Abstract
Numerical simulations are essential tools for studying tsunami generation and evolution and finite-element (FE) methods are widely used, especially because of their capability in modeling water waves in basins with complex bathymetry and irregular coastlines. This paper presents the numerical simulation of an historical Italian tsunami that affected the Tyrrhenian coasts of Calabria and Sicily on 5 February 1783 following a strong destructive earthquake that was the first of a terrible sequence of seismic shocks terrifying the Calabrian population for more than two months. The numerical model is an FE model based on the nonlinear nondispersive shallow-water approximation of the Navier-Stokes equations. Since FE discretization schemes may lead to solutions undesirably affected by noise over coarse grids, in this study numerical noise is controlled by suitably smoothing the FE solution at regular time steps Δt s. The performance of our smoothing algorithm is tested for significant linear cases for which an analytical solution is available.
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References
Baptista, A. M., Priest, G. R. and Murty, T. S.: 1993, Field survey of the 1992 Nicaragua Tsunami,Marine Geodesy 16, 1692–03.
Cotecchia, V., Guerricchio, A. and Melidoro, G.: 1986, The geomorphogenetic crisis triggered by the 1783 earthquake in Calabria (southern Italy),Proc. Symp. Engineering Geology Problems in Seismic Areas, Bari, 13–19 April 1986, Vol. 6, pp. 245–305.
Fletcher, C. A. J.: 1984,Computational Galerkin Methods, Springer Series in Computational Physics, Springer-Verlag, Berlin, 309 pp.
Fukao, Y.: 1979, Tsunami earthquake and subduction processes near deep sea trenches,J. Geophys. Res. 84, 2303–2314.
Gavagni, 1993, Simulazioni numeriche di onde di maremoto mediante un programma di integrazione agli elementi finiti, Tesi di laurea, 115 pp. (in Italian).
Greenberg, D. A., Murty, T. S. and Ruffman, A.: 1993, A numerical model for the Halifax Harbor tsunami due to the 1917 explosion,Marine Geodesy 16, 153–167.
Kanamori, H.: 1972, Mechanism of tsunami earthquakes,Phys. Earth Planet. Inter. 6, 346–359.
Kanamori, H. and Kikuchi, M.: 1993, Mechanism of the 1992 Nicaragua tsunami earthquake,Proc. IUGG/IOC Int. Tsunami Symp., Wakayama, Japan, August 23–27, 1993, 613–625.
Kawahara, M., Takeuchi, N. and Yoshida, T.: 1978, Two step explicit finite element method for tsunami wave propagation analysis,Int. J. Num. Meth. Engng. 12, 331–351.
Kawahara, M., Hirano, H., Tsubota, K. and Inagaki, K.: 1982, Selective lumping finite element method for shallow water flow,Int. J. Num. Meth. Fluids 2, 89–112.
Kawahara, M. and Kashiyama, K.: 1984, Selective lumping finite element method for nearshore current,Int. J. Num. Meth. Fluids 4, 71–97.
Kienle, J., Kowalik, Z. and Murty, T. S.: 1987, Tsunamis generated by eruptions from Mount St. Augustine Volcano, Alaska,Science 236, 1442–1447.
Liu, Ph. L., Synolakis, C. E. and Yeh, H. H.: 1991, Report on the International Workshop on longwave run-up,J. Fluid Mech. 229, 675–688.
Manshina, L. and Smylie, D. E.: 1971, The displacement fields of inclined faults,Bull. Seismol. Soc. Amer. 61, 1433–1440.
Minasi, G.: 1783, Relazione veridica intorno al terribile tremoto accaduto in Scilla a 5 febbraio 1783, Messina (in Italian).
Minasi, G.: 1785, Continuazione ed appendice sopra i tremuoti descritti nella relazione colla data di Scilla de' 30 settembre 1783 con attro che accadde in progresso, Messina (in Italian).
Ogniben, L.: 1973, Schema geotogico della Calabria in base ai dati odierni,Geol. Romana 24, 243–585 (in Italian).
Pelayo, A. M. and Wiens, D. A.: 1992, Tsunami earthquakes: slow thrust-faulting events in the accretionary wedge,J. Geophys. Res. 40, 15321–15337.
