Earth, Planets and Space

, Volume 52, Issue 9, pp 579–586 | Cite as

Amplification of gravity and Rayleigh waves in a layered water-soil model

Open Access


The coupled seismic to gravitational surface wave fields are analyzed in a liquid layer lying on the gravitating elastic, low-rigidity half-space. Solution is obtained within the framework of the normal mode formalism applied to the flat ocean-solid Earth model. From the theory of propagation of coupled surface waves (Rayleigh and Love) in layered media, we find the individual multipliers that determine the surface wave spectrum over the entire frequency range. Spectra of excitation functions are investigated for dip-slip point source in the half-space. Main results can be summarized as follows. When the half-space is filled with sediments, dip-slip excitation functions of gravity and Rayleigh waves are one order of magnitude larger than for the half-space composed of hard rocks. Including gravity in the elastic medium essentially changes the character of gravity wave spectrum, leading to an appearance of the third maximum. At the deepening of the source amplitude of this maximum increases. Theoretical marigrams show that including gravity in the half-space also increases period of the gravity wave excited by deep sources by a factor of two, up to 10 minutes. At the same time, presence of gravity force in the half-space has no effect on the spectrum of the Rayleigh wave.


Surface Wave Gravity Wave Rayleigh Wave Liquid Layer Seismic Moment 
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  1. Aki, K. and G. Richards, Quantative Seismology, v.1., 557 pp., W. H.Freeman, San Francisco, 1980.Google Scholar
  2. Alexeev, A. and V. Gusiakov, Numerical modeling of tsunami and seismic surface wave generationbyasubmarine earthquake, in Tsunami Research Symposium, Bull. R. Soc. N. Z., 15, 243–251, 1976.Google Scholar
  3. Bilek, S. and T. Lay, Rigidity variations with depth along interplate megathrust faults in subduction zones, Nature, 400, 443–446, 1999.CrossRefGoogle Scholar
  4. Comer, R., The tsunami mode of a flat earth and its excitation by earthquake sources, Geophys. J. R. astr. Soc., 77, 1–27, 1984a.CrossRefGoogle Scholar
  5. Comer, R., Tsunami generation: a comparison of traditional and normal mode approaches, Geophys. J. R. astr. Soc., 77, 29–41, 1984b.CrossRefGoogle Scholar
  6. De, S. N. and P. R. Sengupta, Surface waves under the influence of gravity, Gerlands Beitr. Geophys., 85, 311–318, 1976.Google Scholar
  7. Gilbert, F., Gravitationally perturbed elastic waves, Bull. Seism. Soc. Am., 57, 783–794, 1967.Google Scholar
  8. Gusiakov, V., Excitation of Tsunami and Oceanic Rayleigh Waves by Submarine Earthquake. Mathematical Problems in Geophysics, pp. 250–267, Novosibirsk, 1972.Google Scholar
  9. Houston, H., Slow ruptures, roaring tsunamis, Nature, 400, 409, 1999.CrossRefGoogle Scholar
  10. Hwang, L.-S., H. L. Butler, and D. J. Divoky, Tsunami model: Generation and open-sea characteristics, Bull. Seism. Soc. Am., 62, 1579–1596, 1972.Google Scholar
  11. Kanamori, H., Mechanism of tsunami earthquakes, Phys. Earth Planet. Inter., 6, 346–359, 1972.CrossRefGoogle Scholar
  12. Keilis-Borok, V., Seismic Surface Waves in a Laterally Inhomogeneous Earth, 293 pp., Kluwer Academic Publishers, 1989.Google Scholar
  13. Landau, L. and E. Lifshitz, Fluid mechanics, in Courses of Theoretical Physics, v.6, 1980.Google Scholar
  14. Lomnitz, C., Some observations of gravity waves in the 1960 Chile earthquake, Bull. Seism. Soc. Am., 59, 669–670, 1970.Google Scholar
