Skip to main content
SpringerLink
Log in

Surface-Wave Amplitude Theory

  • Chapter
Seismic Waves and Sources

  • 647 Accesses

Abstract

In Section 3.6, we demonstrated the existence of Rayleigh waves in a homogeneous half-space and Love waves in a two-layered half-space. We also derived the general form of the dispersion relations for both Love and Rayleigh waves in a multilayered half-space. In this chapter we intend to obtain the amplitudes of surface waves in multilayered media excited by point dislocations.

I had a feeling once about Mathematics — that I saw it all. Depth beyond Depth was revealed to me — the Byss and the Abyss. I saw a quantity passing through infinity and changing its sign from plus to minus. I saw exactly how it happened and why the tergiversation was inevitable — but it was after dinner and I let it go.

(Winston Churchill)

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  • Aki K (1966) Generation and propagation of G waves from the Niigata earthquake of June 16, 1964. Bull Earthquake Res Inst (Tokyo) 44: 73–88.

    Google Scholar 

  • Arkhangel’skaya VM (1964) A study of short-period seismic surface waves, II. Izv Geophys 9: 1334–1359. (English translation, pp. 807-821.)

    Google Scholar 

  • Avetisyana RA, Yanovskaya TB (1973) Expansion of group velocities of Rayleigh waves in terms of spherical harmonics. Izv Phys Solid Earth 9: 706–710.

    Google Scholar 

  • Backus GE (1962) The propagation of short elastic surface waves on a slowly rotating earth. Bull Seismol Soc Amer 52: 823–846.

    Google Scholar 

  • Backus GE (1964) Geographical interpretation of measurements of average phase velocities of surface waves over great circular and great semicircular paths. Bull Seismol Soc Amer 54: 571–610.

    Google Scholar 

  • BÃ¥th M, López Arroyo A (1962) Attenuation and dispersion of G-waves. Jour Geophys Res 67: 1933–1942.

    Article  Google Scholar 

  • Ben-Menahem A (1961) Radiation of seismic surface waves from finite moving sources. Bull Seismol Soc Amer 51: 401–435.

    Google Scholar 

  • Ben-Menahem A (1971) The force system of the Chilean earthquake of 1960 May 22. Geophys Jour Roy Astron Soc (London) 25: 407–417.

    Google Scholar 

  • Ben-Menahem A (1978) Source mechanism of the 1906 San-Francisco earthquake. Phys Earth Planet Int 17: 163–181.

    Article  Google Scholar 

  • Ben-Menahem A, Aboodi, E (1971) Tectonic patterns in the northern Red-Sea region. Jour Geophys Res 76: 2674–2689.

    Article  Google Scholar 

  • Ben-Menahem A, Aboodi E, Schild R (1974) The source of the great Assam earthquake— an interplate wedge motion. Phys Earth Planet Int 9: 265–289.

    Article  Google Scholar 

  • Ben-Menahem A, Harkrider DG (1964) Radiation patterns of seismic surface waves from buried dipolar point sources in a flat stratified earth. Jour Geophys Res 69: 2605–2620.

    Article  Google Scholar 

  • Ben-Menahem A, Rosenman M, Harkrider DG (1970) Fast evaluation of source parameters from isolated surface wave signals. Bull Seismol Soc Amer 60: 1337–1387.

    Google Scholar 

  • Ben-Menahem A, Toksöz MN (1962) Source mechanism from spectra of long-period seismic surface waves. 1. The Mongolian earthquake of December 4, 1957. Jour Geophys Res 67: 1943–1955.

    Article  Google Scholar 

  • Ben-Menahem A, Toksöz, MN (1963a) Source mechanism from spectra of long-period seismic surface waves. 2. The Kamchatka earthquake of Nov. 4, 1952. Jour Geophys Res 68: 5207–5222.

    Google Scholar 

  • Ben-Menahem A, Toksöz MN (1963b) Source mechanism from spectra of long-period seismic surface waves. 3. The Alaska earthquake of July 10, 1958. Bull Seismol Soc Amer 53: 905–919.

    Google Scholar 

  • Brune JN (1961) Radiation pattern of Rayleigh waves from the southeast Alaska earthquake of July 10, 1958. Publ Dom Obs Ottawa 24: 373–383.

    Google Scholar 

  • Brune JN, Dorman J (1963) Seismic waves and earth structure in the Canadian Shield. Bull Seismol Soc Amer 53: 167–209.

    Google Scholar 

  • Gupta HK, Narain H (1967) Crustal structure in the Himalayan and Tibet plateau region from surface wave dispersion. Bull Seismol Soc Amer 57: 235–248.

    Google Scholar 

  • Gutenberg B (1924) Dispersion und Extinction von seismischen Oberflächen wellen und der Aufbau der obersten Erdschichten. Phys Zeit 25: 377–381.

    Google Scholar 

  • Gutenberg B (1932) Theorie der Erdbebenwellen. Handbuch der Geophysik, Vol 4, No 2, pp 1–298. Berlin, Verlag von Gebrüder Borntraeger.

    Google Scholar 

  • Gutenberg B (1955) Channel waves in the earth’s crust. Geophysics 20: 283–294.

