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This work proposes an advancement in analytical modelling of landslide tsunamis propagating along a plane beach. It is divided into two parts. In the first one, the analytical two-horizontal-dimension model of Sammarco and Renzi (2008) for tsunamis generated by a Gaussian-shaped landslide on a plane beach is revised and extended to realistic landslide shapes. The influence of finiteness and shape of the slide on the propagating waves is investigated and discussed. In the second part, a new model of landslide tsunamis propagating along a semi-plane beach is devised to analyse the role of the continental platform in attenuating the wave amplitude along the shoreline. With these parameters taken into account, the fit with available experimental data is enhanced and the model completed.

This paper presents a new set of 3D experiments aimed to gain insight on the role of the initial acceleration upon the generation process of tsunamis by submerged landslides that may occur at the flanks of conical islands. The experiments have been carried out in a large wave tank by varying the initial acceleration of the landslide model. A novel system, relying on the use of a computer controlled stepped motor, has been employed to control the motion of the landslide model. The experiments have been carried out in a parametric way by changing the initial acceleration of the landslide, aiming to reproduce dierent triggering mechanisms. Preliminary experimental findings confirmed the crucial role of the initial acceleration of the submerged landslide in generating tsunamis.

Landslide-generated tsunamis are lesser-known yet equally destructive than earthquake tsunamis. Indeed, the highest tsunami wave recorded in recent history was generated by a landslide in Lituya Bay (Alaska, July 9, 1958) and produced run-up in excess of 400 m. In this paper, we review the state of the art of landslide tsunami analytical modelling. Within the framework of a linearised shallow-water theory, we illustrate the dynamics of landslide tsunami generation and propagation along beaches and around islands. Finally, we highlight some intriguing new directions in the analytical modelling of landslide tsunamis to support early warning systems.

An analytical forced two-horizontal-dimension model is derived to investigate landslide tsunamis propagating around a conical island lying on a flat continental platform. Separation of variables and Laplace transform are used to obtain the free-surface elevation in the whole domain and the runup at the shoreline in terms of confluent Heun functions. The main properties of these functions and their asymptotic behaviour for large parameters are investigated. Expression of the transient leading wave travelling offshore is also derived. The distinguishing physical features of landslide tsunamis propagating in a round geometry are then pointed out and compared with those of landslide tsunamis propagating along a straight coast. Analytical results satisfactorily agree with available experimental data.

A forced two-horizontal-dimension analytical model is developed to investigate the distinguishing physical features of landslide-induced tsunamis generated and propagating on a plane beach. The analytical solution is employed to study the wave field at small times after the landslide motion starts. At larger times, the occurrence of transient edge waves travelling along the shoreline is demonstrated, showing the differences with the transient waves propagating over a bottom of constant depth. Results are satisfactorily compared with available experimental data. Finally, the validity of non-forced numerical models is discussed.

Tsunamigenic fast movements of the seabed generate pressure waves in weakly compressible seawater, namely hydro-acoustic waves, which travel at the sound celerity in water (about 1500 m s−1). These waves travel much faster than the counterpart long free-surface gravity waves and contain significant information on the source. Measurement of hydro-acoustic waves can therefore anticipate the tsunami arrival and significantly improve the capability of tsunami early warning systems. In this paper a novel numerical model for reproduction of hydro-acoustic waves is applied to analyze the generation and propagation in real bathymetry of these pressure perturbations for two historical catastrophic earthquake scenarios in Mediterranean Sea. The model is based on the solution of a depth-integrated equation, and therefore results are computationally efficient in reconstructing the hydro-acoustic waves propagation scenarios.

The paper presents a numerical model to reproduce the tsunami generation and propagation, which can be applied in real-time to be used as a forecasting tool. Free surface elevation measurements in a point close to the tsunami generation area, allows the real-time prediction of tsunami in the far field. This is possible due to an inversion technique. The measurements and modeling of hydro-acoustic waves could shorten the time for spreading the alarm and reduce the number of false alerts. In the paper new investigation about hydro-acoustic waves are also presented in order to outline their possible use to support Tsunami Early Warning System.

We present a depth-integrated equation for the mechanics of propagation of low-frequency hydroacoustic waves due to a sudden bottom displacement associated with earthquakes. The model equation can be used for numerical prediction in large-scale domains, overcoming the computational difficulties of three-dimensional models and so creating a solid base for tsunami early warning systems.

A forced three-dimension analytical model is developed to investigate the main characteristics of landslide tsunamis propagating on a semi-plane beach. The method of separation of variables and the Fourier transform are employed to obtain the solution in the form of an eigenfunction expansion. Parametric discussion and further comparison with the model of a uniformly sloping beach are finally made.

Pressure waves generated by fast seabed movement in weakly compressible sea water, namely hydro-acoustic waves travel at the sound celerity in water (about 1500 m/s). These waves are precursors of the counterpart long free-surface gravity waves and contain significant information on the tsunamigenic source. Measurement of hydro-acoustic waves can therefore anticipate the tsunami arrival and significantly enhance the promptness and accuracy of tsunami early warning systems. In this paper derivation of a novel depth-integrated numerical model for reproduction of hydroacoustic waves is presented and the application of this computationally ecient model on two devastating historical tsunamis of Mediterranean Sea in real bathymetry analyzed to reveal the eect of variable bathymetry. On the basis of the model results, some hints for deep sea observatory are given.