Abstract
We numerically simulated the propagation of tsunami waves with finite difference methods by using perfectly matched layer (PML) boundary conditions to effectively eliminate artificial reflections from model boundaries. The PML method damps the tsunami height and velocity of seawater only in directions perpendicular to the boundary. Although the additional terms required to implement the PML conditions make the use of the PML technique difficult for linear dispersive tsunami waves, we have proposed an empirical extension of the PML method for modeling dispersive tsunami waves. Even for heterogeneous, realistic bathymetries, numerical tests demonstrated that the PML boundary condition dramatically decreased artificial reflections from model boundaries compared to the use of traditional boundary conditions. The use of PML boundary conditions for numerical modeling of tsunamis is especially useful because it facilitates use of the later phases of tsunamis that would otherwise be compromised by artifacts caused by reflections from model boundaries.
Highlights
Tsunami simulation for a near-field earthquake is usually performed with a bounded-area model having a spatial extent on the order of 100–1000 km (e.g., Tanioka 2006; Furumura et al 2011) rather than with a whole-earth model in the case of a far-field tsunami
Simulations by finite difference methods applied to the long-wave tsunami equation usually utilize a one-way wave equation or the Sommerfeld radiation condition (e.g., Hwang et al 1972; Blumberg and Kantha 1985); alternatively, a sponge condition, which artificially attenuates the wave height in the vicinity of the model boundary, has been widely used (e.g., Cerjan et al 1985; Furumura and Saito 2009)
It is difficult to directly apply the perfectly matched layer (PML) boundary condition to a more realistic linear, dispersive-wave tsunami model, we propose an empirical extension of the PML boundary condition to the linear, dispersive tsunami equation
Summary
Tsunami simulation for a near-field earthquake is usually performed with a bounded-area model having a spatial extent on the order of 100–1000 km (e.g., Tanioka 2006; Furumura et al 2011) rather than with a whole-earth model in the case of a far-field tsunami. We propose the use of an alternative and more effective boundary condition based on the perfectly matched layer (PML) method for finite difference numerical modeling of tsunami propagation.
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