    Article  Google Scholar 

  • Harkrider DG (1964) Surface waves in multilayered elastic media. I. Rayleigh and Love waves from buried sources in a multilayered elastic half-space. Bull Seismol Soc Amer 54: 627–679.

    Google Scholar 

  • Harkrider DG (1970) Surface waves in multilayered elastic media. Part II. Higher mode spectra and spectral ratios from point sources in plane layered earth models. Bull Seismol Soc Amer 60: 1937–1987.

    Google Scholar 

  • Keilis-Borok VI (1951) On the surface waves in a layer overlying a solid half-space (in Russian). Izv Akad Nauk, SSSR Ser Geograf I Geofiz 2: 17–39.

    Google Scholar 

  • Knopoff L, Fonda AA (1975) Upper-mantle structure under the Arabian Peninsula. Tectonophysics 26: 121–134.

    Article  Google Scholar 

  • Kovach RL (1965) Seismic surface waves: some observations and recent developments. In: Ahrens LH, Press F, Runcorn SK, Urey HC (eds) Physics and Chemistry of the Earth, Vol 6, pp 251–314, Pergamon, New York.

    Google Scholar 

  • Kovach RL (1978) Seismic surface waves and crustal and upper mantle structure. Rev Geophys Space Phys 16: 1–13.

    Article  Google Scholar 

  • Nakano H (1930) Love waves in cylindrical coordinates. Geophys Mag (Tokyo) 2: 37–51.

    Google Scholar 

  • Rial JA (1978) The Caracas, Venezuela, earthquake of July 1967: A multiple-source event. Jour Geophys Res 83: 5405–5414.

    Article  Google Scholar 

  • Saito M, Takeuchi H (1966) Surface waves across the Pacific. Bull Seismol Soc Amer 56: 1067–1091.

    Google Scholar 

  • Satô Y (1955) Analysis of dispersed surface waves by means of Fourier transform. Bull Earthquake Res Inst (Tokyo) 33: 33–48.

    Google Scholar 

  • Satô Y (1958) Attenuation, dispersion, and the wave guide of the G wave. Bull Seismol Soc Amer 48: 231–251.

    Google Scholar 

  • Scholte JGJ (1947). The range of existence of Rayleigh and Stoneley waves. Mon Not Roy Astron Soc (London) Geophys Suppl 5: 120–126.

    Google Scholar 

  • Sezawa K (1927a) On the propagation of Rayleigh waves on plane and spherical surfaces. Bull Earthquake Res Inst (Tokyo) 2: 21–28.

    Google Scholar 

  • Sezawa K (1927b) Dispersion of elastic waves propagated on the surface of stratified bodies and on curved surfaces. Bull Earthquake Res Inst (Tokyo) 3: 1–18.

    Google Scholar 

  • Sezawa K (1935) Love waves generated from a source of a certain depth. Bull Earthquake Res Inst (Tokyo) 13: 1–17.

    Google Scholar 

  • Sezawa K, Kanai K (1935) The M2 seismic waves. Bull Earthquake Res Inst (Tokyo) 13: 471–475.

    Google Scholar 

  • Sezewa K, Kanai K (1937) Relation between the thickness of a surface layer and the amplitude of dispersive Rayleigh waves. Bull Earthquake Res Inst (Tokyo) 15: 845–849.

    Google Scholar 

  • Singh BM, Singh SJ, Chopra SD, Gogna ML (1976) On Love waves in a laterally and vertically heterogeneous layered media. Geophys Jour Roy Astron Soc (London) 45: 357–370.

    Google Scholar 

  • Stoneley R (1924) Elastic waves at the surface of separation of two solids. Proc Roy Soc (London) A106: 416–42

    Article  Google Scholar 

  • Stoneley R (1934) The transmission of Rayleigh waves in a heterogeneous medium. Mon Not Roy Astron Soc (London) Geophys Suppl 3: 222–232.

    Google Scholar 

  • Takeuchi H, Dorman J, Saito M (1964) Partial derivatives of surface wave phase velocity with respect to physical parameter changes within the earth. Jour Geophys Res 69: 3429–3441.

    Article  Google Scholar 

  • Takeuchi H, Saito M (1972) Seismic surface waves. In: Bolt BA (ed) Methods of Computational Physics, Vol eleven, p 217–295. Academic Press, New York.

    Google Scholar 

  • Warren DH, Healy JH (1973) Structure of the crust in the conterminous United States. Tectonophysics 20: 203–213.

    Article  Google Scholar 

  • Yanovskaya TB (1958) On the determination of the dynamic parameters of the focus hypocenter of an earthquake from records of surface waves. Izv Geophys Ser 289–301. (English translation, pp 161 167.)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Weizmann Institute of Science, Rehovot, 76100, Israel

    Ari Ben-Menahem (Professor of Geophysics)

  2. Maharshi Dayanand University, Rohtak, 124001, India

    Sarva Jit Singh (Professor of Mathematics)

Authors
  1. Ari Ben-Menahem
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sarva Jit Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1981 Springer-Verlag New York Inc.

About this chapter

Cite this chapter

Ben-Menahem, A., Singh, S.J. (1981). Surface-Wave Amplitude Theory. In: Seismic Waves and Sources. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5856-8_5

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-5856-8_5

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-5858-2

  • Online ISBN: 978-1-4612-5856-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation