Application of a finite difference computational model to the simulation of earthquake generated tsunamis
Authors: 
Evangelia T. Flouri, Nikos Kalligeris, George Alexandrakis, Nikolaos A. Kampanis, Costas E. SynolakisAuthors Info & Claims
Abstract
Tsunamis are long waves and commonly modeled with the shallow-water wave approximation of the equations of motion. The calculation of tsunami inundation remains after two decades of progress a vexing and temperamental computation exquisitely dependent on ad-hoc algorithms. We present computed results using, a splitting method in space to reduce this hyperbolic system in two successive hyperbolic systems, one for each primitive variable. Then, we use dispersive, Godunov type finite difference method and solve the equations in characteristic form. We use the methodology implemented in the code MOST to calculate inundation from four different earthquake scenarios for Heraklion, Greece. MOST has been repeatedly benchmarked. The scenarios are geophysical estimates of the source mechanisms of the 365 AD event, the largest known earthquake in the Eastern Mediterranean in the last two millenia. The earthquake scenarios used allow for defining the seafloor deformation resulting from the parent seismic motions and, after translating them to the water surface, they constitute the initial conditions for computations. We use high resolution bathymetric and topographic data to generate fine resolution grids used in the computations. Our practice allows for a precise identification of the onland inundation and the overland flow depths and currents during tsunami flooding in Heraklion. This is the first time such a quantitative study has been undertaken for Eastern Crete. We conclude that there is substantial hazard, and there is little difference among the four different seismic interpretations of the 365 AD earthquake.
References
[1]
Abgrall, R., Computational methods for compressible flow problems. In: Shaidurov, V.V., Pironneau, O. (Eds.), Encyclopedia of Life Support Systems (EOLSS), Developed under the Auspices of the UNESCO, Eolss Publishers, Oxford, UK.
[2]
Barberopoulou, A., Borrero, J.C., Uslu, B., Legg, M.R. and Synolakis, C.E., A second generation of tsunami inundation maps for the State of California. Pure Appl. Geophys. v168. 1-14.
[3]
Bernard, E.N., Mofjeld, H.O., Titov, V.V., Synolakis, C.E. and González, F.I., Tsunami: scientific frontiers, mitigation, forecasting and policy implications. Philos. Trans. R. Soc. A. v364. 1989-2007.
[4]
Briggs, M.J., Synolakis, C.E. and Harkins, G.S., Tsunami runup on a conical island. In: Proc., Waves-Physical and Numerical Modelling, International Association for Hydraulic Research, Delft, The Netherlands. pp. 446-455.
[5]
Brufau, P., García-Navarro, P. and Vázquez-Cendón, M.E., Zero mass error using unsteady wetting-drying conditions in shallow flows over dry irregular topography. Internat. J. Numer. Methods Fluids. v45. 1047-1082.
[6]
Brufau, P., Vázquez-Cendón, M.E. and García-Navarro, P., A numerical model for the flooding and drying of irregular domain. Internat. J. Numer. Methods Fluids. v39. 247-275.
[7]
Castro, M.J., Ferreiro, A.M., García-Rodriguez, J.A., González-Vida, J.M., Macías, J., Parés, C. and Vázquez-Cendón, M.E., The numerical treatment of wet/dry fronts in shallow flows: application to one-layer and two-layer systems. Math. Comput. Modelling. v42. 419-439.
[8]
Castro, M.J., González-Vida, J. and Parés, C., Numerical treatment of wet/dry fronts in shallow flows with a modified Roe scheme. Math. Models Methods Appl. Sci. v16. 897-931.
[9]
Delis, A.I. and Kampanis, N.A., Numerical flood simulation by depth averaged free surface flow models. In: Sydow, Achim (Ed.), Encyclopedia of Life Support Systems (EOLSS), Developed under the Auspices of the UNESCO, Eolss Publishers, Oxford, UK.
[10]
Delis, A.I., Kazolea, M. and Kampanis, N.A., A robust high resolution finite volume scheme for the simulation of long waves over complex domains. Internat. J. Numer. Methods Fluids. v56. 419-452.
[11]
Di Vita, A., Archaeologists and earthquakes: the case of 365 AD. Ann. Geofis. v38. 971-976.
[12]
Dubois, F., An introduction to finite volume methods. In: Shaidurov, V.V., Pironneau, O. (Eds.), Encyclopedia of Life Support Systems (EOLSS), Developed under the Auspices of the UNESCO, Eolss Publishers, Oxford, UK.
[13]
Flemming, N., Holocene eustatic changes and coastal tectonics in the Northeast Mediterranean: implications for models of crustal consumption. Trans. Roy. Soc. Lond. v289. 405-458.
