Mathematical model of trans-tsunami wave propagation
越洋海啸波传播数学模型的研究

In this paper, we used the method of matching inner and out solutions and the stationary phased method to derive the solution of the wave equation in cylindrical coordinates for the water surface after earthquake, which is the theoretical equation of earthquake tsunami. We then applied this equation to calculate the trans-oceanic tsunami. Based on the Boussinesq equation, a 2D trans-oceanic tsunami wave propagation mathematical model was built, and was used to simulate the trans-ocean tsunami. In this model, the calculation was performed with the finite difference method, and the difference scheme with the Alternating Direction Implicit, that is ADI method. With the trans-ocean tsunami numerical calculation model, an earthquake tsunami was calculated; and the results were in good consistency with that of the earthquake-induced wave calculated by the theoretical wave equation for water surface.