Skip to main content

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

Abstract

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.

References

  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.

    Article  Google 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.

    Article  Google Scholar 

  5. Comer, R., Tsunami generation: a comparison of traditional and normal mode approaches, Geophys. J. R. astr. Soc., 77, 29–41, 1984b.

    Article  Google 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.

    Article  Google 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.

    Article  Google Scholar 

  12. Keilis-Borok, V., Seismic Surface Waves in a Laterally Inhomogeneous Earth, 293 pp., Kluwer Academic Publishers, 1989.

  13. Landau, L. and E. Lifshitz, Fluid mechanics, in Courses of Theoretical Physics, v.6, 1980.

  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.

    Article  Google 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.

    Article  Google 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.

  21. Okal, E., Seismic parameters controlling far-field tsunami amplitudes: a review, Natural Hazards, 1, 67–96, 1988.

    Article  Google 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).

  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.

  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.

    Article  Google Scholar 

  25. Ward, S., Relationships of tsunami generation and an earthquake source, J. Phys. Earth, 28, 441–474, 1980.

    Article  Google Scholar 

  26. Ward, S., On tsunami nucleation: a point source, J. Geophys. Res., 86, 7895–7900, 1981.

    Article  Google Scholar 

  27. Ward, S., On tsunami nucleation: an instantaneous modulated line source. Phys. Earth Planet. Inter., 27, 273–285, 1982.

    Article  Google 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.

    Article  Google Scholar 

  30. Yamashita, T. and R. Sato, Generation of tsunami by a fault model, J. Phys. Earth, 22, 415–440, 1974.

    Article  Google 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.

    Article  Google 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 

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Tatyana Novikova.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Novikova, T., Wen, K. & Huang, B. Amplification of gravity and Rayleigh waves in a layered water-soil model. Earth Planet Sp 52, 579–586 (2000). https://doi.org/10.1186/BF03351666

Download citation

Keywords

  • Surface Wave
  • Gravity Wave
  • Rayleigh Wave
  • Liquid Layer
  • Seismic Moment