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SYNTHETIC TSUNAMI SIMULATIONS FOR THE FRENCH COASTS

M. FRANCIUS 1, E. PELINOVSKY 2, 3, I. RIABOV 3), C. KHARIF 4

1Laboratoire de Mecanique et d'Acoustique, 31 Chemin Joseph Aiguier,

13402 Marseille, Cedex 20, France

2Institute of Applied Physics of the RussianAcademy of Sciences

46 UlyanovStreet, 603600 Nizhniy Novgorod, Russia

3Applied Mathematics Departmen,Nizhny Novgorod State Technical University, 24 Minin Street, 603000,Nizhny Novgorod, Russia

4Institut de Recherche sur les Phenomenes Hors Equilibre,BP 146 49 rue Frederic Joliot-Curie, 13384 Marseille cedex 13, France

Abstract

We analyzed the manifestation of tsunamis for the French coasts of the Mediterranean. Historical data of past tsunamis are analyzed to provide a representative set of potential "seismic" tsunami sources for the LigurianSea. Nonlinear shallow water model was used to simulate the propagation from initial displacements in the tsunami sources that were located at the places of historical tsunamis. The synthetic method was applied to study the characteristics of possible earthquake-generated tsunamis in the Ligurian Sea. It is found that tsunami manifestation on the French coasts has a very local character and that the Western French Mediterranean coasts are protected from tsunamis generated in the Ligurian Sea.

1. Introduction

The tsunami hazard has been less studied for the coasts of the French metropolis than for the coasts of French overseas territories. In fact, this problem is rather difficult because of the lack of historical information and measurements regarding tsunami inundation. Thus a direct statistical analysis is not possible. To provide a preliminary study of the tsunami hazard for the French coast, the synthetic method was used, as for instance did Curtis & Pelinovsky [1]. Large number of numerical simulations of past real events and of future probable tsunamis can be analysed to compare the characteristics of tsunami propagation for different coastal areas, and to make prognostic modelling of the propagation. This method was used for the Ligurian Sea in order to give a preliminary analysis of the tsunami hazard for the French Mediterranean coasts. This study focuses on tsunami induced by earthquakes.

2. Analysis and modelling tsunami propagation

To analyse the tsunami manifestation in the Ligurian Sea, we considered four groups of experiments (see fig. 1). Those groups were chosen according to the analysis of the catalogues of Soloviev et al. [2] and of Tinti & Maramai [3]. The first group concerns

Figure 1. Epicentres of earthquakes induced tsunami on the French coast of the Mediterranean

tsunamis induced by earthquakes with epicentres in the vicinity of Nice and Imperia. In this very shallow zone, tsunamigenic earthquakes have 10-20 km focal depth and can induce significant waves in spite of their relative small magnitude (6.2 – 6.5). The location of epicentres of computed tsunamis was the same as for historical tsunamis 1818, 1831, 1854 and 1887. The second group considers the tsunami propagation from northern Italy to the French coast, which seems to have a very local character. Indeed the weak earthquake of July 2, 1703 in Genoa (magnitude 3.2) generated a local tsunami. In particularthe sea level in the Harbour of Genoa decreased by1.5-2 m. The third group considers the tsunami propagation from the southern Italy. Such tsunamis were never registered in France, but taking into account the large seismicity of southern Italy, this area can be considered like a probable place for generation of strong tsunamis. Finally, we considered the tsunami propagation from the Algerian coast, where a strong earthquake occurred on September 9, 1954 (magnitude 6.7).

The tsunami propagation was considered in the framework of the non-linear shallow-water theory in the form of Saint-Venant equations. For rough estimates of the tsunami source parameters, the simplified piston model was used with a two-parameter tsunami source model (earthquake magnitude and focal depth). The initial data is the fault length in the earthquake source l0related with the earthquake magnitude M0. For prognostic modelling we used for all events an earthquake magnitude M0 = 6.8, an earthquake focal depth of 20 km, a north-east orientation of the tsunami source, and a roughness coefficient m = 0.0012 which is a general hydraulic parameter which accounts for bottom friction. This value of the earthquake magnitude corresponds to the mean value for tsunami-genetic earthquakes in the whole Mediterranean basin. The chosen source orientation is typical for earthquakes of the northern part of the LigurianSea. The parameters have been chosen identical for all simulations to analyse the general features of the tsunami propagation in the LigurianSea. We could also compare the global characteristics of tsunami waves along the coasts, namely the relation between the tsunami heights in different coastal points. In fact, this simplified model can not provide accurate calculations of tsunami heights but the relative distribution of tsunami heights along the coast should be more realistic since it depends mainly on the coastal topography and on the very rough characteristics of the tsunami source (in particular, the source orientation).

