One-dimensional velocity inversion for acoustic waves: Numerical results

  • Samuel Gray
  • Norman Bleistein
Inverse Scattering Theory and Related Topics
Part of the Lecture Notes in Physics book series (LNP, volume 130)


We consider the inverse problem of determining small variations in propagation speed from remote observations of signals which pass through an inhomogeneous medium. Under the conditions (1) that the variations can be written as a small perturbation from a known reference value and (2) that the medium of interest varies in one direction only, an integral equation has been developed for the variations which can be solved in closed form. Here, a technique is presented to obtain and process synthetic data from a scattering profile of arbitrary shape. The results of numerical testing show that, as long as a velocity variation is indeed “small”, both its size and its shape can be reproduced with negligible error by this method.


Wave Field Propagation Speed Wave Equa Seismic Exploration Inverse Scattering Problem 
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Footnotes and References

  1. [1]
    J.K. Cohen, N. Bleistein: “An Inverse Method for Determining Small Variations in Propagation Speed”, SIAM J. Appl. Math. 32, 784–799 (1977)Google Scholar
  2. [2]
    N. Bleistein, J.K. Cohen: “Inverse methods for reflector mapping and sound speed profiling”, in Ocean Acoustics, ed. by J.A. De Santo, Topics in Current Physics, Vol. 8 (Springer, New York, 1979)Google Scholar
  3. [3]
    W.S. Dorn, D.D. McCracken: Numerical Methods with Fortran IV Case Studies (Wiley, New York, 1972)Google Scholar
  4. [4]
    L. Yost: Marathon Oil Company, Denver, Colorado, private communication.Google Scholar
  5. [5]
    B. Gjevik, A. Nilsen, J. Höyen: “An attempt at the inversion of reflection data”, Geophysical Prospecting 24, 592–505 (1976)Google Scholar
  6. [6]
    S. Gray, N. Bleistein, J.K. Cohen, “Direct inversion for strongly depth dependent velocity profiles”, Report MS-R-7902, University of Denver (1978)Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Samuel Gray
    • 1
    • 2
  • Norman Bleistein
    • 3
  1. 1.Naval Research LaboratoryWashington20375
  2. 2.Department of Mathematics and Engineering MechanicsGeneral Motors InstituteFlintUSA
  3. 3.Department of MathematicsUniversity of DenverDenverUSA

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