[14]
Geist, E.L., Complex earthquake rupture and local tsunamis. J. Geophys. Res. v107 iB5. 2086
[15]
González, F.I., Geist, E.L., Jaffe, B., Kínoglu, U., Mofjeld, H., Synolakis, C.E., Titov, V.V., Arcas, D., Bellomo, D., Carlton, D., Horning, T., Johnson, J., Newman, J., Parsons, T., Peters, R., Peterson, C., Priest, G., Venturato, A., Weber, J., Wong, F. and Yalciner, A., Probabilistic tsunami hazard assessment at Seaside, Oregon, for near- and far-field seismic sources. J. Geophys. Res. v114. C11023
[16]
Gopalakrishnan, T.C. and Tung, C.C., Run-up of non-breaking waves: a finite-element approach. Coast. Engrg. v4. 3-32.
[17]
Gusiakov, V.K., Static displacement on the surface of an elastic space. In: Ill-Posed Problems of Mathematical Physics and Interpretation of Geophysical Data, VC SOAN SSSR, Novosibirsk. pp. 23-51.
[18]
Helluy, P., Golay, F., Caltagirone, J.-P., Lubin, P., Vincent, S., Drevard, D., Marcer, R., Fraunie, P., Seguin, N., Grilli, S., Lesage, A.-C., Dervieux, A. and Allain, O., Numerical simulations of wave breaking. ESAIM: Math. Model. Numer. Anal. v39. 591-607.
[19]
Imamura, F., Review of tsunami simulation with finite difference method. In: Yeh, H., Liu, P., Synolakis, C. (Eds.), Long-Wave Runup Models, World Scientific Publishing Co., Singapore. pp. 25-42.
[20]
Kinsman, B., Wind Waves - Their Generation and Propagation on the Ocean Surface. 1965. Dover Publications, Inc.
[21]
Liu, P.L.-F., Cho, Y.-S., Griggs, M.J., Kínog¿lu, U. and Synolakis, C.E., Runup of solitary wave on a circular island. J. Fluid Mech. v302. 259-285.
[22]
Liu, P.L.-F., Synolakis, C.E. and Yeh, H., Impressions from the first international workshop on long wave runup. J. Fluid Mech. v229. 675-688.
[23]
Lorito, S., Tiberti, M.M., Basili, R., Piatanesi, A. and Valensise, G., Earthquake-generated tsunamis in the Mediterranean Sea: Scenarios of potential threats to Southern Italy. J. Geophys. Res. v113. B01301
[24]
Mader, C.L., Numerical Modeling of Water Waves. 2004. CRC Press, Boca Raton.
[25]
Mansinha, L. and Smylie, D.E., The displacement fields of inclined faults. Bull. Seismol. Soc. Amer. v61. 1433-1440.
[26]
Okada, Y., Surface deformation due to shear and tensile faults in a half space. Bull. Seismol. Soc. Amer. v75. 1135-1154.
[27]
Okal, E.A., A student's guide to teleseismic body-wave amplitudes. Seismol. Res. Lett. v63. 169-180.
[28]
Okal, E.A., Synolakis, C.E. and Kalligeris, N., Tsunami simulations for regional sources in the South China and adjoining seas. Pure Appl. Geophys. v168. 1153-1173.
[29]
Okal, E.A., Synolakis, C.E., Uslu, B., Kalligeris, N. and Voukouvalas, E., The 1956 earthquake and tsunami in Amorgos, Greece. Geophys. J. Int. v178. 1533-1554.
[30]
Papadimitriou, E.E. and Karakostas, V.G., Rupture model of the great AD 365 Crete earthquake in the southwestern part of the Hellenic Arc. Acta Geophys. v56. 293-312.
[31]
Pirazzoli, P., Laborel, J. and Stiros, S., Earthquake clustering in the Eastern Mediterranean during historical times. J. Geophys. Res. v101 iB3. 6083-6097.
[32]
Pirazzoli, P., Thommeret, J., Thommeret, Y., Laborel, J. and Montagionni, L., Crustal block movements from Holocene shorelines: Crete and Antikythira (Greece). Tectonophysics. v68. 27-43.
[33]
Remacle, J.-F., Soares Frazao, S., Li, X. and Shephard, M.S., An adaptive discretization of shallow-water equations based on discontinuous Galerkin methods. Internat. J. Numer. Methods Fluids. v52. 903-923.
[34]
Saiac, J.-H., Finite element method. In: Vladimir, V.V., Shaidurov, V., Pironneau, O. (Eds.), Encyclopedia of Life Support Systems (EOLSS), Developed under the Auspices of the UNESCO, Eolss Publishers, Oxford, UK.