Each “computer” tide-gauge is located in the “last” sea point w(t) (depth of about 20 m). In this point the assumption of a vertical wall is used and the oscillations of the water level on the shoreline are calculated according to the formula of Kaistrenko et al. [4]. With the assumptions that the beach is plane and that the waves come on almost onshore direction, the run-up height may be calculated with the formula

where T is a travel time from last sea point to shore, and t >T. This combination of 2D model with 1D model has been tested, and it generally improves the agreement between observed and computed data, see Choi et al. [5].

3. Results and discussion

Our model is tested with data of the 1887 tsunami. Characteristic amplitude and period of the spectral maximum are in good agreement with observed tide-gauge records and calculations of Eva & Rabinovich [6]. The western part of the Mediterranean coast is protected from these tsunamis by the southern part of the French Riviera. Tsunamis generated in southern Italy affect more Corsica which “screens” partly the French coasts. Tsunamis generated in the vicinity of the African continent are weak on French coasts. In general long duration of tsunami record is characteristic of the French Riviera coasts and this should be accounted in tsunami warning and forecasting. The average total duration of the tsunami record is of about 10 – 20 hrs (see fig. 2) and this should be accounted by tsunami warning. Characteristic period of oscillations varies from one point to another point (20 – 30 min), but it is less for the northern part of LigurianSea than for the western part of the Mediterranean (30 – 45 min), see fig. 3. The travel time of tsunamis depends on the location of the earthquake and it is several hrs for Italian and African earthquakes. If the tsunami is generated in the vicinity of Nice – Imperia, the travel time to Nice is a few minutes for Nice and Cannes, and 1-2 hrs – for the western part of the Mediterranean. Wave heights on the tsunami records have an order of a few cm for the points far from earthquakes, and a few ten cm for the nearest points. The run-up process is characterised by an average amplification factor of 2.5.

Figure 2. Computed tsunami records for the 1887 event.

Figure 3. Computed spectra of the 1887 event

Nevertheless, it is important to notice that information on tsunami tide-gauge records and observed wave heights on the beach for the 1887 Ligurian and 1979 Nice tsunamis, the amplification factor can reach 10 at selected points. It means that the nearest earthquakes in the vicinity of Cannes – Imperia can generate tsunami waves with maximum run-up of a 1-2 meters and induce significant damages on the coast. For the next step, the resonance properties of the bottom topography and the run-up process should be investigated in details for the French coasts of the Mediterranean in order to obtain more accurate tsunami risk estimates.

References

1. Curtis, G.D. and Pelinovsky, E.N. (1999) Evaluation of tsunami risk for mitigation and warning, Sci. Tsunami Hazards 17, n° 3, 187-192.

2. Soloviev, S.L., Go, C.N., Kim, K.S., Solovieva, O.N. and Shetnikov, N.A. (1997), Tsunamis in the Mediterranean sea 2000 B.C. – 1991 A.D., Institute of Oceanology, Moscow.

3. Tinti, S. and Maramai, A. (1996), Catalogue of tsunamis generated in Italy and in Cote d’Azur, France: a step towards a unified catalogue of tsunamis in Europe, Annali di Geofisica, 39, 1253 – 1299.

4. Kaistrenko, V., Go, C.N. and Chung, J.Y. (1999) A simple method for tsunami wave form recalculation through the shelf, IOC-IUGG Joint International Workshop on Tsunami Warning Beyond 2000 Theory, Practice and Plans, Korea, Seoul, 15.

5. Choi, B.H., Pelinovsky, E., Hong, S. and Ryabov, I. (2002) Distribution Functions of tsunami wave heights, Natural Hazards 25, 1-21.

6. Eva, C. and Rabinovich, A. (1997) The February 23, 1887 tsunami recorded on the Ligurian coast, western Mediterranean, Geophys. Research Letters24, n° 17, 2211–2214.