Comparison between three-dimensional linear and nonlinear tsunami generation models

Abstract

The modeling of tsunami generation is an essential phase in understanding tsunamis. For tsunamis generated by underwater earthquakes, it involves the modeling of the sea bottom motion as well as the resulting motion of the water above it. A comparison between various models for three-dimensional water motion, ranging from linear theory to fully nonlinear theory, is performed. It is found that for most events the linear theory is sufficient. However, in some cases, more sophisticated theories are needed. Moreover, it is shown that the passive approach in which the seafloor deformation is simply translated to the ocean surface is not always equivalent to the active approach in which the bottom motion is taken into account, even if the deformation is supposed to be instantaneous.

Dynamic tsunami generation due to sea-bottom deformation: Analytical representation based on linear potential theory

“…This was derived by Takahashi (1942) in cylindrical coordinates. Similar equations were obtained by Kervella et al (2007) and Levin and Nosov (2009) for the Cartesian coordinates using the inverse Laplace transform. It is necessary to integrate over the angular frequency ω in order to obtain a solution in the time domain.…”

“…Using linear potential theory, in which the velocity potential is introduced and wave linearity is assumed, the spatial and temporal change of the surface height due to bottom deformation are well reproduced in many instances, as observed in laboratory experiments and calculated in numerical simulations (e.g., Hammack, 1973;Kervella et al, 2007). One of the notable consequences of the theory is that the height distribution at the surface is not always identical to the bottom deformation (e.g., Kajiura, 1963;Ward, 2001).…”

“…The solution has only been obtained through a formal expression using an inverse Fourier/Laplace transform, or for very limited situations. and Kervella et al (2007) theoretically derived the velocity distribution only at the sea surface, but not over the sea depth. They also derived the pressure at the sea bottom, but only after an instantaneous sea-bottom deformation.…”

Modified shallow water equations for significantly varying seabeds

“…The function T (t) provides us a complete information on the dynamics of the bottom motion. In tsunami wave literature, it is called a dynamic scenario [21,33,37]. Obviously, other choices of the time dependence are possible.…”

Numerical simulation of March 11, 2011 Honshu, Japan tsunami

“…Improvements in the availability of sea-level observations and advances in numerical modeling techniques increase the potential for tsunami warnings based on numerical model forecasts. Numerical tsunami propagation and inundation models are well developed [4,5], but there presents a challenge for them in actual applications. In order to obtain deeper understanding of tsunamis and reduce their damage to human beings, we carried out the numerical simulation of this tsunami in Honshu, Japan, which can provide validation of our numerical model and further amendments.…”