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Studia Geophysica et Geodaetica

, Volume 46, Issue 2, pp 267–282 | Cite as

Asymptotic Ray Theory for Seismic Surface Waves in Laterally Inhomogeneous Media

  • T. B. Yanovskaya
Article

Abstract

A recurrence procedure is outlined for constructing asymptotic series for surface wave field in a half-space with weak lateral heterogeneity. Both horizontal variations of the elastic parameters and of the wave field are assumed small on the distances comparable with the wavelength. This is equivalent to the condition that the frequency ω is large. The Surface Wave Asymptotic Ray Theory (SWART) is an analog of the asymptotic ray theory (ART) for body waves. However the case of surface waves presents additional difficulty: the rate of amplitude variation is different in vertical and horizontal directions. In vertical direction it is proportional to the large parameter ω. To overcome this difficulty the transformation ‘equalizing’ vertical and horizontal coordinated is suggested, Z = ωz. In the coordinates x,y,Z the wave field is represented as an asymptotic series in inverse powers of ω. The amplitudes of successive terms of the series are determined from a recurrent system of equations. Attention is paid to similarity and difference of the procedures for constructing the ray series in SWART and ART. Applications of SWART to interpretation of seismological observations are discussed.

surface waves asymptotic ray theory SWART lateral heterogeneity 

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References

  1. Alekseev A.S., Babich V.M. and Gelchinsky B.Ya., 1961. Ray method for computation of intensities of the wave fronts. In: Problems of Dynamic Theory of Seismic Wave Propagation, 5. Leningad State University Press, Leningrad. 3-21 (in Russian).Google Scholar
  2. Babich V.M., 1956. Ray method for calculation of intensities of the wave fronts. Dokl. AN SSSR, 110, No.3, 355-357 (in Russian).Google Scholar
  3. Babich V.M. and Buldyrev V.S., 1972. Asymptotic Methods in the Problems of Short-Wave Diffraction. Nauka, Moscow (in Russian).Google Scholar
  4. Babich V.M., Chikhachev B.A. and Yanovskaya T.B., 1976. Surface waves in a vertically inhomogeneous elastic half space with weak horizontal inhomogeneity. Izv. Acad. Sci. USSR, Physics Solid Earth, 4, 25-32 (in Russian).Google Scholar
  5. Bukchin B.G., 1995. Determination of stress glut moments of total degree 2 from teleseismic surface waves amplitude spectra. Tectonophysics, 218, 185-191.Google Scholar
  6. Červený V., 2001. Seismic Ray Theory. Cambridge Univ. Press, Cambridge.Google Scholar
  7. Červený V., Molotkov I.A. and Pýen ík I., 1977. Ray Method in Seismology. Charles University, Prague.Google Scholar
  8. Dahlen F.A. and Tromp J., 1998. Theoretical Global Seismology. Princeton Univ. Press, New Jersey, USA.Google Scholar
  9. Karal F.C. and Keller J.B., 1959. Elastic wave propagation in homogeneous and inhomogeneous media. J. Acoustic Soc. Amer., 28, 694-705.Google Scholar
  10. Lasserre C., Bukchin B., Bernard P., Tapponnier P., Gaudemer Y., Mostinsky A. and Rong Dailu, 2001. Source parameters and tectonic origin of the June 1st, 1996 Tianzhu (Mw=5.2) and July 18st, 1995 Yongden (Mw=5.6) earthquakes, near Haiyuan fault (Gansu, China). Geophys. J. Int., 144, 206-220Google Scholar
  11. Levshin A.L., Yanovskaya T.B., Lander A.V., Bukchin B.G., Barmin M.P., Its E.N. and Ratnikova L.I., 1989 (ed. V.I. Keilis-Borok) Seismic Surface Waves in Laterally Inhomogeneous Earth. Kluwer Publ., Dordrecht.Google Scholar
  12. Litvina E.P. and Yanovskaya T.B., 2001. Polarization Anomalies of Love Waves in a Horizontally Heterogeneous Medium. Izv. Phys. Solid Earth, 37, 215-222.Google Scholar
  13. Molotkov I.A., 1970. Generation of surface waves by diffraction on an impedance boundary. Notes of Scientific Seminars LOMI AN SSSR, 17, 151-167 (in Russian).Google Scholar
  14. Munirova L.M. and Yanovskaya T.B., 2001. Spectral Ratio of the Horizontal and Vertical Rayleigh Wave Components and Its Application to Some Problems of Seismology. Izv. Phys. Solid Earth, 37, 709-716.Google Scholar
  15. Neunhoffer H. and Malischewki P., 1981. Anomalous polarization of Love waves indicating anisotropy along paths in Eurasia. Gerlands Beitrag. Geophys., 90, 179-186.Google Scholar
  16. Panza G.F., Romanelli F. and Vaccari F., 2001. Seismic wave propagatiion in laterally heterogeneous anelastic media: theory and applications to seismic zonation. Advances in Geophysics, 43, 1-95.Google Scholar
  17. Ritzwoller M. and Levshin A.L., 1998. Eurasian surface wave tomography: group velocities. J. Geophys. Res., 103, 4839-4878.Google Scholar
  18. Woodhouse J.H., 1974. Surface waves in a laterally varying layered structure. Geophys. J. Roy. astr. Soc., 37, 461-490.Google Scholar
  19. Yanovskaya T.B. and Roslov Yu.V., 1989. Peculiarities of surface wave fields in laterally inhomogeneous media in the framework of ray theory. Geophys. J. Int., 99, 297-303.Google Scholar
  20. Yanovskaya T.B., 1996. Ray tomography based on azimuthal anomalies. Pure Appl. Geophys., 148, 319-336.Google Scholar
  21. Yanovskaya T.B., Antonova L.M. and Kozhevnikov V.M., 2000. Lateral variations of the upper mantle structure in Eurasia from group velocities of surface waves. Phys. Earth Planet. Inter., 93, 19-32.Google Scholar
  22. Yomogida K., 1985. Gaussian beams for surface waves in laterally slowly-varying media. Geophys. J. Roy. astr. Soc. 82, 511-533.Google Scholar
  23. Yomogida K., 1988. Surface waves in weakly heterogeneous media. Mathematical Geophysics. Reidel Publ.Co., 53-75.Google Scholar
  24. Yu Y. and Park J., 1993. Upper mantle anisotropy and couple-mode long-period surface waves. Geophys. J. Int. 114, 473-489.Google Scholar

Copyright information

© StudiaGeo s.r.o. 2002

Authors and Affiliations

  • T. B. Yanovskaya
    • 1
  1. 1.Institute of PhysicsSt. Petersburg UniversitySt. PetersburgRussian Federation

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