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

Submarine earthquakes are the major cause of generation of tsunami. A correct
modeling of the wave field generated by seabed movement is mandatory to
understand the physics of the tsunami and its propagation. Most of the
hydraulic tsunami models make use of the water incompressibility hypothesis.
Nevertheless a sudden movement of the seabed, triggered by underwater
earthquake, compresses the water column and generates pressure waves
(hydro-acoustic waves) that propagate in the sea at the celerity of sound in
water. The present analysis involves only the first-order effects of
compressibility on the generation of surface (tsunami) and hydro-acoustic
waves, and does not consider the secondary wave-to-wave interaction

Since the hydro-acoustic waves travel much faster than the surface waves,
their real-time recording allows the anticipation of the tsunami arrival.
Moreover, the hydro-acoustic wave signals contain significant information on
the tsunamigenic source

Earlier studies on tsunami evolution in weakly compressible water
have been carried out by

In this paper the results and the physical implications of a large
geographical scale application of the numerical model based on the
depth-integrated equation of

The simulation of hydro-acoustic wave propagation in real bathymetry enables
the investigation of the correlation between the hydro-acoustic waves and the
generation mechanism, the source location, the bottom topography and the
depth of the pressure recording point. The model is based on the hypothesis
of rigid seabed; however, it is worth citing

In the portion of the Mediterranean Sea considered in the present research, two deep-sea observatories are located off-shore of the eastern Sicilian coast. These observatories, described later in more details, are equipped, among others instruments, with low-frequency and large-bandwidth hydrophones. Therefore the numerically reproduced scenarios provide indications on the attended hydro-acoustic signals in the case of submarine earthquake occurrence.

The paper is structured as follows: the next section deals with the description of the numerical model; Sect. 3 describes the large-scale numerical simulations of the two selected historical tsunamis; in Sect. 4 discussions and conclusions are given.

Consider the problem of wave propagation in weakly compressible inviscid
fluid, where waves are generated by a seabed motion. In the framework of
linearized theory the governing equation and boundary conditions for the
fluid potential

The solution of Eq. (

In Eq. (

More details on the wave derivation can be found in

The numerical model makes use of the finite element method and solves the
hyperbolic equation by means of a time-marching numerical scheme. The model
uses the generalized-

Magnitude

Mediterranean Sea bathymetry relative to the numerical domain.

Two historical tsunami scenarios have been reproduced by means of the
numerical solution of the depth-integrated MSEWC (Eq.

Seismic parameters of AD 365 Crete earthquake, as reconstructed by

The AD 365 earthquake was an undersea earthquake that occurred on 21 July AD 365 in the eastern Mediterranean, with an assumed hypo-center located off western Crete, along a major thrust fault parallel to the western Hellenic Trench. Geologists today estimate that the quake intensity was 8.5 on the Richter scale or higher, causing widespread destruction in central and southern Greece, Libya, Egypt, Cyprus, and Sicily. In Crete nearly all towns were destroyed. This earthquake was followed by a tsunami which devastated the Mediterranean coasts, killing thousands of people and hurling ships 3 km inland.

This work considers a reconstructed scenario of this earthquake, in order to
numerically reproduce the generated hydro-acoustic waves. Following the works
of

In Fig.

Residual vertical seabed dislocation,

Seismic parameters of the 1693 Sicily earthquake, as reconstructed
by

The comparison results have been used to set up some computational parameters
of the large-scale simulation and to optimize the number of frequencies and
number of modes to solve in order to obtain a good reproduction of the
hydro-acoustic signal, minimizing the computational costs. For the AD 365
earthquake scenario in the whole domain, the frequency range

Upper panels: vertical sections AB and CB of Fig.

Free-surface time series (left column) and their relative frequency
spectra (right column) at the CTS point (

Snapshots of the free surface (

Pressure time series (left column) and their frequency spectra
(right column) at Catania Test Site point (upper plots) and at Capo Passero
point (lower plots), resulting from the numerical solution of the
depth-integrated Eq. (

The results of the numerical model application in terms of free-surface
elevation are represented in Fig.