[35]
Shaw, B., Ambraseys, N.N., England, P.C., Floyd, M.A., Gorman, G.J., Higham, T.F.G., Jackson, J.A., Nocquet, J.-M., Pain, C.C. and Piggott, M.D., Eastern Mediterranean tectonics and tsunami hazard inferred from the AD 365 earthquake. Nature Geosci. v1. 268-276.
[36]
Stiros, S.C., The AD 365 Crete earthquake and possible seismic clustering during the 4-6th centuries AD in the Eastern Mediterranean: a review of historical and archaeological data. J. Struct. Geol. v23. 545-562.
[37]
Stiros, S.C., The 8.5+ magnitude, AD365 earthquake in Crete: Coastal uplift, topography changes, archaeological and historical signature. Quat. Internat. v216. 54-63.
[38]
Stiros, S. and Papageorgiou, S., Seismicity of western Crete and the destruction of the town of Kisamos at AD365: archaeological evidence. J. Seismol. v5. 381-397.
[39]
Stiros, S. and Drakos, A., A fault-model for the tsunami-associated, magnitude ≤ 8.5 Eastern Mediterranean, AD365 earthquake. Z. Geomorphol. v146. 125-137.
[40]
Synolakis, C.E., Tsunami and seiche. In: Chen, W.F, Scawthorn, C. (Eds.), Earthquake Engineering Handbook, CRC Press.
[41]
Synolakis, C.E. and Bernard, E.N., Tsunami science before and beyond Boxing Day 2004. Philos. Trans. R. Soc. A. v364. 2231-2265.
[42]
Synolakis, C.E., Bernard, E.N., Titov, V.V., Kínog¿lu, U. and González, F.I., Validation and verification of tsunami numerical models. Pure Appl. Geophys. v165. 2197-2228.
[43]
Tadepalli, S. and Synolakis, C.E., The run-up of N waves on sloping beaches. Proc. R. Soc. Lond. A. v445. 99-112.
[44]
Taymaz, T., Jackson, J. and Westaway, R., Earthquake mechanisms in the Hellenic Trench near Crete. Geophys. J. Int. v102. 695-731.
[45]
V.V. Titov, Numerical modeling of long wave runup, PhD dissertation, University of Southern California, 1997.
[46]
Titov, V.V. and Synolakis, C.E., Modeling of breaking and nonbreaking long wave evolution and runup using VTCS-2. J. Waterway, Port, Coastal, Ocean Eng. v121. 308-316.
[47]
Numerical modeling of tidal wave runup. J. Waterway, Port, Coastal, Ocean Eng. v124. 157-171.
[48]
Wang, J.-W. and Liu, R.-X., Combined finite volume-finite element method for shallow water equations. Comput. & Fluids. v34. 1199-1222.
[49]
. In: Yeh, H., Liu, P.L.-F., Synolakis, C.E. (Eds.), Long-Wave Run-Up Models, World Scientific Publishing, Singapore.
[50]
Zelt, J.A., The run-up of nonbreaking and breaking solitary waves. Coast. Engrg. v15. 205-246.
- Application of a finite difference computational model to the simulation of earthquake generated tsunamis
Recommendations
Finite volume schemes for dispersive wave propagation and runup
Finite volume schemes are commonly used to construct approximate solutions to conservation laws. In this study we extend the framework of the finite volume methods to dispersive water wave models, in particular to Boussinesq type systems. We focus ...
Water waves generated by local disturbance: Serre's model validity
ICECT'03: Proceedings of the third international conference on Engineering computational technologyA numerical model based on Boussinesq equations (Serre's model) is used to describe water waves generated by local disturbance. Landslides in natural lakes or reservoirs of dams, avalanches, debris-flows, etc, can generate these sort of waves. Similar ...
From the paddle to the beach - A Boussinesq shallow water numerical wave tank based on Madsen and Sørensen's equations
This article describes a one-dimensional numerical model of a shallow-water flume with an in-built piston paddle moving boundary wavemaker. The model is based on a set of enhanced Boussinesq equations and the nonlinear shallow water equations. Wave ...
Comments
Please enable JavaScript to view thecomments powered by Disqus.Information & Contributors
Information
Published In
Copyright © © 2011.
Publisher
Elsevier Science Publishers B. V.
Netherlands
Publication History
Published: 01 May 2013
Author Tags
Qualifiers
- Article
Contributors
Other Metrics
Bibliometrics & Citations
Bibliometrics
Article Metrics
- 0Total Citations
- 0Total Downloads
- Downloads (Last 12 months)0
- Downloads (Last 6 weeks)0
Reflects downloads up to 12 Nov 2024
Other Metrics
Citations
View Options
View options
Get Access
Login options
Check if you have access through your login credentials or your institution to get full access on this article.
Sign in