Advertisement

Seismology and Seismo-Acoustics

  • Michael D. Collins
  • William L. Siegmann
Chapter

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.

References

  1. 1.
    H. Kolsky, Stress Waves in Solids (Dover, New York, 1963).zbMATHGoogle Scholar
  2. 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).ADSCrossRefGoogle Scholar
  3. 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).ADSCrossRefGoogle Scholar
  4. 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).ADSCrossRefGoogle Scholar
  5. 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).ADSMathSciNetCrossRefGoogle Scholar
  6. 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).ADSCrossRefGoogle Scholar
  7. 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).ADSCrossRefGoogle Scholar
  8. 8.
    COMSOL Multiphysics® v. 5.2 (COMSOL AB, Stockholm, Sweden).Google Scholar
  9. 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).MathSciNetCrossRefGoogle Scholar
  10. 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).ADSCrossRefGoogle Scholar
  11. 11.
    M.D. Collins, “A single-scattering correction for the seismo-acoustic parabolic equation,” J. Acoust. Soc. Am. 131, 2638–2642 (2012).ADSCrossRefGoogle Scholar
  12. 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).MathSciNetCrossRefGoogle Scholar
  13. 13.
    R.T. Bachman, “Acoustic anisotropy in marine sediments and sedimentary rocks,” J. Geophys. Res. 84, 7661–7663 (1979).ADSCrossRefGoogle Scholar
  14. 14.
    R.T. Bachman, “Elastic anisotropy in marine sedimentary rocks,” J. Geophys. Res. 88, 539–545 (1983).ADSCrossRefGoogle Scholar
  15. 15.
    D.W. Oakley and P.J. Vidmar, “Acoustic reflection from transversely isotropic consolidated sediments,” J. Acoust. Soc. Am. 73, 513–519 (1983).ADSCrossRefGoogle Scholar
  16. 16.
    A.J. Fredricks, W.L. Siegmann, and M.D. Collins, “A parabolic equation for anisotropic elastic media,” Wave Motion 31, 139–146 (2000).CrossRefGoogle Scholar

Copyright information

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

Authors and Affiliations

  • Michael D. Collins
    • 1
  • William L. Siegmann
    • 2
  1. 1.Naval Research LaboratoryWashington, DCUSA
  2. 2.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroyUSA

Personalised recommendations