Seismic Plane Waves in a Layered Half-Space

  • Ari Ben-Menahem
  • Sarva Jit Singh


When seismic waves impinge on the earth’s surface or on an internal surface of discontinuity, the laws of reflection and refraction of a plane wave at a plane surface of discontinuity can be applied only approximately because both the wavefront and the surface are, in fact, curved. However, in many applications this approximation is quite satisfactory.


Surface Wave Phase Velocity Rayleigh Wave Amplitude Ratio Love Wave 
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  1. Alsop LE (1970) The leaky-mode period equation—a plane-wave approach. Bull Seismol Soc Amer 60: 1989–1998.Google Scholar
  2. Alsop LE, Goodman AS, Gregersen S (1974) Reflection and transmission of inhomo-geneous waves with particular application to Rayleigh waves. Bull Seismol Soc Amer 64: 1635–1652.Google Scholar
  3. Båth M (1954) The density ratio at the boundary of the earth’s core. Tellus 6: 408–414.CrossRefGoogle Scholar
  4. Biot, MA (1957) General theorems on the equivalence of group velocity and energy transport. Phys Rev 105: 1129–1137.CrossRefGoogle Scholar
  5. Costain JK, Cook KL, Algermissen ST (1963) Amplitude, energy and phase angles of plane SV waves and their application to earth crustal studies. Bull Seismol Soc Amer 53: 1039–1074; Corrigendum 55: 567-575, 1965.Google Scholar
  6. Friedlander FG (1948) On the total reflection of plane waves. Quart Jour Mech Appl Math 1: 376–384.CrossRefGoogle Scholar
  7. Gilbert F, Backus GE (1966) Propagator matrices in elastic wave and vibration problems. Geophysics 31: 326–332.CrossRefGoogle Scholar
  8. Harkrider DG (1968) The perturbation of Love wave spectra. Bull Seismol Soc Amer 58: 861–880.Google Scholar
  9. Haskell NA (1953) The dispersion of surface waves on multilayered media. Bull Seismol Soc Amer 43: 17–34.Google Scholar
  10. Haskell NA (1962) Crustal reflection of plane P-and SV-waves. Jour Geophys Res 67: 4751–4767.CrossRefGoogle Scholar
  11. Havelock TH (1972) The Propagation of Disturbances in Dispersive Media. New York, N.Y., Hafner Publishing Co. p. 87.Google Scholar
  12. Jeffreys H (1961) Small corrections in the theory of surface waves. Geophys Jour Roy Astron Soc (London) 6: 115–117.Google Scholar
  13. Knopoff L, Fredricks RW, Gangi AF, Porter LD (1957) Surface amplitudes of reflected body waves. Geophysics 22: 842–847.CrossRefGoogle Scholar
  14. Knott CG (1899) Reflection and refraction of elastic waves with seismological applications. Phil Mag 48: 64–97.Google Scholar
  15. Love AEH (1911) Some Problems of Geodynamics. Cambridge, Engl., Cambridge, at the University Press.Google Scholar
  16. McCamy K, Meyer RP, Smith TJ (1962) Generally applicable solutions of Zoeppritz’ amplitude equations. Bull Seismol Soc Amer 52: 923–955.Google Scholar
  17. Meissner E (1926) Elastische Oberflächen-Querwellen. Proc Second Internatl Congr Appl Mech, Zurich, 3–11.Google Scholar
  18. Pilant WL (1972) Complex roots of the Stoneley-wave equation. Bull Seismol Soc Amer 62: 285–299.Google Scholar
  19. Rayleigh (Lord), (JW Strutt) (1885) On waves propagated along the plane surface of an elastic solid. Proc Lond Math Soc (Ser 1) 17: 4–11.CrossRefGoogle Scholar
  20. Singh SJ, Ben-Menahem A, Shimshoni M (1970) Comments on papers by Costain et al. [1963] and McCamy et al. [1962] on the solution of Zoeppritz’ amplitude equations. Bull Seismol Soc Amer 60: 277–280.Google Scholar
  21. Thomson WT (1950) Transmission of elastic waves through a stratified medium. Jour Appl Phys 21: 89–93.CrossRefGoogle Scholar
  22. Thrower EN (1965) The computation of the dispersion of elastic waves in layered media. Jour Sound Vib 2: 210–226.CrossRefGoogle Scholar
  23. Woodhouse JH (1976) On Rayleigh’s principle. Geophys Jour Roy Astron Soc (London) 46: 11–22.Google Scholar
  24. Zoeppritz K (1919) Über Reflection und Durchgang seismischer Wellen durch Unstetig-keitsflächen. Erdbebenwellen VIIb, Göttingen, Nachrichten 1: 66–84.Google Scholar

Copyright information

© Springer-Verlag New York Inc. 1981

Authors and Affiliations

  • Ari Ben-Menahem
    • 1
  • Sarva Jit Singh
    • 2
  1. 1.Weizmann Institute of ScienceRehovotIsrael
  2. 2.Maharshi Dayanand UniversityRohtakIndia

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