Huge landslides, mobilizing hundreds to thousands of km(3) of sediment and rock are ubiquitous in submarine settings ranging from the steepest volcanic island slopes to the gentlest muddy slopes of submarine deltas. Here, we summarize current knowledge of such landslides and the problems of assessing their hazard potential. The major hazards related to submarine landslides include destruction of seabed infrastructure, collapse of coastal areas into the sea and landslide-generated tsunamis. Most submarine slopes are inherently stable. Elevated pore pressures (leading to decreased frictional resistance to sliding) and specific weak layers within stratified sequences appear to be the key factors influencing landslide occurrence. Elevated pore pressures can result from normal depositional processes or from transient processes such as earthquake shaking; historical evidence suggests that the majority of large submarine landslides are triggered by earthquakes. Because of their tsunamigenic potential, ocean-island flank collapses and rockslides in fjords have been identified as the most dangerous of all landslide related hazards. Published models of ocean-island landslides mainly examine 'worst-case scenarios' that have a low probability of occurrence. Areas prone to submarine landsliding are relatively easy to identify, but we are still some way from being able to forecast individual events with precision. Monitoring of critical areas where landslides might be imminent and modelling landslide consequences so that appropriate mitigation strategies can be developed would appear to be areas where advances on current practice are possible.

[1] The likelihood of a large scale tsunami from the La Palma Island is considered small by most. Nevertheless, the potential catastrophic consequences call for attention. Here we report on numerical simulations of a tsunami that might result from the extreme case of a flank collapse of the Cumbre Vieja volcano at the La Palma Island, done by combining a multimaterial model for the wave generation with Boussinesq models for the far-field propagation. Our simulations show that the slide speed is close to critical, effectively generating an initial wave of several hundred meters height. Our main focus is the wave propagation which is genuinely dispersive. In the far-field, propagation becomes increasingly complex due to the combined effects of dispersion, refraction, and interference in the direction of propagation. Constructive interference of the trailing waves are found to decrease the decay of the maximum amplitude with distance compared to classical asymptotic theory at transatlantic distances. Thus, the commonly used hydrostatic models fail to describe the propagation. Consequences of the La Palma scenario would be largest at the Canary Islands, but our findings also suggests that the whole central Atlantic would face grave consequences. However, the largest surface elevations are smaller than the most pessimistic reports found in literature. We also find undular bores towards the shorelines of America.

This review presents modelling techniques and processes that govern landslide tsunami generation, with emphasis on tsunamis induced by fully submerged landslides. The analysis focuses on a set of representative examples in simplified geometries demonstrating the main kinematic landslide parameters influencing initial tsunami amplitudes and wavelengths. Scaling relations from laboratory experiments for subaerial landslide tsunamis are also briefly reviewed. It is found that the landslide acceleration determines the initial tsunami elevation for translational landslides, while the landslide velocity is more important for impulsive events such as rapid slumps and subaerial landslides. Retrogressive effects stretch the tsunami, and in certain cases produce enlarged amplitudes due to positive interference. In an example involving a deformable landslide, it is found that the landslide deformation has only a weak influence on tsunamigenesis. However, more research is needed to determine how landslide flow processes that involve strong deformation and long run-out determine tsunami generation.

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.

This paper presents experiments on run-up of strongly nonlinear waves on a beach of 10.54° inclination. Velocity fields are obtained by the PIV (particle image velocimetry) technique. Acceleration measurements are also attempted, but it is difficult to obtain useful results in every case. In addition, free-surface profiles are extracted from digital images and wave resistance probes. The investigation focuses on the dynamics of the early stages of the run-up, when steep fronts evolve in the vicinity of the equilibrium shoreline, but maximum run-up heights are also reported. Measurements on moderately nonlinear waves are compared to results from long-wave theories, including a numerical Boussinesq model and analytic shallow-water results from the literature. In particular the applicability of the long-wave theories is addressed. However, most attention is given to run-up of high incident solitary waves that are on the brink of breaking at the shoreline. In one case a temporarily slightly overturning wave front is found that neither develops into a plunger or displays appreciable spilling. This feature is discussed in view of measured velocity and acceleration patterns and with reference to the dam-break problem. Effects of scaling, as well as viscous damping, are also briefly discussed.

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[1] Most tsunami models apply dislocation models that assume uniform slip over the entire fault plane, followed by standard analytical models based on Volterra's theory of elastic dislocations for the seabed deformation. In contrast, we quantify tsunami runup variability for an earthquake with fixed magnitude but with heterogeneous rupture distribution assuming plane wave propagation (i.e., an infinitely long rupture). A simple stochastic analysis of 500 slip realizations illustrates the expected variability in coseismic slip along a fault plane and the subsequent runup that occurs along a coastline in the near field. Because of the need for systematically analyzing different fault geometries, grid resolutions, and hydrodynamic models, several hundred thousand model runs are required. Thus, simple but efficient linear models for the tsunami generation, propagation, and runup estimation are used. The mean value and variability of the maximum runup is identified for a given coastal slope configuration and is analyzed for different dip angles. On the basis of the ensemble runs, nonhydrostatic effects are discussed with respect to their impact on generation, nearshore propagation, and runup. We conclude that for the geometry and magnitude investigated, nonhydrostatic effects reduce the variability of the runup; that is, hydrostatic models will produce an artificially high variability.Citation: Løvholt, F., G. Pedersen, S. Bazin, D. Kühn, R. E. Bredesen, and C. Harbitz (2012), Stochastic analysis of tsunami runup due to heterogeneous coseismic slip and dispersion,

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