  15. Lomnitz, C., Mexico 1985: the case for gravity waves, Geophys. J. Int., 102, 569–572, 1990.CrossRefGoogle Scholar
  16. Lomnitz, C., On the transition between Rayleigh waves and gravity waves, Bull. Seism. Soc. Am., 81, 273–275, 1991.Google Scholar
  17. Matuzawa, T., On the possibility of the gravitational waves in soil and allied problems, J. Inst. Astr. Geophys. Tokyo, 3, 161–174, 1925.Google Scholar
  18. Mooney, W., G. Laske, and T. Masters, Crust 5.1: A global crustal model at 50x50, J. Geophys. Res., 103, 727–747, 1998.CrossRefGoogle Scholar
  19. Nafe, J. and C. Drake, Physical properties of marine sediments, in The Sea, vol. 3, edited by M. H. Hill, pp. 794–815, Interscience Publishers, New York, 1963.Google Scholar
  20. Novikova, T., Numerical modeling of the tsunami generation by seismic sources, Ph.D. thesis Earth Physics Department, Institute of Physics, St. Petersburg University, 98 pp., 1997.Google Scholar
  21. Okal, E., Seismic parameters controlling far-field tsunami amplitudes: a review, Natural Hazards, 1, 67–96, 1988.CrossRefGoogle Scholar
  22. Pod”yapol’sky, G. S., Excitation of a long gravitational wave in the ocean from a seismic source in the crust, Izv. AN SSSR, Fizika Zemli, 1, 1968 (in Russian).Google Scholar
  23. Pod”yapol’sky, G. S., Generation of the tsunami wave by the earthquake in Tsunamis in the Pacific Ocean, edited by W. M. Adams, pp. 19–32, East-west Center Press, Honolulu, 1970.Google Scholar
  24. Satake, K., The mechanism of the 1983 Japan Sea earthquake as inferred from long-period Surface waves and tsunamis, Phys. Earth Planet. Inter., 37, 249–260, 1985.CrossRefGoogle Scholar
  25. Ward, S., Relationships of tsunami generation and an earthquake source, J. Phys. Earth, 28, 441–474, 1980.CrossRefGoogle Scholar
  26. Ward, S., On tsunami nucleation: a point source, J. Geophys. Res., 86, 7895–7900, 1981.CrossRefGoogle Scholar
  27. Ward, S., On tsunami nucleation: an instantaneous modulated line source. Phys. Earth Planet. Inter., 27, 273–285, 1982.CrossRefGoogle Scholar
  28. Weidner, D., Rayleigh waves from mid ocean ridge earthquakes: source and path effects, Ph.D. thesis, Harvard College, 253 pp., 1967.Google Scholar
  29. Westbrook, G. et al., Lasser Antilles subduction zone in the vicinity of Barbados, Nature Phys. Sci., 244, 118–120, 1973.CrossRefGoogle Scholar
  30. Yamashita, T. and R. Sato, Generation of tsunami by a fault model, J. Phys. Earth, 22, 415–440, 1974.CrossRefGoogle Scholar
  31. Yamashita, T. and R. Sato, Correlation of tsunami and sub-oceanic Rayleigh wave amplitudes. Possibility of the use of Rayleigh wave in tsunami warning system, J. Phys. Earth, 24, 397–416, 1976.CrossRefGoogle Scholar
  32. Yoshii, Y. et al., Crustal structure of Tosa deep-sea terrace and Nankani trough (in Japan), in Island Arc and Ocean, edited by M. Hoshino and H. Aoki, pp. 93–103, Tokai University Press, Tokyo, 1970.Google Scholar

Copyright information

© The Society of Geomagnetism and Earth, Planetary and Space Sciences (SGEPSS); The Seismological Society of Japan; The Volcanological Society of Japan; The Geodetic Society of Japan; The Japanese Society for Planetary Sciences. 2000

Authors and Affiliations

  • Tatyana Novikova
    • 1
  • Kuo-Liang Wen
    • 2
  • Bor-Shouh Huang
    • 1
  1. 1.Institute of Earth SciencesAcademia SinicaTaiwan
  2. 2.Institute of GeophysicsNCUTaiwan

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