Abstract
New numerical algorithm of determining the moving tsunami wave height for linear source at the characteristic surface \(t=\tau (x,y)\) is proposed where \(\tau (x,y)\) is a solution of Cauchy problem for eikonal equation. This algorithm based on and representation of fundamental solution of linear shallow water equations in the singular and regular parts. This approach allows one to reduce computational time. We get the expression of the moving tsunami wave height for the linear and arbitrary sources. Numerical results are discussed.
O. Krivorotko–This work is partially supported by the Ministry of Education and Science of the Russian Federation and the Republic of Kazakhstan N. 1746/GF4 “Theory and numerical methods for solving inverse and ill-posed problems of nature”.
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References
Kabanikhin, S., Hasanov, A., Marinin, I., Krivorotko, O., Khidasheli, D.: A variational approach to reconstruction of an initial tsunami source perturbation. Appl. Numer. Math. 83, 22–37 (2014)
Babich, V.M., Buldyrev, V.S., Molotkov, I.A.: Space-Time Ray Method: Linear and Nonlinear Waves (in Russian). Leningrad University Publisher, Leningrad (1985)
Dobrokhotov, S.Y., Nekrasov, R.V., Tirozzi, B.: Asymptotic solutions of the linear shallow-water equations with localized initial data. J. Eng. Math. 69, 225–242 (2011)
Maslov, V.P.: The Complex WKB Method for Nonlinear Equations I: Linear Theory. Birkhäuser Basel, Basel, Boston, Berlin (1994)
Shokin, Y.I., Chubarov, L.B., Fedotova, Z.I., Gusyakov, V.K., Babailov, V.V., Beisel, S.A., Eletsky, S.V.: Mathematical modelling in application to regional tsunami warning systems operations. In: Notes on Numerical Fluid Mechanics and Multidisciplinary Design, vol. 101, pp. 52–68 (2008)
Beisel, S.A., Chubarov, L.B., Didenkulova, I., Kit, E., Levin, A., Pelinovsky, E., Shokin, Y.I., Sladkevich, M.: The 1956 Greek Tsunami Recorded at Yafo (Israel) and Its Numerical Modeling. J. Geophys. Res. 114, C09002 (2009)
Dutykh, D., Mitsotakis, D., Chubarov, L.B., Shokin, Y.I.: On the contribution of the horisontal sea-bed displacements into the tsunami generation process. Ocean Model. 56, 43–56 (2012)
Kabanikhin, S.I.: Linear regularization of multidimensional inverse problems for hyperbolic equations (in Russian). Sobolev Institute of Mathematics. Preprint No. 27 (1988)
Romanov, V.G.: Inverse Problems of Mathematical Physics (in Russian). Nauka, Moscow (1984)
Romanov, V.G.: Stability in Inverse Problems (in Russian). Nauchniy Mir, Moscow (2005)
Kabanikhin, S.I., Krivorotko, O.I.: A numerical method for determining the amplitude of a wave edge in shallow water approximation. Appl. Comput. Math. 12, 91–96 (2013)
Voronina, T.A., Tcheverda, V.A.: Reconstruction of tsunami initial form via level oscillation. Bull. Novosib. Comput. Cent., Ser. Math. Model. Geophys. 4, 127–136 (1998)
Voronina, T.A.: Determination of spatial distribution of oscillation sources by remote measurements on a finite set of points. Siberian Journal of Numerical Mathematics 3, 203–211 (2004)
Voronina, T.A.: Reconstruction of initial tsunami waveforms by a truncated SVD method. J. Inverse Ill-Posed Probl. 19, 615–629 (2011)
Marchuk, A., Marinin, I., Komarov, V., Krivorotko, O., Karas, A., Khidasheli, D.: 3D GIS integrated natural and man-made hazards research and information system. In: Proceedings of The Joint International Conference on Human-Centered Computer Environments (HCCE) 2012, pp. 225–229. Aizu-Wakamatsu (2012)
Kabanikhin, S.I.: Inverse and Ill-Posed Problems: Theory and Applications. De Gruyter, Berlin (2011)
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Kabanikhin, S., Krivorotko, O. (2015). Mathematical Algorithm for Calculation of the Moving Tsunami Wave Height. In: Danaev, N., Shokin, Y., Darkhan, AZ. (eds) Mathematical Modeling of Technological Processes. CITech 2015. Communications in Computer and Information Science, vol 549. Springer, Cham. https://doi.org/10.1007/978-3-319-25058-8_7
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DOI: https://doi.org/10.1007/978-3-319-25058-8_7
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