Skip to main content
Log in

Numerical modeling of the long surface waves scattering for the 2011 Japan tsunami: Case study

  • Published:
Izvestiya, Atmospheric and Oceanic Physics Aims and scope Submit manuscript

Abstract

The March 11, 2011, megaquake caused a catastrophic tsunami recorded throughout the Pacific. This paper presents an analysis of the sea-level records obtained from deep-water tsunami meters (DART and NEPTUNE). To evaluate the effect of the sea-level oscillations’ decay, a statistical analysis of observations and numerical modeling of tsunami generation and propagation have been conducted. The main goal is to uncover physical mechanisms of the tsunami wave field formation and evolution at scales up to tens of thousands of kilometers in space and a few days in time. It is shown that the tsunami lifetime is related to the wave-energy diffusion and dissipation processes. The decay time of the variance of the tsunami-generated level oscillations is about 1 day. Multiple reflections and scattering by irregularities of the bottom topography make the field of the secondary tsunami waves stochastic and incoherent: the distribution of the wave energy in the ocean reaches a statistical equilibrium in accordance with the Rayleigh-Jeans law of equipartition of the wave energy per degree of freedom. After the tsunami front has passed, the secondary-wave energy density turns out to be inversely proportional to the water depth.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. W. H. Munk, “Some comments regarding diffusion and absorption of tsunamis,” in Proc. Tsunami Meetings, 10th Pacific Science Congress, IUGG Monograph 24 (Paris, 1963), pp. 31–41.

    Google Scholar 

  2. S. A. Ermakov and E. N. Pelinovsky, “Anomalous attenuation of tsunamis in a stratified ocean with statistically rough bottom,” Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 15(6), 662–668 (1979).

    Google Scholar 

  3. A. B. Rabinovich, L. I. Lobkovsky, I. V. Fine, R. E. Thomson, T. N. Ivelskaya, E. A. Kulikov, “Near-source observations and modeling of the Kuril Islands tsunamis of 15 November 2006 and 13 January 2007,” Adv. Geosci. 14, 105–116 (2008).

    Article  Google Scholar 

  4. F. Imamura, “Review of tsunami simulation with a finite difference method,” in Long-Wave Run-up Models, Ed. by H. Yeah, P. Liu, and C. Synolakis (World Scientific, London, 1996), pp. 25–42.

    Google Scholar 

  5. Y. Okada, “Surface deformation due to shear and tenisle faults in a half-space,” Bull. Seismol. Soc. Am. 75, 1135–1154 (1985).

    Google Scholar 

  6. G. Hayes, Finite Fault Model. Updated Result of the Mar 11, 2011 M w 9.0 Earthquake Offshore Honshu, Japan, 2011. http://earthquake.usgs.gov/earth-quakes/eqinthenews/2011/usc0001xgp/finite_fault.php.

    Google Scholar 

  7. Z. Kowalik, J. Horrillo, W. Knight, and T. Logan, “Kuril Islands tsunami of November 2006: 1. Impact at Crescent City by distant scattering,” J. Geophys. Res. Oceans 113, C01020 (2008). doi: 10.1029/2007JC004402

    Article  Google Scholar 

  8. K. Kajiura, “The leading wave of a tsunami,” Bull. Earthquake Res. Inst., Univ. Tokyo 41(3), 535–571 (1963).

    Google Scholar 

  9. I. V. Fine and E. A. Kulikov, “Calculation of sea surface displacements in a tsunami source area caused by instantaneous vertical deformation of the seabed due to an underwater earthquake,” Vychisl. Tekhnol. 16(2), 111–118 (2011).

    Google Scholar 

  10. M. A. Nosov and S. V. Kolesov, “Optimal initial conditions for simulation of seismotectonic tsunamis,” Pure Appl. Geophys. 168(6–7), 1223–1237 (2011).

    Article  Google Scholar 

  11. A. B. Rabinovich, R. N. Candella, and R. E. Thomson, “The open ocean energy decay of three recent trans-Pacific tsunamis,” Geophys. Res. Lett. 40 (2013). doi: 10.1002/grl.50625

  12. T. Saito, D. Inazu, S. Tanaka, and T. Miyoshi, “Tsunami coda across the Pacific Ocean following the 2011 Tohoku-Oki earthquake,” Bull. Seismol. Soc. Am. 103(2B), 1429–1443 (2013).

    Article  Google Scholar 

  13. B. W. Levin and M. A. Nosov, Physics of Tsunami and Related Phenomena in the Ocean (Yanus-K, Moscow, 2005) [in Russian].

    Google Scholar 

  14. W. G. van Dorn, “Some tsunami characteristic deducible from tide records,” J. Phys. Oceanogr. 14, 353–363 (1984).

    Article  Google Scholar 

  15. T. H. Bell, “Statistical features of sea-floor topography,” Deep-Sea Res. 22, 883–892 (1975).

    Google Scholar 

  16. G. V. Shevchenko and V. N. Patrikeev, “Statistical characteristics of abyssal roughnesses in the northwestern part of the Pacific Ocean and their possible impact on the character of tsunami propagation,” Tikhookean. Geol. 31(6), 44–48 (2012).

    Google Scholar 

  17. I. V. Fine, E. A. Kulikov, and J. Y. Cherniawsky, “Japan’s 2011 tsunami: Characteristics of wave propagation from observations and numerical modelling,” Pure Appl. Geophys. 170(6–8), 1295–1307 (2012). doi: 10.1007/s00024-012-0555-8

    Google Scholar 

  18. F. R. S. Rayleigh, “Remarks upon the law of complete radiation,” Philos. Mag. 49, 539–540 (1900).

    Article  Google Scholar 

  19. J. H. Jeans, “On the partition of energy between matter and aether,” Philos. Mag. 10, 91–98 (1905).

    Article  Google Scholar 

  20. E. A. Kulikov, “Measurements of the ocean level and tsunami forecast,” Meteorol. Gidrol., No. 6, 61–68 (1990).

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to E. A. Kulikov.

Additional information

Original Russian Text © E.A. Kulikov, I.V. Fine, O.I. Yakovenko, 2014, published in Izvestiya AN. Fizika Atmosfery i Okeana, 2014, Vol. 50, No. 5, pp. 567–577.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kulikov, E.A., Fine, I.V. & Yakovenko, O.I. Numerical modeling of the long surface waves scattering for the 2011 Japan tsunami: Case study. Izv. Atmos. Ocean. Phys. 50, 498–507 (2014). https://doi.org/10.1134/S0001433814050053

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001433814050053

Keywords

Navigation