Volume 37 Number 1
  • E-ISSN: 1365-2478



A new approximate method to calculate the space‐time acoustic wave motion generated by an impulsive point source in a horizontally layered configuration is presented. The configuration consists of a stack of fluid layers between two acoustic half‐spaces where the source and the receiver are located in the upper half‐space. A distorted‐wave Born approximation is introduced; the important feature of the method is the assumption of a background medium with vertical varying root‐mean‐square acoustic wave speed. A closed‐form expression for the scattered field in space and time as a function of the contrast parameters is deduced. The result agrees closely with rigorously calculated synthetic seismograms. In the inverse scheme the wave speed and mass density can be reconstructed within a single trace. Results of the inversion scheme applied to synthetic data are shown.


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  1. Aki, K. and Richards, P.G.1980. Body waves in media with depth‐dependent properties. Quantitiave Seismology I, chapter 9. W.H. Freeman & Co.
    [Google Scholar]
  2. Beylkin, G. and Oristaglio, M.L.1985. Distorted‐wave Born and distorted‐wave Rytov approximation. Optics Communications53, 213–216.
    [Google Scholar]
  3. Bleistein, N. and Gray, S.H.1985. An extension of the Born inversion method to a depth‐dependent reference profile. Geophysical Prospecting33, 999–1022.
    [Google Scholar]
  4. Clayton, R.W. and Stolt, R.H.1981. A Born‐WKBJ inversion method for acoustic reflection data. Geophysics46, 1559–1567.
    [Google Scholar]
  5. Cohen, J.K. and Bleistein, N.1977. An inverse method for determining small variations in propagation speed. Society for Industrial and Applied Mathematics. Journal of Applied Mathematics32, 784–799.
    [Google Scholar]
  6. Cohen, J.K. and Bleistein, N.1979. Velocity inversion procedure for acoustic waves. Geophysics44, 1077–1087.
    [Google Scholar]
  7. DE Hoop, A.T.1960. A modification of Cagniard's method for solving seismic pulse problems. Applied Scientific Research, Section B8, 349–356.
  8. Drijkoningen, G.G. and Fokkema, J.T.1987. The exact seismic response of an ocean and a N‐layer configuration. Geophysical Prospecting35, 33–61.
    [Google Scholar]
  9. Foster, D.J. and Carrion, Ph.M.1984. Born inversion with a variable background velocity. Geophysics49, 1794–1797.
    [Google Scholar]
  10. Helbig, K.1981. Ray geometric migration in seismic prospecting. The Solution of the Inverse Problem in Geophysical Prospecting, R.Cassinis (ed.), 147–177. Plenum Press.
    [Google Scholar]
  11. Raz, S.1981a. Direct reconstruction of velocity and density profiles for scattered field data. Geophysics46, 832–836.
    [Google Scholar]
  12. Raz, S.1981b. Three‐dimensional velocity profile inversion from finite offset data. Geophysics46, 837–842.
    [Google Scholar]
  13. Weglein, A.B., Violette, P.B. and Keho, T.H.1986. Using multiparameter Born theory to obtain certain exact multiparameter inversion goals. Geophysics51, 1069–1074.
    [Google Scholar]
  • Article Type: Research Article
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