Abstract:
Within the framework of the potential theory of an incompressible fluid, under the instantaneous sea-bottom deformation assumption, a two-dimensional ($0xz$) numerical
model is developed, which makes it possible to calculate the initial elevation of the water
surface in the tsunami source in a basin of variable depth. Through the use of the $\sigma$-coordinate, the model makes it possible to take into account the contribution of the horizontal component of the bottom deformation and the “smoothing effect” of the water
layer. To test the numerical model, we obtained an analytical solution to the problem of
the initial elevation in a basin with a flat sloping bottom with bottom deformation of a
triangular shape. The results of the test show that for a spatial step typical for numerical
tsunami models, there is a good agreement between the numerical and analytical solutions. Using the developed $\sigma$-model, we calculated the initial elevations of the water surface during the Kuril earthquake on January 13, 2007 and the Great East Japan Tohoku
earthquake on March 11, 2011 (along selected 2D sections). The results obtained are
used to test an approximate method for calculating the initial elevation, known as the Kajiura filter, in which the ocean depth is assumed to be constant throughout the entire tsunami source area.
Citation:
K. A. Sementsov, M. A. Nosov, “Calculation of the initial elevation of the water surface at the tsunami source in the basin with arbitrary bottom topography”, Mat. Model., 35:2 (2023), 75–94; Math. Models Comput. Simul., 15:4 (2023), 746–758
\Bibitem{SemNos23}
\by K.~A.~Sementsov, M.~A.~Nosov
\paper Calculation of the initial elevation of the water surface at the tsunami source in the basin with arbitrary bottom topography
\jour Mat. Model.
\yr 2023
\vol 35
\issue 2
\pages 75--94
\mathnet{http://mi.mathnet.ru/mm4443}
\crossref{https://doi.org/10.20948/mm-2023-02-06}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4548101}
\transl
\jour Math. Models Comput. Simul.
\yr 2023
\vol 15
\issue 4
\pages 746--758
\crossref{https://doi.org/10.1134/S2070048223040166}
Linking options:
https://www.mathnet.ru/eng/mm4443
https://www.mathnet.ru/eng/mm/v35/i2/p75
This publication is cited in the following 3 articles:
Alice Abbate, José M. González Vida, Manuel J. Castro Díaz, Fabrizio Romano, Hafize Başak Bayraktar, Andrey Babeyko, Stefano Lorito, “Modelling tsunami initial conditions due to rapid coseismic seafloor displacement: efficient numerical integration and a tool to build unit source databases”, Nat. Hazards Earth Syst. Sci., 24:8 (2024), 2773
Ritika Das, Santu Das, “Surface wave generation from a constant-slope-inducing asymmetric ocean floor motion: influence of compressible ocean”, Meccanica, 2024
K A Sementsov, T Baba, S V Kolesov, Y Tanioka, M A Nosov, “The effect of earthquake fault rupture kinematics on tsunami generation: a numerical study of real events”, Geophysical Journal International, 240:2 (2024), 920
Citation in format AMSBIB
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