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Analysis of Surface Waves in an Elastic Medium with a Porous Saturated Layer

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Radiophysics and Quantum Electronics Aims and scope

We study the propagation of seismoacoustic waves in a three-layered medium consisting of a uniform isotropic deformable solid layer that is loaded with a uniform porous layer saturated with fluid. In turn, the porous layer covers a homogeneous isotropic solid half-space. This medium models the geological section in which the upper ground layer is separated from the deep rocks by a porous layer containing a significant amount of fluid. The obtained dispersion relation is analyzed and its solutions for the practically important cases are presented. The effects due to the liquid-phase motion with respect to the relatively deformable solid skeleton during the wave propagation are pointed out. The features of the dispersion curves and the spatial distribution of the mode fields, which allow one not only to determine the presence of a fluid-saturated porous layer under the upper ground layer, but also estimate the thickness and occurrence depth of the porous layer, are revealed.

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References

  1. E. V. Koposov, ed., The Methods for Protection of Urbanized Territories from Environmental and Technogenic Influence [in Russian], Nizhny Novgorod State Architectural and Civil-Engineering University, Nizhny Novgorod (2013).

  2. L. Hatton, M. H. Worthington, and J. Makin, Seismic Data Processing: Theory and Practice, Blackwell Scientific, Oxford (1986).

    Google Scholar 

  3. Öz. Yilmas, Seismic Data Analysis, Vols. 1 and 2, Soc. Explor. Geophys., Tulsa, OK (2001), pp. 1028, 1053 p.

  4. R. Ghose, V. Nijhof, J. Brouwer, et al., Geophysics, 63, No. 4, 1295 (1998).

    Article  ADS  Google Scholar 

  5. A. Zhubayev and R. Ghose, J. Acoust. Soc. Am., 131, No. 2, EL170 (2012).

    Article  ADS  Google Scholar 

  6. N. N. Goryainov and F. M. Lyakhovitsky, Seismic Methods in Engineering Geology [in Russian], Nedra, Moscow (1979).

  7. V. N. Nikitin, Fundamentals of Engineering Seismics [in Russian], Moscow State Univ., Moscow (1981).

  8. A. G. Averbukh, A Study of Composition and Properties of Rocks during Seismic Exploration [in Russian], Nedra, Moscow (1982).

  9. K. H. Stokoe, G. R. Rix, and S. Nazarian, in: Proc. 12th Int. Conf. Soil Mech. Found. Eng., 1, 331 (1989).

  10. C. B. Park, R. D. Miller, and J. Xia, Geophysics, 64, No. 3, 800 (1999).

    Article  ADS  Google Scholar 

  11. J. Xia, C. B. Park, and R. D. Miller, Geophysics, 64, No. 3, 691 (1999).

    Article  ADS  Google Scholar 

  12. R. Miller, J. Xia, C. B. Park, and J. M. Ivanov, The Leading Edge, 27, 268 (2008).

    Google Scholar 

  13. M. Maraschini, “A new approach for the inversion of Rayleigh and Scholte waves in site characterization”, Ph.D. thesis, Dottorato di Ricerca in Ingegneria Geotecnica (XX ciclo), Politecnico di Torino, Torino (2008).

  14. B. Albers, Modeling of surface waves in poroelastic saturated materials by means of a two component continuum: Lecture Notes”, Preprint No. 952, Weierstraß-Institut für Angewandte Analysis und Stochastik, Berlin (2004).

  15. N. S. Gorodetskaya, Akust. Visn., 10, No. 2, 43 (2007).

    Google Scholar 

  16. M. G. Markov, Acoust. Phys., 52, No. 4, 429 (2006).

    Article  ADS  Google Scholar 

  17. W. M. Ewing, W. S. Jardetzky, and F. Press, Elastic Waves in Layered Media, McGraw-Hill, New York (1957).

    Book  Google Scholar 

  18. L. M. Brekhovskikh, Waves in Layered Media, Academic Press, New York (1980).

    MATH  Google Scholar 

  19. A. V. Razin and A. L. Sobisevich, Geoacoustics of Layered Media [in Russian], Schmidt Inst. Phys. Earth, Moscow (2012).

