Wave propagation in periodic fluid-solid layered media

Authors

  • Yu.V. Roganov
  • V.Yu. Roganov

DOI:

https://doi.org/10.24028/gzh.0203-3100.v38i6.2016.91877

Keywords:

periodic fluid-solid medium, dispersion equation, Floquet wave, slowness curve, velocity indicatrix

Abstract

Dispersion equation is derived for the Floquet waves in a horizontal periodically layered fluid-solid medium. It is shown that the dispersion equation consists of four factors. This representation explains the splitting of parameters (frequency, horizontal slowness) in passing and stop bands. The Floquet waves with horizontal group velocity can be computed individually from each of these factors. The properties of horizontally propagated waves are considered. The equations for the ratios of the components of polarization vectors and the amplitudes of partial waves are derived. Proposed theory is illustrated in one numerical example

References

Brekhovskikh L. M., 1973. Waves in layered media. Moscow: Nauka, 343 p. (in Russian)

Molotkov L. A., 2001. The study of wave propagation in porous and fractured media based on effective models of BIO and layered media. St. Petersburg: Nauka, 348 p. (in Russian)

Molotkov L. A., 1984. The matrix method in the theory of wave propagation in layered elastic and fluid media. Leningrad: Nauka, 201 p. (in Russian)

Molotkov L. A., 1988. Wave propagation in laminar models of cracked media. Zapiski Nauchnykh Seminarov LOMI 173(180), 123—133 (in Russian)

Molotkov L. A., 1979. Equivalence of periodically layered and transversally isotropic media. Zapiski Nauchnykh Seminarov LOMI 89, 219—233 (in Russian)

Molotkov L. A., Khilo A. E., 1983. The investigation of propagation of three-dimensional waves in stratified elastic and elasticfluid systems. Zapiski Nauchnykh Seminarov LOMI 128 (13), 116—129 (in Russian)

Roganov V. Yu., 2013. Modeling of wavefields for media with fluid and anisotropic elastic layers based on Haskell-Thomson method. Geofizicheskiy zhurnal 35 (3), 84—92 (in Russian)

Rytov S. M., 1956. The elastic properties of small-layered medium. Akusticheskiy zhurnal 2(1), 71—83 (in Russian)

Sibiryakov B. P., Maksimov L. A., Tatarnikov M. A., 1980. Anisotropy and dispersion of elastic waves in layered periodic structures. Novosibirsk: Nauka, 72 p. (in Russian)

Yakubovich V. A., Starzhinskiy V. M., 1975. Linear differential equations with periodic coefficients and their applications. Moscow: Nauka, 720 p. (in Russian)

Braga A. M., Herrmann G., 1992. Floquet waves in anisotropic periodically layered composites. J. Acoust. Soc. Am. 91(3), 1211—1227. http://dx.doi.org/10.1121/1.402505

Chicone C., 1999. Ordinary Differential Equations with Applications. New York: Springer-Verlag, 561 p

Floquet G., 1883. Sur les equations differentielles lineaires a coefficients periodiques. Annales Scientifiques de l’Ecole Normale Superieure 12, 47—88

Haskell N. A., 1953. The dispersion of surface waves on multilayered media. Bull. Seismol. Soc. Amer. 43(1), 17—34

Korneev V. A., 2011. Krauklis wave in a stack of alternating fluid-elastic layers. Geophysics 76(6), N47—N53. http://dx.doi.org/10.1190/geo2011-0086.1

Norris A. N., Grinfeld M. A., 1995. Nonlinear poroelasticity for a layered medium. J. Acoust. Soc. Am. 98(2), 1138—1146. http://dx.doi.org/10.1121/1.413612

Roganov Yu., Stovas A., 2011. Caustics in a periodically layered transversely isotropic medium with vertical symmetry axis. Geophys. Prospect. 59(3), 375—385. http://dx.doi.org/10.1111/j.1365-2478.2010.00924.x

Roganov Yu., Stovas A., 2012. Low-frequency wave propagation in periodically layered media. Geophys. Prospect. 60(5), 825—837. http://dx.doi.org/10.1111/j.1365-2478.2011.01028.x

Schoenberg M., 1983. Wave propagation in a finely laminated elastoacoustic medium. Appl. Phys. Lett. 42(2), 350—352. http://dx.doi.org/10.1063/1.93929

Schoenberg M., 1984. Wave propagation in alternating solid and fluid layers. Wave Motion 6, 303—320. doi: 10.1016/0165-2125(84) 90033-7

Thomson W. T., 1950. Transmission of classic waves through a stratified solid material. J. Appl. Phys. 21(1), 89—93

Published

2016-12-01

How to Cite

Roganov, Y., & Roganov, V. (2016). Wave propagation in periodic fluid-solid layered media. Geofizičeskij žurnal, 38(6), 101–117. https://doi.org/10.24028/gzh.0203-3100.v38i6.2016.91877

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Articles