Tsunami generation by dynamic displacement of sea bed due to dip-slip faulting. (English) Zbl 1178.86010
Summary: In classical tsunami-generation techniques, one neglects the dynamic sea bed displacement resulting from fracturing of a seismic fault. The present study takes into account these dynamic effects. Earth’s crust is assumed to be a Kelvin-Voigt material. The seismic source is assumed to be a dislocation in a viscoelastic medium. The fluid motion is described by the classical nonlinear shallow water equations (NSWE) with time-dependent bathymetry. The viscoelastodynamic equations are solved by a finite-element method and the NSWE by a finite-volume scheme. A comparison between static and dynamic tsunami-generation approaches is performed. The results of the numerical computations show differences between the two approaches and the dynamic effects could explain the complicated shapes of tsunami wave trains.
MSC:
| 86A15 | Seismology (including tsunami modeling), earthquakes |
| 76M25 | Other numerical methods (fluid mechanics) (MSC2010) |
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
Software:
FreeFem++References:
| [1] | Benkhaldoun, F.; Quivy, L., A non homogeneous Riemann solver for shallow water and two phase flows, Flow Turbulence Combust., 76, 391-402 (2006) · Zbl 1108.76043 |
| [2] | Dutykh, D.; Dias, F., Water waves generated by a moving bottom, (Kundu, A., Tsunami and Nonlinear Waves (2007), Springer Verlag (Geo Sci.)), 63-94 |
| [3] | Dutykh, D.; Dias, F.; Kervella, Y., Linear theory of wave generation by a moving bottom, C. R. Acad. Sci. Paris Ser. I, 343, 499-504 (2006) · Zbl 1102.76005 |
| [4] | Freund, L. B.; Barnett, D. M., A two-dimensional analysis of surface deformation due to dip-slip faulting, Bull. Seism. Soc. Am., 66, 667-675 (1976) |
| [5] | Ghidaglia, J.-M.; Kumbaro, A.; Le Coq, G., On the numerical solution to two fluid models via cell centered finite volume method, Eur. J. Mech. B/Fluids, 20, 841-867 (2001) · Zbl 1059.76041 |
| [6] | Ghidaglia, J.-M.; Pascal, F., The normal flux method at the boundary for multidimensional finite volume approximations in CFD, Eur. J. Mech. B/Fluids, 24, 1-17 (2005) · Zbl 1060.76076 |
| [7] | Hammack, J., A note on tsunamis: their generation and propagation in an ocean of uniform depth, J. Fluid Mech., 60, 769-799 (1973) · Zbl 0273.76010 |
| [8] | Haskell, N. A., Elastic displacements in the near-field of a propagating fault, Bull. Seism. Soc. Am., 59, 865-908 (1969) |
| [9] | F. Hecht, O. Pironneau, A. Le Hyaric, K. Ohtsuka, FreeFem++, Laboratoire JL Lions, University of Paris VI, France.; F. Hecht, O. Pironneau, A. Le Hyaric, K. Ohtsuka, FreeFem++, Laboratoire JL Lions, University of Paris VI, France. |
| [10] | Kajiura, K., Tsunami source, energy and the directivity of wave radiation, Bull. Earthquake Res. Inst., 48, 835-869 (1970) |
| [11] | Kervella, Y.; Dutykh, D.; Dias, F., Comparison between three-dimensional linear and nonlinear tsunami generation models, Theor. Comput. Fluid Dyn., 21, 245-269 (2007) · Zbl 1161.76440 |
| [12] | Madariaga, R., Radiation from a finite reverse fault in half space, Pure Appl. Geophys., 160, 555-577 (2003) |
| [13] | Mansinha, L.; Smylie, D. E., The displacement fields of inclined faults, Bull. Seism. Soc. Am., 61, 1433-1440 (1971) · Zbl 0227.73169 |
| [14] | Masterlark, T., Finite element model predictions of static deformation from dislocation sources in a subduction zone: sensivities to homogeneous, isotropic, Poisson-solid, and half-space assumptions, J. Geophys. Res., 108, 2540 (2003) |
| [15] | Megna, A.; Barba, S.; Santini, S., Normal-fault stress and displacement through finite-element analysis, Ann. Geophys., 48, 1009-1016 (2005) |
| [16] | Ohmachi, T.; Tsukiyama, H.; Matsumoto, H., Simulation of tsunami induced by dynamic displacement of seabed due to seismic faulting, Bull. Seism. Soc. Am., 91, 1898-1909 (2001) |
| [17] | Okada, Y., Surface deformation due to shear and tensile faults in a half-space, Bull. Seism. Soc. Am., 75, 1135-1154 (1985) |
| [18] | Okal, E. A.; Synolakis, C. E., Source discriminants for near-field tsunamis, Geophys. J. Int., 158, 899-912 (2004) |
| [19] | Okumura, Y.; Kawata, Y., Effects of rise time and rupture velocity on tsunami, (Proc. 17th Int. Offshore and Polar Engineering Conf., vol. III (2007)) |
| [20] | J. Quiblier, Propagation des ondes en géophysique et en géotechnique, Modélisation par méthodes de Fourier, Editions Technip, Paris, 1997.; J. Quiblier, Propagation des ondes en géophysique et en géotechnique, Modélisation par méthodes de Fourier, Editions Technip, Paris, 1997. |
| [21] | Synolakis, C. E.; Bernard, E. N., Tsunami science before and beyond Boxing Day 2004, Philos. Trans. R. Soc. A, 364, 2231-2265 (2006) |
| [22] | Tadepalli, S.; Synolakis, C. E., The runup of N-waves, Proc. R. Soc. Lond. A, 445, 99-112 (1994) · Zbl 0807.76011 |
| [23] | Tadepalli, S.; Synolakis, C. E., Model for the leading waves of tsunamis, Phys. Rev. Lett., 77, 2141-2144 (1996) |
| [24] | Todorovska, M. I.; Trifunac, M. D., Generation of tsunamis by a slowly spreading uplift of the sea floor, Soil Dyn. Earthquake Eng., 21, 151-167 (2001) |
| [25] | Titov, V. V.; Synolakis, C. E., Numerical modeling of tidal wave runup, J. Waterway Port Coast. Ocean Eng., 124, 157-171 (1998) |
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