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Analytical modeling of wave fields at extremely long distances and experimental research of water waves

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Abstract

The analytical algorithm developed in this work is intended for modeling wave fields at extremely long distances; it has no limitations on accuracy, media models, and observation databases and makes it possible to calculate the dynamics of individual waves (primary waves, ghost waves, etc). Comparison with experimental marine data is performed with a program developed for the calculation of wave fields. The modeling performed shows that the incorporation of absorption in the Earth ensures a good agreement between the model and the observed wave fields. The formula for the ratio between waves of different multiplicities corroborated by experimental and mathematical modeling data is obtained to a first approximation for large source-receiver separation. An analytical modeling of full wave fields has been performed, some types of waves are analyzed, and the physics of multiple waves in a layer of water is studied numerically

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References

  1. K. Aki and P. Richards, Quantitative Seismology, 2nd ed. (Univ. Science Books, 2002).

  2. A.S. Alekseev and B. G. Mikhailenko, “The method of Calculation of Theoretical Seismograms for Complexly Structured Model of a Medium,” Sov. Phys. Dokl. 240(5) (1978)

  3. P. G. Bergmann et al.; Physical Foundations of Underwater Acoustics (Sov. Radio, Moscow, 1955) [in Russian].

    Google Scholar 

  4. L. M. Brekhovskikh and O. A. Godin; Acoustics of Layered Media (Nauka, Moscow, 1989) [in Russian].

    Google Scholar 

  5. L. M. Brekhovskikh and Yu. P. Lysanov Theoretical Foundations of Ocean Acoustics (Nauka, Moscow, 2007) [in Russian].

    Google Scholar 

  6. V. Yu. Burmin, “Seismic Wave Velocities in the Earth Crust,” Fizika Zemli, No.6, 24 (2004) [Izvestiya, Physics of the Solid Earth 40 (6) (2004)].

  7. R. H Cole, Underwater Explosions (Prinston Univ. Press, Prinston, New Jersey, 1948).

    Google Scholar 

  8. Deep Seismic Sounding of Lithosphere on the Angola-Brazil Geotraverse, Ed. by S. M. Zverev, I. P. Kosminskaya, and Yu. V. Tulina (MGK, Moscow, 1996).

    Google Scholar 

  9. A. G. Fat’yanov, Nonstationary Seismic Wave Fields in Heterogeneous Anisotropic Media with Energy Absorption, (Akad. Nauk. SSSR, Siberian Division, Novosibirsk, 1989).

    Google Scholar 

  10. A. G. Fat’yanov, “Semi-analytical Method of Solving Direct Dynamic Problems in Layered Media,” Dokl. Akad. Nauk SSSR, 310(2), 323 (1990).

    Google Scholar 

  11. A. G. Fat’yanov, “Forward and Inverse Problems for the Seismic Momentum Tensor in Layered Media,” Dokl. Akad. Nauk SSSR, 317(6), 1357 (1991).

    Google Scholar 

  12. A. G. Fat’yanov, “Mathematical Modeling of Wave Fields in Media with Curvilinear Boundaries,” Dokl.Phys., 401(4), 529 (2005).

    Google Scholar 

  13. O. K. Kondrat’ev, Seismic Waves in Absorbing Media (Nedra, Moscow, 1986) [in Russian].

    Google Scholar 

  14. A. N. Konovalov, Numerical Solution of Problems of the Elasticity Theory in Terms of Stresses (Novosibirsk State Univ., Novosibirsk, 1964) [in Russian].

    Google Scholar 

  15. L. A. Molotkov, Matrix Method in the Theory of Wave Propagation in Layered Elastic and Liquid Media (Nauka, Leningrad, 1984) [in Russian]

    Google Scholar 

  16. G. I. Petrashen’, “The Method of the Solution Construction for Problems of Seismic Wave Propagation in Isotropic Media with Thick Plane-Parallel Layers,” in Voprosy Dinamicheskoi Teorii Rasprostraneniya Seismicheskikh Voln, (Gostopizdat, Leningrad, 1957), No.1, pp. 7–69.

    Google Scholar 

  17. A. A. Samarskii, Theory of Finite-Difference Schemes (Nauka, Moscow, 1977) [in Russan].

    Google Scholar 

  18. V. I. Smirnov and S. L. Sobolev, “On a New Method in a 2-D Problem of Elastic Oscillations,” Trudy Seismologicheskogo Inst., No. 20, (1932).

  19. Yu. V. Tulina, V. Yu. Burmin, I. B. Shmeleva, and N. A. Alekseeva, “On Geological Origin of Differences in Seismic Fields along Various Directions in the Angola Basin,” Fizika Zemli, No. 6 (2003b) [Izvestiya, Physics of the Solid Earth 39 (6) (2003)].

  20. Yu.V. Tulina, V. Yu. Burmin, and I. B. Shmeleva, “Is it Possible to Construct Velocity Section by the DSS method from Data on Seismic Waves Recorded in First Arrivals?,” in Sbornik Trudov Sed’mykh Chtenii im. A.A. Fedynskogo, (Nauchnyi Mir, Moscow, 2006), pp. 114–128.

    Google Scholar 

  21. S. M. Zverev, Seismic Studies at Sea (Moscow State Univ., Moscow, 1996) [in Russian].

    Google Scholar 

  22. N. V. Zvolinskii, “Reflected and Head Waves Arising at a Planar Interface,” Izv. AN SSSR, ser. Geofiz., No. 10. (1964).

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Authors and Affiliations

  1. Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, ul. Bol’shaya Gruzinskaya 10, Moscow, 123995, Russia

    V. Yu. Burmin & A. G. Fat’yanov

  2. Institute of Computational Mathematics and Mathematical Geophysics, Siberian Division, Russian Academy of Sciences, Novosibirsk, Russia

    V. Yu. Burmin & A. G. Fat’yanov

Authors
  1. V. Yu. Burmin
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  2. A. G. Fat’yanov
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Correspondence to A. G. Fat’yanov.

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Original Russian Text © V.Yu. Burmin, A.G. Fat’yanov, 2009, published in Fizika Zemli, 2009, No. 4, pp. 43–55.

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Burmin, V.Y., Fat’yanov, A.G. Analytical modeling of wave fields at extremely long distances and experimental research of water waves. Izv., Phys. Solid Earth 45, 313–325 (2009). https://doi.org/10.1134/S1069351309040041

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  • DOI: https://doi.org/10.1134/S1069351309040041

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