E. Bortolucci

Tsunami Excitation by Submarine Slides in Shallow-water Approximation

Abstract— Landslide-induced tsunamis are receiving increased attention since there is evidence that recent large devastating events have been caused by underwater mass failures. Normally, numerical models are used to simulate tsunami excitation, most of which are based on shallow water, known also as long wave, approximation to the full equations of hydrodynamics. Analytical studies may handle only simplified problems, but help understand the basic features of physical processes. This paper is an analytical investigation of long-water waves excited by rigid bodies sliding on the sea bottom, based on the shallow-water approximation, which is here derived by properly scaling Euler equations for an inviscid, incompressible and irrotational ocean. In one-dimensional (1-D) cases (where motion depends only on one horizontal coordinate), under the further assumptions of small-height slide, which permits the recourse to linear theory, and of flat ocean floor, a solution for arbitrary body shape and velocity is deduced by applying the Duhamel theorem. It is also shown that this theorem can be advantageously used to obtain a general solution in case of a non-flat ocean floor, when the sea bottom follows a special power law, that can be adapted to study reasonable bottom profiles. The characteristics of the excited tsunamis are then evaluated by computing solutions in numerous examples, with special focus on wave pattern and wave evolution. The energy of the wave system is shown to depend on time: it grows expectedly in the initial phase of tsunami generation, when the moving body transfers energy to the water, but it may also diminish later, implying that a certain amount of energy may pass back from water waves to the slide.

Computer simulations of tsunamis due to sector collapse at Stromboli, Italy

Abstract Stromboli is an island volcano of the Aeolian Volcanic Arc, characterised by persistent activity. The cone rises about 2500–3000 m from its submarine base with very steep slopes; its summit at 924 m above the sea level. The subaerial growth of Stromboli, occurred in the last 100 ka, has been marked by repeated episodes of large gravitational collapses especially affecting the NW flank of the island in the last 13 ka. The last one occurred less than 5000 years ago forming the deep depression on the NW seaward flank, named Sciara del Fuoco (SdF), and it produced very likely large water waves. This paper envisages a scenario where a huge mass of volcanic material collapses into the sea in the same sector in which the SdF collapse took place in Holocenic times and it computes possible tsunami evolutions assuming the present-day bathymetry. Numerical simulations are performed by means of two distinct models; one for the mass collapse and one for the tsunami. Slope failure dynamics are calculated with the aid of a Lagrangian model: the landslide is subdivided into blocks, and the motion of each constituent block is calculated by applying the basic principle of mechanical momentum conservation, with block–block and block–ambient interactions being taken into account. Water waves are computed by solving a system of shallow-water equations including a forcing term dependent on the sliding mass motion. The finite-element (FE) technique is employed since it permits the use of non-uniform grids, which are adequate to account for marine basins with irregular coastlines. In addition to the sensitivity analysis concerning the main parameters governing the slide motion, two main cases are explored, differing in the slide path followed by the mass. The resulting tsunami is very large, with giant waves as high as several meters (tens of meters in the worst cases) impinging the coast. Due to the strong wave refraction induced by bathymetry, waves travel around the island, affecting even the island coast opposite the source.

A block-based theoretical model suited to gravitational sliding

An original theoretical model has been devised to simulate mass flow over hill slopes due to gravitational sliding. The sliding mass is discretized into a sequence of contiguous blocks which are subjected to gravitational forces, to bottom friction and to surface resistance stresses that are generally negligible for subaerial flows, but are relevant for submarine slides. The blocks interact with each other while sliding down the hill flanks because of internal forces that dissipate mechanical energy and produce a momentum exchange between the individual blocks, yet conserving the total momentum of the mass. Internal forces are expressed in terms of interaction coefficients depending on the instantaneous distance between the block centers of mass, which is a measure of the deformation experienced by the blocks: the functional dependence includes three parameters, namely the interaction intensity ¯λ, the deformability parameter σ and the shape parameter γ, by means of which a wide range of interaction types can be fully accounted for. The time integration is performed numerically by solving the equations for the block velocities and positions at any time ti by means of the block accelerations at the previous time ti-1, and by subsequently updating the block accelerations, which allows to proceed iteratively to the following times. The model has been tested against laboratory results available from literature and by means of several numerical experiments involving a simplified geometry both for the sliding body and the basal surface, with the purpose of clarifying the influence of the model parameters on the slide dynamics. The model improves the performance of the existing kinematic models for slides, moreover preserving an equivalent numerical simplicity. Future applications and possible improvements of this model are suggested.

The Tsunami of August 17, 1999 in Izmit Bay, Turkey

The Kocaeli 1999 Earthquake with an Mw = 7.4 caused major hazards throughout the NW of Turkey from Tekirdag to Bolu. Historical data indicates that some of the earthquakes around Izmit Bay have caused tsunamis. In this study, tsunami research for the Kocaeli 1999 Earthquake has been made also taking into consideration historical data. In this research more than about 70 data at 35 localities have been used to determine the tsunami evidences in the bay. Coastal observations indicated runups which were ranging from 1 to 2.5 m along the shores. However, the wave runups are more complex along the south coast due to the presence of coastal landslides (Değirmendere, Halidere, Ulasli, Karamürsel) and subsided areas (Kavakli to Yeniköy) along the shore. West of Yalova, evidence of tsunami rapidly diminished. In addition, possible tectonic mechanism has been determined by using 33 single-channel high-resolution digital seismic reflection profiles which were acquired following the Kocaeli 1999 Earthquake. As a result it has been determined that the Kocaeli Earthquake has created tsunami in Izmit Bay.

