Dispersion of tsunamis: does it really matter?

Abstract

Abstract. This article focuses on the effect of dispersion in the field of tsunami modeling. Frequency dispersion in the linear long-wave limit is first briefly discussed from a theoretical point of view. A single parameter, denoted as "dispersion time", for the integrated effect of frequency dispersion is identified. This parameter depends on the wavelength, the water depth during propagation, and the propagation distance or time. Also the role of long-time asymptotes is discussed in this context. The wave generation by the two main tsunami sources, namely earthquakes and landslides, are briefly discussed with formulas for the surface response to the bottom sources. Dispersive effects are then exemplified through a semi-idealized study of a moderate-strength inverse thrust fault. Emphasis is put on the directivity, the role of the "dispersion time", the significance of the Boussinesq model employed (dispersive effect), and the effects of the transfer from bottom sources to initial surface elevation. Finally, the experience from a series of case studies, including earthquake- and landslide-generated tsunamis, is presented. The examples are taken from both historical (e.g. the 2011 Japan tsunami and the 2004 Indian Ocean tsunami) and potential tsunamis (e.g. the tsunami after the potential La Palma volcanic flank collapse). Attention is mainly given to the role of dispersion during propagation in the deep ocean and the way the accumulation of this effect relates to the "dispersion time". It turns out that this parameter is useful as a first indication as to when frequency dispersion is important, even though ambiguity with respect to the definition of the wavelength may be a problem for complex cases. Tsunamis from most landslides and moderate earthquakes tend to display dispersive behavior, at least in some directions. On the other hand, for the mega events of the last decade dispersion during deep water propagation is mostly noticeable for transoceanic propagation.

The effect of uncertainty in earthquake fault parameters on the maximum wave height from a tsunami propagation model

“…the choice of wave equation (linear and non-linear shallow water wave equations, Boussinesq-type or full NavierStokes equations) and their corresponding capacity to incorporate the factors mentioned above also has an influence on the accuracy of the simulation. Glimsdal et al (2013) also found that dispersion is also a function of the dominant wavelength of the tsunami and the depth of the water at the source.…”

“…Previous studies into what affects the tsunami wavefield have mostly focused on various physical parameters such as source effects (Geist, 1999), bathymetry (Geist, 2009), tides (Weisz and Winter, 2005), dispersion of wave propagation (Glimsdal et al, 2013), Coriolis force (Shuto, 1991), effects of friction (Myers and Baptista, 2001) and land cover roughness when propagating onshore (Kaiser et al, 2011). The accuracy of tsunami simulation not only depends on the consideration of these factors in the numerical implementation, but also on the variability and uncertainties associated with them.…”

Effects of Seabed Surface Rupture Versus Buried Rupture on Tsunami Wave Modeling: A Case Study for the 2011 Tohoku, Japan, Earthquake

“…Consequently, the impact due to steeper dip angles is less pronounced for this case. Moreover, Figure 2c compares the vertical deformation profiles along cross section 1 for dip 10°and H top 0 or 5 km by considering the effects of the hydrodynamic response filter by Kajiura (1963) (see also Glimsdal et al, 2013). The hydrodynamic response filter makes the vertical deformation profile smoother (and continuous even for H top 0 km).…”

“…In tsunami modeling, vertical deformation of ocean bottom is often substituted for initial water surface (i.e., boundary conditions for tsunami simulation), ignoring the hydrodynamic response of sea water. More rigorous approaches that account for the hydrodynamic behavior of water in response to abrupt seabed deformation are available through tsunami simulation using a nonhydrostatic, dispersive model (Yamazaki et al, 2009(Yamazaki et al, , 2011, and filtering of (nonphysical) sharp peaks of seabed deformation (Kajiura, 1963;Gusman et al, 2012;Løvholt et al, 2012;Glimsdal et al, 2013). Albeit simple and approximate, the substitution approach based on Okada equations is prevalent in numerous tsunami studies and is focused upon in this study.…”

Application of a Combined Finite Element—Finite Volume Method to a 2D Non-hydrostatic Shallow Water Problem

“…H(x, y,t) a significant impact in the water depth for the propagation of tsunamis [10], [4]. The paper is organized as follows.…”