Postpischl, D. (ed): 1985, Catalogo dei Terremoti Italiani dall'anno 1000 al 1980, Progetto Finalizzato Geodinamica, CNR, Rome.
Potter, D.: 1977,Computational Physics, Wiley Chichester, 304 pp.
Sarconi, M.: 1784, Istoria de' fenomeni del tremuoto avvenuto nelle Calabrie e nel Valdemone nell'anno 1783 posta in luce dalla Reale Accademia delle Scienze e delle Belle Lettere di Napoli, Napoli (in Italian).
Spielvoget, L. Q.: 1975, Single-wave run-up on sloping beaches,J. Fluid Mech. 74, 685–694.
Synolakis, C. E.: 1987, The run-up of solitary waves,J. Fluid Mech. 185, 523–545.
Tinti, S: 1991a, Assessment of tsunami hazard in the Italian Seas,Natural Hazards 4, 267–283.
Tinti, S.: 1991b, Tsunami potential in Southern Italy,Science of Tsunami Hazards 9, 5–14.
Tinti, S.: 1993, Evaluation of tsunami hazard in Calabria and eastern Sicily, Italy, in Tsunamis in the World, S. Tinti (ed),Advances in Natural and Technological Hazards Research, Vol. 1, Kluwer Academic Publishers, Dordrecht, pp. 141–157.
Tinti, S. and Mulargia, F.: 1983, Numerical simulation of the 1908 Messina tsunami: preliminary results,Proc. XVIII General Assembly of ESC, Ed. Akademie der Wissenschaften der DDR, Potsdam, pp. 407–411.
Tinti, S. and Guidoboni, E.: 1987, Study of the historical tsunamis generated in 1783 off Calabria Coasts (Southern Italy),Proc. Int. Tsunami Symp. 1987, NOAA/PMEL, pp. 103–108.
Tinti, S. and Guidoboni, E.: 1988, Revision of the tsunamis occurred in 1783 in Calabria and Sicily (Italy),Science of Tsunami Hazards 6, 17–22.
Tinti, S. and Piatanesi, A.: 1995, The wave propagator in finite-element modeling of tsunamis,Marine Geodesy (in press).
Tinti, S., Gavagni, I. and Piatanesi, A.: 1994, A finite-element numerical approach for modeling tsunamis,Ann. Geofis. 37, 1009–1026.
Tinti, S. and Vannini, C.: 1994, Theoretical investigation on tsunamis induced by seismic faults near ocean islands,Marine Geodesy 17, 193–212.
Tortorici, L., Tapponier, P. and Winter, T.: 1986, Faulting during the 1783 Calabria earthquakes and tectonics of the Messina Straits,EOS Transactions AGU 67, (abstract).
Valensise, G. and Pantosti, D.: 1992, A 125 Kyr-long geological record of seismic source repeatability: the Messina Straits (southern Italy) and the 1908 earthquake (M s 7(1/2)),Terra Nova 4, 472–483.
Valensise, G. and D'Addezio, G.: 1994, I1 contributo della geologia di superficie all'identificazione delle strutture sismogenetiche della Piana di Gioia Tauro, ING Internal Report, April 1994, Rome (in Italian).
Vivenzio, G.: 1788, Istoria de' tremuoti avvenuti nella provincia della Calabria Ulteriore e nella città di Messina nel 1783, Napoli (in Italian).
Werner, F. E. and Lynch, D. R.: 1987, Field verification of wave equation tidal dynamics in the English Channel and southern North Sea,Advances Water Resources 10, 115–130.
Zienkiewicz, O. C. and Taylor, R. L.: 1991,The Finite Element Method, 4th edn, Vol. 2, McGraw-Hill, Maidenhead, 807 pp.
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Tinti, S., Gavagni, I. A smoothing algorithm to enhance finite-element tsunami modelling: An application to the 5 February 1783 Calabrian case, Italy. Nat Hazards 12, 161–197 (1995). https://doi.org/10.1007/BF00613075
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DOI: https://doi.org/10.1007/BF00613075