  20. Yu. V. Petukhov, A. V. Razin, A. L. Sobisevich, and V. I. Kulikov, Seismoacoustic and Acousto-Gravitational Waves in Layered Media [in Russian], Schmidt Inst. Phys. Earth, Moscow (2013).

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

  22. A. I. Kon’kov, A. V. Lebedev, and A. V. Razin, Radiophys. Quantum Electron., 59, No. 4, 289 (2016).

    Article  ADS  Google Scholar 

  23. J. G. Berryman, J. Acoust. Soc. Am., 69, No. 2, 416 (1981).

    Article  ADS  Google Scholar 

  24. V. S. Averbakh, A. V. Lebedev, A. P. Maryshev, and V. I. Talanov, Acoust. Phys., 54, No. 4, 526 (2008).

    Article  ADS  Google Scholar 

  25. R. D. Stoll, Sediment Acoustics, Springer-Verlag, New York (1989).

    Google Scholar 

  26. V. V. Gushchin, V. P. Dokuchaev, Yu. M. Zaslavsky, and I. D. Konyukhova, in: The Earth Study by Non-Explosive Seismic Sources [in Russian], Nauka, Moscow (1981), p. 113.

  27. M. A. Biot, J. Acoust. Soc. Am., 28, No. 2, 168 (1956).

    Article  ADS  Google Scholar 

  28. S. Lopatnikov and J. W. Gillespie, Jr., Transp. Porous Med., 93, 597 (2012).

    Article  Google Scholar 

  29. L. D. Landau and E. M. Lifshitz, Theory of Elasticity, Butterworth-Heinemann, Oxford (1986).

    MATH  Google Scholar 

  30. P. N. J. Rasolofosaon, Appl. Phys. Lett., 52, No. 10, 780 (1988).

    Article  ADS  Google Scholar 

  31. F. B. Jensen, W. A. Kuperman, M. B. Porter, and H. Schmidt, Computational Ocean Acoustics, Springer, New York (2011).

    Book  Google Scholar 

  32. G. Mavko, T. Mukerji, and J. Dvorkin, The Rock Physics Handbook: Tools for Seismic Analysis in Porous Media, Cambridge Univ. Press, Cambridge (2009).

    Book  Google Scholar 

  33. F. Gassmann, Geophysics, 16, No. 4, 673 (1951).

    Article  ADS  Google Scholar 

  34. M. I. Rabinovich and D. I. Trubetskov, Oscillations and Waves in Linear and Nonlinear Systems, Kluwer, Dordrecht (1989).

    Book  Google Scholar 

  35. M. Sahimi, Heterogeneous Materials I: Linear Transport and Optical Properties, Springer, New York (2006).

    MATH  Google Scholar 

  36. S. P. Timoshenko and S. Voinovsky-Kriger, Plates and Shells [in Russian], Nauka, Moscow (1966).

  37. V. C. Averbakh, N. N. Gribov, A. I. Konkov, et al., Bull. Russ. Acad. Sci. Phys., 80, No. 10, 1185 (2016).

    Article  Google Scholar 

  38. A. I. Konkov, A. V. Lebedev, and S. A. Manakov, eds., in: W. Freeden, M. Z. Nashed, and T. Sonar, Handbook of Geomathematics, Springer, Berlin (2015), p. 2189.

  39. D. L. Johnson and T. J. Plona, J. Acoust. Soc. Am., 72, No. 2, 556 (1982).

    Article  ADS  Google Scholar 

  40. N. P. Chotiros, Acoustics of the Seabed as a Poroelastic Medium, Springer, New York (2017).

    Book  Google Scholar 

  41. L. D. Landau and E. M. Lifshitz, Fluid Mechanics, Butterworth-Heinemann, Oxford (1987).

    Google Scholar 

  42. F. Gassmann, Vier. Natur. Gesellschaft Zürich, 96, 1 (1951).

    MathSciNet  Google Scholar 

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Correspondence to A. V. Lebedev.

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Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 62, No. 6, pp. 469–489, June 2019.

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Lebedev, A.V. Analysis of Surface Waves in an Elastic Medium with a Porous Saturated Layer. Radiophys Quantum El 62, 420–438 (2019). https://doi.org/10.1007/s11141-019-09988-5

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  • DOI: https://doi.org/10.1007/s11141-019-09988-5

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