Finite-element simulations of the 28 december 1908 Messina Straits (Southern Italy) tsunami

Abstract The earthquake we are dealing with occurred on December 28, 1908: because of the number of victims (about 60,000) and the extension of the destroyed area (6,000 km 2 ), this earthquake with the epicentral MCS intensity XI may be considered the strongest event ever reported for Italy along with the 1693 eastern Sicily earthquake. The shock produced a large tsunami that caused severe damage and many victims. In all places the first sea movement was a withdrawal for a few minutes, followed by a flooding of the coast with at least three big waves. A post-event survey allowed to estimate flooding and run-up heights (more than 10 m in some places). In this work we perform some numerical simulations of the tsunami generation and propagation, taking into account different source faults: the model is based on the shallow water equations, solved numerically by means of a finiteelement method. The computational domain, covered by a mesh consisting of triangular elements, includes the Messina Straits and the sea facing the northeastern coast of Sicily and southern Calabria.

Identification of the source fault of the 1908 Messina earthquake through tsunami modelling. Is it a possible task

Abstract The 1908 Messina Straits tsunami is the last catastrophic event that hit the Italian coast. The parent earthquake may be considered one of the strongest shocks reported in Italian seismic catalogues. Several source models have been; proposed in the literature that are quite different with regard to almost all the fault parameters. The aim of this work is to evaluate whether tsunami data can add reliable inforiration for the identification of the fault mechanism of this earthquake. Tsunamis generated by two of the faults proposed in the literature were simulated via finite-element modelling in a former work (see Piatanesi et al., 1998): the results were in good agreement with the observations as regards the polarity of the first wave, whereas a relevant disagreement was found as far as run-up data were concerned. In this paper, that may be considered the continuation of the previous work, we focus on a particular fault, the one proposed by Capuano et al. (1988), and simulate the consequent tsunami adding two new features to possibly improve the agreement with run-up observations: i) an algorithm allowing for the effect of the sea bottom bathymetry on the tsunami initial condition, and ii) a heterogeneous slip distribution on the fault.

Modeling a possible holocenic landslide-induced tsunami at stromboli Volcano, Italy

Abstract Stromboli is a volcanic island in the Aeolian archipelago, located in SE Tyrrhenian sea, Italy. It is characterised by a steep depression along the NW flank of the volcano called Sciara del Fuoco, that is interpreted as the partially filled scar of a large flank collapse that took place circa 5000 years ago. The large volume of material estimated to be involved in the collapse was very likely responsible for the generation of big ocean waves. This paper presents some numerical simulations concerning a tsunami scenario to the Holocene event. For the landslide we used a Lagrangian model based on the discratization of the total sliding mass in blocks of constant volume subjected to external and internal forces. Three possible slide evolutions are considered, differing by the modality of the block-block interaction. In all three cases the tsunami is simulated using a finite-element (FE) model based on the non-linear hydrodynamic equations with the addition of a forcing term to account for the excitation of sea waves by the landslide. Wave propagation and time histories all around the island are computed. The tsunami results to be very etc. Though most of the energy is radiated seaward, nonetheless very huge waves, in the order of tens of meters, attack the island, this result being almost independent from the landslide model used.

The finite-element wave propagator approach and the tsunami inversion problem

Abstract Inversion of tsunami data is of great importance since it provides independent and reliable information on tsunami source processes. Good results on estimation of heterogeneous slip distribution along the causative seismic fault have been recently achieved, both by inversion of tsunami tide-gauge records and run-up data. This work addresses some questions of the general ill-posed problem of inversion of tsunami tide-gauge records, from a new point of view, namely the Wave Propagator (WP) approach. The WP is a time dependent linear operator that describes the physical system completely. It is to be stressed that, while the direct problem is well posed, for its solution is obtained by simply applying the WP to the initial perturbation, on the contrary, the inversion of one or more tide-gauge records to determine the initial perturbation results into an ill-posed problem. For illustrative purposes, we will conduct our discussion by taking into account a simple case, that is, the linear propagation of an initial bulge along a rectangular flat channel. First we will point out some important properties of the Greens functions concerning symmetry and the symmetry rupture owing to the boundary conditions. Subsequently some numerical experiments will be illustrated in order to discuss the main features of the inversion procedure. In particular we will study the dependence of the goodness of the inverted fields on some parameters, namely the sampling interval of the tide-gauge records, the number and the spatial distribution of tide-gauge records and the perturbing noise on the records.

The wave propagator in finite-element modeling of tsunamis

Abstract Finite-element methods are one of the most powerful numerical approaches to compute the evolution of tsunami waves over basins of any shape. In this work it is shown that the finite-element space discretization of the shallow-water equations over a suitable grid leads to a system of ordinary differential equations that are first order in time. Basing on a linearized version of the governing equations the solution at any time can be computed by applying a linear operator, we call the wave propagator (WP), to the initial condition. The WP can be defined both for problems without and with boundary conditions and named free WP and constrained WP respectively. In this work the spectral features of the WP are investigated, such as the shape of the eigenvalues spectrum and the eigenvalues dependence on the bathymetry of the basin and on the size of the grid elements. It is also shown that all the eigenvectors of the constrained WP satisfy the boundary conditions. Furthermore some spectral formal properties are discussed, such as the invariance of the spectrum under rotation of the basin and under scaling of the equations.