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Studia Geophysica et Geodaetica

, Volume 48, Issue 1, pp 251–264 | Cite as

Quasi-Rayleigh Waves in Transversely Isotropic Half-Space with Inclined Axis of Symmetry

  • T.B. Yanovskaya
  • L.S. Savina
Article
  • 64 Downloads

Abstract

A method for determination of characteristics of quasi-Rayleigh (qR) wave in a transversely isotropic homogeneous half-space with inclined axis of symmetry is outlined. The solution is obtained as a superposition of qP, qSV and qSH waves, and surface wave velocity is determined from the boundary conditions at the free surface and at infinity, as in case of Rayleigh wave in an isotropic half-space. Though the theory is simple enough, a numerical procedure for calculation of surface wave velocity presents some difficulties. The difficulty is caused by necessity to calculate complex roots of a non-linear equation, which in turn contains functions determined as roots of non-linear equations with complex coefficients. Numerical analysis shows that roots of the equation corresponding to the boundary conditions do not exist in the whole domain of azimuths and inclinations of the symmetry axis. The domain of existence of qR wave depends on the ratio of the elastic parameters: for some strongly anisotropic models the wave cannot exist at all. For some angles of inclination qR-wave velocities deviate from those calculated on the basis of the perturbation method valid for weak anisotropy, though they have the same tendency of variation with azimuth. The phase of qR wave varies with depth unlike Rayleigh wave in an isotropic half-space. Unlike Rayleigh wave in an isotropic half-space, qR wave has three components - vertical, radial and transverse. Particle motion in horizontal plane is elliptic. Direction of the major axis of the ellipsis coincides with the direction of propagation only in azimuths 0° (180°) and 90° (270°).

transverse isotropy Rayleigh waves velocity polarization 

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References

  1. Anderson D.L., 1961. Elastic wave propagation in layered anisotropic media. J. Geophys. Res., 66, 2953–2963.Google Scholar
  2. Crampin S., 1970. The dispersion of surface waves in multilayered anisotropic media. Geophys. J. Roy. astr. Soc., 21, 387–402.Google Scholar
  3. Crampin S., 1975. Distinctive particle motion of surface waves as a diagnostic of anisotropic layering. Geophys. J. Roy. astr. Soc., 40, 177–186.Google Scholar
  4. Crampin S. and Taylor D.B., 1971, The propagation of surface waves in anisotropic media, Geophys. J. Roy. astr. Soc., 25, 71–87.Google Scholar
  5. Farnell G.W., 1970. Properties of elastic surface waves. In: W.P. Mason (Ed.), Physical Acoustics VI, Academic Press, New York, 109–166.Google Scholar
  6. Forsyth D.W., 1975. The early structural evolution and anisotropy of oceanic upper mantle. Geophys. J. Roy. astr. Soc., 43, 103–162.Google Scholar
  7. Laske G. and Masters G., 1998. Surface wave polarization data and global anisotropic structure. Geophys. J. Int., 132, 508–520.Google Scholar
  8. Lothe J. and Barnett D.M., 1976. On the existence of Rayleigh (surface) wave solutions for anisotropic half-spaces with free surface. J. Appl. Phys., 47, 428–433.Google Scholar
  9. Maupin V., 1989. Surface waves in weakly anisotropic structures: on the use of ordinary or quasi-degenerate perturbation methods. Geophys. J. Int., 98, 553–563.Google Scholar
  10. Maupin V., 2001. A multiple-scattering scheme for modelling surface wave propagation in isotropic and anisotropic three-dimensional structures. Geophys. J. Int., 146, 332–348.Google Scholar
  11. McEvilly T.V., 1964. Central U.S. crust-upper mantle structure from Love and Rayleigh wave phase velocity inversion. Bull. Seism. Soc. Am., 54, 1997–2015.Google Scholar
  12. Montagner J-P. and Nataf H.C., 1986. On inversion of the azimuthal anisotropy of surface waves. J. Geophys. Res., 91, 511–520.Google Scholar
  13. Montagner J-P. and Tanimoto T., 1990. Global anisotropy in the upper mantle inferred from the regionalization of phase velocities. J. Geophys. Res., 95, 4797–4819.Google Scholar
  14. Nishimura C.L., and Forsyth D.W., 1989. The anisotropic structure of the upper mantle in the Pacific. Geophys. J. Int., 96, 203–229.Google Scholar
  15. Park J., 1996. Surface waves in layered anisotropic structures. Geophys. J. Int., 126, 173–184.Google Scholar
  16. Petterson O. and Maupin V., 2002. Lithospheric anisotropy on the Kergelen hotspot track inferred from Rayleigh wave polarization anomalies. Geophys. J. Int., 149, 225–246.Google Scholar
  17. Smith M.L. and Dahlen F.A., 1973. The azimuthal dependence of Love and Rayleigh wave propagation in a slightly anisotropic medium. J. Geophys. Res., 78, 3321–3333.Google Scholar
  18. Smith M.L. and Dahlen F.A., 1975. Correction to “The azimuthal dependence of Love and Rayleigh wave propagation in a slightly anisotropic medium”. J. Geophys. Res., 80, 1923.Google Scholar
  19. Suetsugu D. and Nakanishi I., 1987. Regional and azimuthal dependence of phase velocities of mantle Rayleigh waves in the Pacific ocean. Phys. Earth Planet. Int., 47, 230–245.Google Scholar
  20. Tanimoto T. and Anderson D.L., 1985. Lateral heterogeneity and azimuthal anisotropy of the upper mantle: Love and Rayleigh waves 100–250 s. J. Geophys. Res., 90, 1842–1858.Google Scholar
  21. Thomson C.J., 1997. Modelling surface waves in anisotropic structures. 1. Theory. Phys. Earth Planet. Int., 103, 195–206.Google Scholar
  22. Yu Y. and Park J., 1994. Hunting for azimuthal anisotropy beneath the Pacific Ocean region. J. Geophys. Res., 99, 15399–15422.Google Scholar

Copyright information

© StudiaGeo s.r.o. 2004

Authors and Affiliations

  • T.B. Yanovskaya
    • 1
  • L.S. Savina
    • 1
  1. 1.Institute of PhysicsSt. Petersburg State UniversitySt. PetersburgRussia

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