1995423916040017}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000391192300001}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85002901384}
Linking options:
https://www.mathnet.ru/eng/sjvm622
https://www.mathnet.ru/eng/sjvm/v19/i4/p343
This publication is cited in the following 11 articles:
Mikhail Lavrentiev, Konstantin Lysakov, Andrey Marchuk, Konstantin Oblaukhov, “Fundamentals of Fast Tsunami Wave Parameter Determination Technology for Hazard Mitigation”, Sensors, 22:19 (2022), 7630
T. A. Voronina, V. V. Voronin, “A study of implementation features of the r-solution method for tsunami source recovery in the case of the Illapel Tsunami 2015”, Pure Appl. Geophys., 178:12, SI (2021), 4853–4863
T A Voronina, A V Loskutov, “Applying the R-solution method for designing a tsunami observational system”, J. Phys.: Conf. Ser., 2099:1 (2021), 012063
M. Lavrentiev, K. Lysakov, A. Marchuk, K. Oblaukhov, M. Shadrin, “Hardware acceleration of tsunami wave propagation modeling in the southern part of japan”, Appl. Sci.-Basel, 10:12 (2020), 4159
I. E. Mulia, A. R. Gusman, A. L. Williamson, K. Satake, “An optimized array configuration of tsunami observation network off southern Java, Indonesia”, J. Geophys. Res.-Solid Earth, 124:9 (2019), 9622–9637
T. A. Voronina, V. V. Voronin, V. A. Cheverda, “The 2015 Illapel tsunami source recovery by inversion of DART tsunami waveforms using the R-solution method”, Pure Appl. Geophys., 176:7, SI (2019), 2985–2993
Ch. An, Ph. L.-F. Liu, L. Meng, “A sensitivity analysis of tsunami inversions on the number of stations”, Geophys. J. Int., 214:2 (2018), 1313–1323
M. J. Hossen, A. Gusman, K. Satake, Ph. R. Cummins, “An adjoint sensitivity method applied to time reverse imaging of tsunami source for the 2009 Samoa earthquake”, Geophys. Res. Lett., 45:2 (2018), 627–636
I. E. Mulia, A. R. Gusman, K. Satake, “Optimal design for placements of tsunami observing systems to accurately characterize the inducing earthquake”, Geophys. Res. Lett., 44:24 (2017), 12106–12115
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