- Article
- Published:
Amplification of gravity and Rayleigh waves in a layered water-soil model
Earth, Planets and Space volume 52, pages 579–586 (2000)
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
Aki, K. and G. Richards, Quantative Seismology, v.1., 557 pp., W. H.Freeman, San Francisco, 1980.
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.
Bilek, S. and T. Lay, Rigidity variations with depth along interplate megathrust faults in subduction zones, Nature, 400, 443–446, 1999.
Comer, R., The tsunami mode of a flat earth and its excitation by earthquake sources, Geophys. J. R. astr. Soc., 77, 1–27, 1984a.
Comer, R., Tsunami generation: a comparison of traditional and normal mode approaches, Geophys. J. R. astr. Soc., 77, 29–41, 1984b.
De, S. N. and P. R. Sengupta, Surface waves under the influence of gravity, Gerlands Beitr. Geophys., 85, 311–318, 1976.
Gilbert, F., Gravitationally perturbed elastic waves, Bull. Seism. Soc. Am., 57, 783–794, 1967.
Gusiakov, V., Excitation of Tsunami and Oceanic Rayleigh Waves by Submarine Earthquake. Mathematical Problems in Geophysics, pp. 250–267, Novosibirsk, 1972.
Houston, H., Slow ruptures, roaring tsunamis, Nature, 400, 409, 1999.
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.
Kanamori, H., Mechanism of tsunami earthquakes, Phys. Earth Planet. Inter., 6, 346–359, 1972.
Keilis-Borok, V., Seismic Surface Waves in a Laterally Inhomogeneous Earth, 293 pp., Kluwer Academic Publishers, 1989.
Landau, L. and E. Lifshitz, Fluid mechanics, in Courses of Theoretical Physics, v.6, 1980.
Lomnitz, C., Some observations of gravity waves in the 1960 Chile earthquake, Bull. Seism. Soc. Am., 59, 669–670, 1970.
Lomnitz, C., Mexico 1985: the case for gravity waves, Geophys. J. Int., 102, 569–572, 1990.
Lomnitz, C., On the transition between Rayleigh waves and gravity waves, Bull. Seism. Soc. Am., 81, 273–275, 1991.
Matuzawa, T., On the possibility of the gravitational waves in soil and allied problems, J. Inst. Astr. Geophys. Tokyo, 3, 161–174, 1925.
Mooney, W., G. Laske, and T. Masters, Crust 5.1: A global crustal model at 50x50, J. Geophys. Res., 103, 727–747, 1998.
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.
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.
Okal, E., Seismic parameters controlling far-field tsunami amplitudes: a review, Natural Hazards, 1, 67–96, 1988.
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).
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.
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.
Ward, S., Relationships of tsunami generation and an earthquake source, J. Phys. Earth, 28, 441–474, 1980.
Ward, S., On tsunami nucleation: a point source, J. Geophys. Res., 86, 7895–7900, 1981.
Ward, S., On tsunami nucleation: an instantaneous modulated line source. Phys. Earth Planet. Inter., 27, 273–285, 1982.
Weidner, D., Rayleigh waves from mid ocean ridge earthquakes: source and path effects, Ph.D. thesis, Harvard College, 253 pp., 1967.
Westbrook, G. et al., Lasser Antilles subduction zone in the vicinity of Barbados, Nature Phys. Sci., 244, 118–120, 1973.
Yamashita, T. and R. Sato, Generation of tsunami by a fault model, J. Phys. Earth, 22, 415–440, 1974.
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.
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Novikova, T., Wen, KL. & Huang, BS. 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
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1186/BF03351666