Table of Contents
ISRN Applied Mathematics
Volume 2014, Article ID 874230, 27 pages
http://dx.doi.org/10.1155/2014/874230
Research Article

Three-Dimensional Modeling of Tsunami Generation and Propagation under the Effect of Stochastic Seismic Fault Source Model in Linearized Shallow-Water Wave Theory

Department of Basic and Applied Science, College of Engineering and Technology, Arab Academy for Science, Technology and Maritime Transport, P.O. Box 1029, Abu Quir Campus, Alexandria, Egypt

Received 12 September 2013; Accepted 27 November 2013; Published 19 March 2014

Academic Editors: Z. Hou, J. Shen, H. C. So, and X. Wen

Copyright © 2014 Allam A. Allam et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. S. Abou-Dina and F. M. Hassan, “Generation and propagation of nonlinear tsunamis in shallow water by a moving topography,” Applied Mathematics and Computation, vol. 177, no. 2, pp. 785–806, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  2. F. M. Hassan, “Boundary integral method applied to the propagation of non-linear gravity waves generated by a moving bottom,” Applied Mathematical Modelling, vol. 33, no. 1, pp. 451–466, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  3. N. Zahibo, E. Pelinovsky, T. Talipova, A. Kozelkov, and A. Kurkin, “Analytical and numerical study of nonlinear effects at tsunami modeling,” Applied Mathematics and Computation, vol. 174, no. 2, pp. 795–809, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  4. H. S. Hassan, K. T. Ramadan, and S. N. Hanna, “Numerical solution of the rotating shallow water ows with topography using the fractional steps method,” Applied Mathematics, vol. 1, no. 2, pp. 104–117, 2010. View at Publisher · View at Google Scholar
  5. V. V. Titov and C. E. Synolakis, “Modeling of breaking and nonbreaking long-wave evolution and runup using VTCS-2,” Journal of Waterway, Port, Coastal & Ocean Engineering, vol. 121, no. 6, pp. 308–316, 1995. View at Publisher · View at Google Scholar · View at Scopus
  6. B. Gurevich, A. Jeffrey, and E. N. Pelinovsky, “A method for obtaining evolution equations for nonlinear waves in a random medium,” Wave Motion, vol. 17, no. 3, pp. 287–295, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. A. de Bouard, W. Craig, O. Díaz-Espinosa, P. Guyenne, and C. Sulem, “Long wave expansions for water waves over random topography,” Nonlinearity, vol. 21, no. 9, pp. 2143–2178, 2008. View at Publisher · View at Google Scholar · View at MathSciNet
  8. A. Nachbin, “Discrete and continuous random water wave dynamics,” Discrete and Continuous Dynamical Systems A, vol. 28, no. 4, pp. 1603–1633, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  9. J. L. Hammack, “A note on tsunamis: their generation and propagation in an ocean of uniform depth,” Journal of Fluid Mechanics, vol. 60, pp. 769–799, 1973. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. M. I. Todorovska and M. D. Trifunac, “Generation of tsunamis by a slowy spreading uplift of the sea floor,” Soil Dynamics and Earthquake Engineering, vol. 21, no. 2, pp. 151–167, 2001. View at Publisher · View at Google Scholar · View at Scopus
  11. M. I. Todorovska, A. Hayir, and M. D. Trifunac, “A note on tsunami amplitudes above submarine slides and slumps,” Soil Dynamics and Earthquake Engineering, vol. 22, no. 2, pp. 129–141, 2002. View at Publisher · View at Google Scholar · View at Scopus
  12. M. D. Trifunac, A. Hayir, and M. I. Todorovska, “A note on the effects of nonuniform spreading velocity of submarine slumps and slides on the near-field tsunami amplitudes,” Soil Dynamics and Earthquake Engineering, vol. 22, no. 3, pp. 167–180, 2002. View at Publisher · View at Google Scholar · View at Scopus
  13. A. Hayir, “The effects of variable speeds of a submarine block slide on near-field tsunami amplitudes,” Ocean Engineering, vol. 30, no. 18, pp. 2329–2342, 2003. View at Publisher · View at Google Scholar · View at Scopus
  14. D. Dutykh, F. Dias, and Y. Kervella, “Linear theory of wave generation by a moving bottom,” Comptes Rendus Mathématique. Académie des Sciences. Paris, vol. 343, no. 7, pp. 499–504, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  15. D. Dutykh and F. Dias, “Water waves generated by a moving bottom,” in Tsunami and Nonlinear Waves, pp. 65–95, Springer, Berlin, Germany, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  16. Y. Kervella, D. Dutykh, and F. Dias, “Comparison between three-dimensional linear and nonlinear tsunami generation models,” Theoretical and Computational Fluid Dynamics, vol. 21, no. 4, pp. 245–269, 2007. View at Publisher · View at Google Scholar · View at Scopus
  17. H. S. Hassan, K. T. Ramadan, and S. N. Hanna, “Generation and propagation of tsunami by a moving realistic curvilinear slide shape with variable velocities in linearized shallow-water wave theory,” Engineering, vol. 2, no. 7, pp. 529–549, 2010. View at Publisher · View at Google Scholar
