Advertisement

An Inverse Method for Obtaining the Attenuation Profile and Small Variations in the Sound Speed and Density Profiles of the Ocean Bottom

  • Subramaniam D. Rajan
  • George V. Frisk

Abstract

An inverse method is presented for the determination of the compressional wave speed, compressional wave attenuation, and density as a function of depth for a horizontally stratified ocean bottom. It is based on a perturbation technique for which the required input information is the plane-wave reflection coefficient of the bottom as a function of incident angle at a fixed frequency. The reflection coefficient is related to variations of the acoustic properties about known reference values through a nonlinear integral equation which is then linearized using the Born approximation. An acceptable stable solution of the integral equation is obtained using a priori constraints on the solution. Resolution of the solution obtained is studied using the resolving power theory of Backus and Gilbert1. Examples of inversions using synthetic data are presented using noise-free and noisy data. Results obtained with noise-free data show good agreement between true and reconstructed profiles. Inversions performed with noisy data yield stable, acceptable results.

Keywords

Sound Speed Background Model Born Approximation Fredholm Integral Equation Acoustic Parameter 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    G. Backus and F. Gilbert, The resolving power of gross earth data, Geophys. J. R. Astr. Soc., 16: 169, (1968).ADSzbMATHGoogle Scholar
  2. 2.
    R. D. Stoll, Marine sediment acoustics, J. Acoust. Soc. Am., 77: 1789, (1985).ADSCrossRefGoogle Scholar
  3. 3.
    Keiiti Aki and P. G. Richards, “Quantitative Seismology: Theory and Methods, Vol. I”, Freeman, San Francisco, (1980).Google Scholar
  4. 4.
    G. V. Frisk, A. V. Oppenheim, and D. R. Martinez, A technique for measuring the plane-wave reflection coefficient of the ocean bottom, J. Acoust. Soc. Am., 68: 602, (1980).MathSciNetADSCrossRefGoogle Scholar
  5. 5.
    A. Merab, “Reconstruction of ocean bottom velocity profiles from monochromatic scattering data,” Sc.D. Thesis, M.I.T./W.H.O.I. Joint Program, Cambridge, MA and Woods Hole, MA (August 1986).Google Scholar
  6. 6.
    Subramaniam D. Rajan, “An inverse method for obtaining the attenuation profile and small variations in the sound speed and density profiles of the ocean bottom,” Ph.D Thesis, M.I.T./W.H.O. I. Joint Program, Cambridge, MA and Woods Hole, MA (May 1985).Google Scholar
  7. 7.
    D. C. Stickler, Inverse scattering in a stratified medium, J. Acoust.Soc. Am., 74: 994, (1983).MathSciNetADSzbMATHCrossRefGoogle Scholar
  8. 8.
    D. L. Phillips, A technique for numerical solution of Fredholm integral equations of the first kind, J. Assoc. Compt. Mach., 9: 84, (1962).zbMATHGoogle Scholar
  9. 9.
    S. Twomey, On the numerical solution of the Fredholm integral equation of the first kind by the inversion of the linear system produced by quadrature, J. Assoc. Compt. Mach., 10: 97, (1963).zbMATHGoogle Scholar

Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • Subramaniam D. Rajan
    • 1
  • George V. Frisk
    • 1
  1. 1.Woods Hole Oceanographic InstitutionWoods HoleUSA

Personalised recommendations