At the two points where the submarine stations are located, CTS and CP, the
simulated pressure perturbations associated with hydro-acoustic first mode
are calculated at the sea bottom. Figure

Since most of the seabed motion occurs at a water depth of 3 km, the
generated hydro-acoustic waves oscillate at a frequency close to the cutoff
value of the first hydro-acoustic mode, i.e.,

Residual vertical seabed dislocation,

On 11 January 1693 a powerful earthquake occurred offshore of the east coast of
Sicily, Italy. This earthquake was preceded by a damaging foreshock on
9 January. It had an estimated magnitude of 7.2, one of the most powerful in
Italian history, destroying at least 70 towns and cities and causing the
death of about 60 000 people. The earthquake was followed by tsunamis that
devastated the coastal villages at the Ionian Sea coasts and in the Strait of
Messina

Again, the depth-integrated model is tested by comparison with the 3-D
solution at two vertical sections of the sea. The position of these sections
is represented in Fig.

Upper panels: vertical sections FG and DE of Fig.

Figure

The large-scale depth-integrated simulation has been carried out in the
domain represented in Fig.

Snapshots of the free-surface elevation from

Free-surface time series (left column) and their relative frequency
spectra (right column) at the CP point (

Snapshots of the free surface (

Pressure time series (left column) and their frequency spectra
(right column) at Catania point (upper plots) and at Capo Passero point
(lower plots), resulting from the numerical solution of the depth-integrated
Eq (

The results of the large-scale depth-integrated simulation are presented at
the two observation points, CTS and CP, in terms of bottom pressure. Figure

The Mediterranean seabed is affected by intense seismic activities. The
potential tsunamis can therefore be destructive since the coasts are densely
populated and very close: the travel time of tsunami wave towards the
coast is in the order of few minutes up to 1 h. Rapid detection of the
tsunami generation in this region is mandatory for future development of
early warning systems, and the use of the hydro-acoustic signals can cope with
this necessity. This appealing feature of hydro-acoustic waves has recently
been considered by

The proposed model reproduces the mechanism of propagation of hydro-acoustic
waves due to a sudden bottom displacement associated with earthquakes,
solving the mild-slope equation in weakly compressible fluid of

The numerical model results highlight that the seabed motion energy is transferred to hydro-acoustic waves mainly at the frequencies just after the cutoff values of each acoustic mode. Close to the generation area the frequency spectra clearly show energy peaks for each acoustic mode, while during wave propagation the hydro-acoustic energy will distribute along frequencies higher than the cutoff values. The simulation of the 1693 earthquake scenario shows that 100 km far from the epicenter, at Capo Passero observation site, the hydro-acoustic waves recorded still allow the identification of the energy associated with each acoustic mode. The numerical simulations confirm that the first mode is the one which carries most of the energy. The hydro-acoustic modes propagate undisturbed in water layers equal to or deeper than the one where they have been generated. As the waves propagate in shallower water depth, characterized by higher cutoff frequencies, the components with frequencies lower than the cutoff become evanescent: when hydro-acoustic waves propagate towards shallower sea depth, the water layer acts as a frequency filter.

It is worth mentioning that landslides are the second major cause of tsunami generation. The present model is in principle able to reproduce a submarine motion of rigid landslide. However, due to the occurrence of landslides mainly near the shore, and since during its motion the landslide would generated pressure waves at different water depths, further studies need to be addressed on this topic.

To implement innovative tsunami early warning systems based on measurement and analysis of hydro-acoustic signals, the complete modeling of hydro-acoustic waves in real bathymetry has proven to be extremely useful. The numerical model simulations show that the hydrophones must be placed in waters deep enough to record larger frequency ranges and, if possible, not shielded by seamounts. However these instruments should be connected to the shore by submarine cables to guarantee fast data transmission; therefore their location can not be too far from the coastline. Hence the model can help choose the right positioning of the hydrophone system. For the portion of the Mediterranean Sea here analyzed, the numerical simulation results suggest that offshore of the Sicilian east coast, where the instruments have been placed, and offshore of the Greek west coast, the waters are deep enough to record and identify the hydro-acoustic waves generated by seismic activities in both the Hellenic arc and the Ionian Sea (southern Italy).

This work was carried out under the research project FIRB 2008-FUTURO IN RICERCA (“Design, construction and operation of the Submarine Multidisciplinary Observatory experiment”), funded by the Italian Ministry for University and Scientific Research (MIUR). We wish to thank G. Riccobene, scientific coordinator of the mentioned FIRB project, for the useful discussions. Edited by: M. Gonzalez Rodríguez Reviewed by: E. Renzi and one anonymous referee