Calculation of the Initial Elevation of the Water Surface at the Source of a Tsunami in a Basin with Arbitrary Bottom Topography

• Published in: Mathematical models and computer simulations 2023-08, Vol.15 (4), p.746-758
• Main Authors: Semenstov, K. A., Nosov, M. A.
• Format: Article
• Language: English
• Subjects: Deformation effects; Earthquakes; Elevation; Exact solutions; Fluid flow; Incompressible flow; Incompressible fluids; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Model testing; Numerical models; Potential theory; Simulation and Modeling; Tsunamis
• ISSN: 2070-0482; 2070-0490
• DOI: 10.1134/S2070048223040166

A two-dimensional (0 xz ) numerical model that makes it possible to calculate the initial elevation of the water surface in the source of a tsunami in a basin of variable depth is developed in the potential theory of an incompressible fluid under the approximation of an instantaneous deformation of the sea bottom. 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 through the use of the σ coordinate. 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 a bottom deformation of a triangular shape. The results of the test show that for a spatial step typical for numerical tsunami models, there is close agreement between the numerical and analytical solutions. Using the developed σ model, we calculate 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 the 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 area of the source of the tsunami.