Skip to main content

Seismology and Seismo-Acoustics

  • Chapter
  • First Online:
Parabolic Wave Equations with Applications

Abstract

This chapter covers parabolic equation techniques for elastic waves, which include compressional, shear, boundary, and interface waves in solid materials. Compressional waves correspond to longitudinal motion (parallel to the direction of propagation) and perturbations in volume. Shear waves correspond to transverse motion (orthogonal to the direction of propagation) and perturbations in shape. Boundary and interface waves propagate along boundaries and interfaces and decay exponentially in the transverse direction. Applications of the elastic parabolic equation include seismology and ocean acoustics problems in which the ocean bottom or ice cover supports shear waves.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 89.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 119.99
Price excludes VAT (USA)
  • Durable hardcover 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

References

  1. H. Kolsky, Stress Waves in Solids (Dover, New York, 1963).

    MATH  Google Scholar 

  2. R.R. Greene, “A high-angle one-way wave equation for seismic wave propagation along rough and sloping interfaces,” J. Acoust. Soc. Am. 77, 1991–1998 (1985).

    Article  ADS  Google Scholar 

  3. M.D. Collins, “A higher-order parabolic equation for wave propagation in an ocean overlying an elastic bottom,” J. Acoust. Soc. Am. 86, 1459–1464 (1989).

    Article  ADS  Google Scholar 

  4. M.D. Collins, “Higher-order Padé approximations for accurate and stable elastic parabolic equations with application to interface wave propagation,” J. Acoust. Soc. Am. 89, 1050–1057 (1991).

    Article  ADS  Google Scholar 

  5. B.T.R. Wetton and G.H. Brooke, “One-way wave equations for seismoacoustic propagation in elastic waveguides,” J. Acoust. Soc. Am. 87, 624–632 (1990).

    Article  ADS  MathSciNet  Google Scholar 

  6. W. Jerzak, W.L. Siegmann, and M.D. Collins, “Modeling Rayleigh and Stoneley waves and other interface and boundary effects with the parabolic equation,” J. Acoust. Soc. Am. 117, 3497–3503 (2005).

    Article  ADS  Google Scholar 

  7. M.D. Collins and W.L. Siegmann, “Treatment of a sloping fluid-solid interface and sediment layering with the seismo-acoustic parabolic equation,” J. Acoust. Soc. Am. 137, 492–497 (2015).

    Article  ADS  Google Scholar 

  8. COMSOL Multiphysics® v. 5.2 (COMSOL AB, Stockholm, Sweden).

    Google Scholar 

  9. K. Woolfe, M.D. Collins, D.C. Calvo, and W.L. Siegmann, “Seismo-acoustic benchmark problems involving sloping solid-solid interfaces and variable topography,” J. Comp. Acoust. 24, 1650019 (2016).

    Article  MathSciNet  Google Scholar 

  10. D.A. Outing, W.L. Siegmann, M.D. Collins, and E.K. Westwood, “Generalization of the rotated parabolic equation to variable slopes,” J. Acoust. Soc. Am. 120, 3534–3538 (2006).

    Article  ADS  Google Scholar 

  11. M.D. Collins, “A single-scattering correction for the seismo-acoustic parabolic equation,” J. Acoust. Soc. Am. 131, 2638–2642 (2012).

    Article  ADS  Google Scholar 

  12. K. Woolfe, M.D. Collins, D.C. Calvo, and W.L. Siegmann, “Seismo-acoustic benchmark problems involving sloping fluid-solid interfaces,” J. Comp. Acoust. 24, 1650022 (2016).

    Article  MathSciNet  Google Scholar 

  13. R.T. Bachman, “Acoustic anisotropy in marine sediments and sedimentary rocks,” J. Geophys. Res. 84, 7661–7663 (1979).

    Article  ADS  Google Scholar 

  14. R.T. Bachman, “Elastic anisotropy in marine sedimentary rocks,” J. Geophys. Res. 88, 539–545 (1983).

    Article  ADS  Google Scholar 

  15. D.W. Oakley and P.J. Vidmar, “Acoustic reflection from transversely isotropic consolidated sediments,” J. Acoust. Soc. Am. 73, 513–519 (1983).

    Article  ADS  Google Scholar 

  16. A.J. Fredricks, W.L. Siegmann, and M.D. Collins, “A parabolic equation for anisotropic elastic media,” Wave Motion 31, 139–146 (2000).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Science+Business Media, LLC, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Collins, M.D., Siegmann, W.L. (2019). Seismology and Seismo-Acoustics. In: Parabolic Wave Equations with Applications. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-9934-7_3

Download citation

  • DOI: https://doi.org/10.1007/978-1-4939-9934-7_3

  • Published:

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4939-9932-3

  • Online ISBN: 978-1-4939-9934-7

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics