Advertisement

Tsunami Generation

  • Tatsuhiko Saito
Chapter
Part of the Springer Geophysics book series (SPRINGERGEOPHYS)

Abstract

This chapter theoretically investigates tsunami generation. When an earthquake occurs in an offshore region, seismic waves, ocean acoustic waves, and tsunami are excited. Although the compressibility and elasticity of the sea layer are important for the propagation of ocean acoustic waves and high-frequency seismic waves, we may assume that the sea layer is incompressible for tsunami. This chapter is based on incompressible fluid dynamics. The theory gives the analytical solutions for tsunami generation and propagation, by which we would be able to understand the mechanism behind these phenomena in addition to describing the motion. Section 5.1 explains the difference between ocean acoustic waves and tsunami. In Sect. 5.2, a linear potential theory is formulated for the tsunami generation process in a water with uniform depth. Analytical solutions for the sea-surface displacement, velocity, and pressure field in the seawater are derived. In Sect. 5.3, we examine the analytical solutions for tsunami generation and propagation. The mathematical equations can directly provide us with a clear perspective on the tsunami mechanism. In Sect. 5.4, we bridge the gap between the analytical solutions derived under a constant sea-depth assumption and tsunami simulations with realistic bathymetry. The theoretical background of the initial conditions in the numerical simulations is explained.

Keywords

Linear potential theory Incompressible fluid Initial tsunami height distribution Dynamic pressure change Static pressure change 

References

  1. Aki K, Richards P (2002) Quantitative seismology. University Science Books, SausalitoGoogle Scholar
  2. An C, Cai C, Zheng Y, Meng L, Liu P (2017) Theoretical solution and applications of ocean bottom pressure induced by seismic seafloor motion. Geophys Res Lett 44:10,272–10,281.  https://doi.org/10.1002/2017GL075137 CrossRefGoogle Scholar
  3. Ewing WM, Jardetzky WS, Press F (1957) Elastic waves in layered media. McGraw-Hill Book Company, Inc, New YorkCrossRefGoogle Scholar
  4. Filloux JH (1982) Tsunami recorded on the open ocean floor. Geophys Res Lett 9(1):25–28CrossRefGoogle Scholar
  5. Fujii Y, Satake K (2008) Tsunami sources of the November 2006 and January 2007 great Kuril earthquakes. Bull Seismol Soc Am 98(3):1559–1571.  https://doi.org/10.1785/0120070221 CrossRefGoogle Scholar
  6. Gill AE (1982) Atmosphere-ocean dynamics, International geophysics series, vol 30. Academic Press, New YorkGoogle Scholar
  7. Gradshteyn IS, Ryshik IM (2000) Table of integrals, series and products (6th Ed. In Engl., ed. A. Jeffrey and D. Zwillinger). Academic Press, San DiegoGoogle Scholar
  8. Gusman AR, Tanioka Y, Sakai S, Tsushima H (2012) Source model of the great 2011 Tohoku earthquake estimated from tsunami waveforms and crustal deformation data. Earth Planet Sci Lett 341:234–242.  https://doi.org/10.1016/j.epsl.2012.06.006 CrossRefGoogle Scholar
  9. Hooper A et al (2013) Importance of horizontal seafloor motion on tsunami height for the 2011 Mw= 9.0 Tohoku-Oki earthquake. Earth Planet Sci Lett 361:469–479.  https://doi.org/10.1016/j.epsl.2012.11.013 CrossRefGoogle Scholar
  10. Ito Y et al (2011) Frontal wedge deformation near the source region of the 2011 Tohoku-Oki earthquake. Geophys Res Lett 38(7):L00G05.  https://doi.org/10.1029/2011GL048355 CrossRefGoogle Scholar
  11. Kajiura K (1963) The leading wave of a tsunami. Bull Earthq Res Inst 41:535–571Google Scholar
  12. Kakinuma T, Akiyama M (2007) Numerical analysis of tsunami generation due to seabed deformation. Coast Eng 2006:1490–1502.  https://doi.org/10.1142/9789812709554_0127 CrossRefGoogle Scholar
  13. Kambe T (2007) Elementary fluid mechanics, vol 258. World Scientific, SingaporeCrossRefGoogle Scholar
  14. Kennett BL (2001) The seismic Wavefield: volume I, introduction and theoretical development. Cambridge University Press, CambridgeGoogle Scholar
  15. Kervella Y, Dutykh D, Dias F (2007) Comparison between three-dimensional linear and nonlinear tsunami generation models. Theor Comput Fluid Dyn 21(4):245–269.  https://doi.org/10.1007/s00162-007-0047-0 CrossRefGoogle Scholar
  16. Kubota T, Hino R, Inazu D, Ito Y, Iinuma T (2015) Complicated rupture process of the Mw 7.0 intraslab strike-slip earthquake in the Tohoku region on 10 July 2011 revealed by near-field pressure records. Geophys Res Lett 42(22):9733–9739.  https://doi.org/10.1002/2015GL066101 CrossRefGoogle Scholar
  17. Kubota T, Saito T, Suzuki W, Hino R (2017) Estimation of seismic centroid moment tensor using ocean bottom pressure gauges as seismometers. Geophys Res Lett 44:10,907–10,915.  https://doi.org/10.1002/2017GL075386 CrossRefGoogle Scholar
  18. Lotto GC, Nava G, Dunham EM (2017) Should tsunami simulations include a nonzero initial horizontal velocity? Earth Planets Space 69:117.  https://doi.org/10.1186/s40623-017-0701-8 CrossRefGoogle Scholar
  19. Murotani S, Iwai M, Satake K, Shevchenko G, Loskutov A (2015) Tsunami forerunner of the 2011 Tohoku Earthquake observed in the Sea of Japan. Pure Appl Geophys 172(3–4):683–697.  https://doi.org/10.1007/s00024-014-1006-5 CrossRefGoogle Scholar
  20. Nosov MA (1999) Tsunami generation in compressible ocean. Phys Chem Earth (B) 24(5):437–441CrossRefGoogle Scholar
  21. Nosov MA, Kolesov SV (2011) Optimal initial conditions for simulation of seismotectonic tsunamis. Pure Appl Geophys 168(6–7):1223–1237.  https://doi.org/10.1007/s00024-010-0226-6 CrossRefGoogle Scholar
  22. Okada Y (1985) Surface deformation due to shear and tensile faults in a half-space. Bull Seismol Soc Am 75(4):1135–1154Google Scholar
  23. Pedlosky J (2013) Waves in the ocean and atmosphere: introduction to wave dynamics. Springer Science & Business Media, New YorkGoogle Scholar
  24. Saito T (2013) Dynamic tsunami generation due to sea-bottom deformation: analytical representation based on linear potential theory. Earth Planets Space 65:1411–1423.  https://doi.org/10.5047/eps.2013.07.004 CrossRefGoogle Scholar
  25. Saito T (2017) Tsunami generation: validity and limitations of conventional theories. Geophys J Int 210(3):1888–1900.  https://doi.org/10.1093/gji/ggx275 CrossRefGoogle Scholar
  26. Saito T, Furumura T (2009) Three-dimensional tsunami generation simulation due to sea-bottom deformation and its interpretation based on the linear theory. Geophys J Int 178(2):877–888.  https://doi.org/10.1111/j.1365-246X.2009.04206.x CrossRefGoogle Scholar
  27. Saito T, Tsushima H (2016) Synthesizing ocean bottom pressure records including seismic wave and tsunami contributions: toward realistic tests of monitoring systems. J Geophys Res Solid Earth 121(11):8175–8195.  https://doi.org/10.1002/2016JB013195 CrossRefGoogle Scholar
  28. Satake K, Kanamori H (1991) Abnormal tsunamis caused by the June 13, 1984, Torishima, Japan, earthquake. J Geophys Res Solid Earth 96(B12):19933–19939.  https://doi.org/10.1029/91JB01903 CrossRefGoogle Scholar
  29. Satake K, Fujii Y, Harada T, Namegaya Y (2013) Time and space distribution of coseismic slip of the 2011 Tohoku earthquake as inferred from tsunami waveform data. Bull Seismol Soc Am 103(2B):1473–1492.  https://doi.org/10.1785/0120120122 CrossRefGoogle Scholar
  30. Song YT, Mohtat A, Yim SC (2017) New insights on tsunami genesis and energy source. J Geophys Res Oceans 122:4238–4256.  https://doi.org/10.1002/2016JC012556 CrossRefGoogle Scholar
  31. Takahashi R (1942) On seismic sea waves caused by deformations of the sea bottom. Bull Earthq Res Inst 20:357–400Google Scholar
  32. Tanioka Y, Satake K (1996) Tsunami generation by horizontal displacement of ocean bottom. Geophys Res Lett 23(8):861–864.  https://doi.org/10.1029/96GL00736 CrossRefGoogle Scholar
  33. Tanioka Y, Seno T (2001) Sediment effect on tsunami generation of the 1896 Sanriku tsunami earthquake. Geophys Res Lett 28(17):3389–3392CrossRefGoogle Scholar
  34. Tsushima H, Hino R, Tanioka Y, Imamura F, Fujimoto H (2012) Tsunami waveform inversion incorporating permanent seafloor deformation and its application to tsunami forecasting. J Geophys Res Solid Earth 117(B03311).  https://doi.org/10.1029/2011JB008877
  35. Yamamoto T (1982) Gravity waves and acoustic waves generated by submarine earthquakes. Soil Dyn Earthq Eng 1(2):75–82Google Scholar

Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  • Tatsuhiko Saito
    • 1
  1. 1.National Research Institute for Earth Science and Disaster ResilienceTsukubaJapan

Personalised recommendations