  18. K. T. Ramadan, H. S. Hassan, and S. N. Hanna, “Modeling of tsunami generation and propagation by a spreading curvilinear seismic faulting in linearized shallow-water wave theory,” Applied Mathematical Modelling, vol. 35, no. 1, pp. 61–79, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  19. K. T. Ramadan, M. A. Omar, and A. A. Allam, “Modeling of tsunami generation and propagation by a spreading seismic faulting in two orthogonal directions in linearized shallow-water wave theory,” 2012, http://etms-eg.org/.
  20. R. L. Wiegel, Earthquake Engineering, Prentice-Hall, Englewood Cliffs, NJ, USA, 1970.
  21. O. Rascón and A. G. Villarreal, “On a stochastic model to estimate tsunami risk,” Journal of Hydraulic Research, vol. 13, no. 4, pp. 383–403, 1975. View at Publisher · View at Google Scholar · View at Scopus
  22. S. Nakamura, “Estimate of exceedance probability of tsunami occurrence in the eastern pacific,” Marine Geodesy, vol. 10, no. 2, pp. 195–209, 1986. View at Publisher · View at Google Scholar · View at Scopus
  23. E. L. Geist, “Complex earthquake rupture and local tsunamis,” Journal of Geophysical Research B, vol. 107, no. 5, pp. 2086–2100, 2002. View at Google Scholar · View at Scopus
  24. E. L. Geist, “Rapid tsunami models and earthquake source parameters: far-field and local applications,” ISET Journal of Earthquake Technology, vol. 42, no. 4, pp. 127–136, 2005. View at Google Scholar · View at Scopus
  25. W. Craig, P. Guyenne, and C. Sulem, “Water waves over a random bottom,” Journal of Fluid Mechanics, vol. 640, pp. 79–107, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  26. H. Manouzi and M. Seaïd, “Solving Wick-stochastic water waves using a Galerkin finite element method,” Mathematics and Computers in Simulation, vol. 79, no. 12, pp. 3523–3533, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  27. D. Dutykh, C. Labart, and D. Mitsotakis, “Long wave run-up on random beaches,” Physical Review Letters, vol. 107, no. 18, Article ID 184504, 2011. View at Publisher · View at Google Scholar · View at Scopus
  28. M. A. Omar, A. A. Allam, and K. T. Ramadan, “Generation and propagation of tsunami wave under the effect of stochastic bottom topography,” 2012, http://etms-eg.org/.
  29. K. T. Ramadan, M. A. Omar, and A. A. Allam, “Modeling of tsunami generation and propagation under the effect of stochastic submarine landslides and slumps spreading in two orthogonal directions,” Ocean Engineering, vol. 75, pp. 90–111, 2014. View at Publisher · View at Google Scholar
  30. F. C. Klebaner, Introduction to Stochastic Calculus with Applications, Imperial College Press, London, UK, 2nd edition, 2005. View at MathSciNet
  31. P. E. Kloeden and E. Platen, Numerical Solution of Stochastic Differential Equations, Springer, Berlin, Germany, 1992. View at MathSciNet
  32. B. Øksendal, Stochastic Differential Equations: An Introduction with Applications, Springer, Berlin, Germany, 1995. View at MathSciNet
  33. M. A. Omar, A. Aboul-Hassan, and S. I. Rabia, “The composite Milstein methods for the numerical solution of Stratonovich stochastic differential equations,” Applied Mathematics and Computation, vol. 215, no. 2, pp. 727–745, 2009. View at Publisher · View at Google Scholar · View at MathSciNet
  34. M. A. Omar, A. Aboul-Hassan, and S. I. Rabia, “The composite Milstein methods for the numerical solution of Ito stochastic differential equations,” Journal of Computational and Applied Mathematics, vol. 235, no. 8, pp. 2277–2299, 2011. View at Publisher · View at Google Scholar · View at MathSciNet
  35. H. H. Sherief, N. M. El-Maghraby, and A. A. Allam, “Stochastic thermal shock problem in generalized thermoelasticity,” Applied Mathematical Modelling, vol. 37, no. 3, pp. 762–775, 2013. View at Publisher · View at Google Scholar · View at MathSciNet
  36. H. Kanamori and G. S. Stewart, “A slowly earthquake,” Physics of the Earth and Planetary Interiors, vol. 18, pp. 167–175, 1972. View at Google Scholar
  37. P. G. Silver and T. H. Jordan, “Total-moment spectra of fourteen large earthquakes,” Journal of Geophysical Research, vol. 88, no. 4, pp. 3273–3293, 1983. View at Publisher · View at Google Scholar · View at Scopus
  38. M. D. Trifunac and M. I. Todorovska, “A note on differences in tsunami source parameters for submarine slides and earthquakes,” Soil Dynamics and Earthquake Engineering, vol. 22, no. 2, pp. 143–155, 2002. View at Publisher · View at Google Scholar · View at Scopus
  39. M. D. Trifunac, A. Hayir, and M. I. Todorovska, “Was grand banks event of 1929 a slump spreading in two directions?” Soil Dynamics and Earthquake Engineering, vol. 22, no. 5, pp. 349–360, 2002. View at Publisher · View at Google Scholar · View at Scopus
  40. A. Hayir, “Ocean depth effects on tsunami amplitudes used in source models in linearized shallow-water wave theory,” Ocean Engineering, vol. 31, no. 3-4, pp. 353–361, 2004. View at Publisher · View at Google Scholar · View at Scopus