Volume 28 Number 2
  • E-ISSN: 1365-2478



A Kunetz equation is often used as the starting point in the development of solutions for the inversion of one‐dimensional, noise free, normal incident seismograms, for which ||= 1. In this paper we demonstrate a need for a Kunetz‐type equation in which filtered signals can be used, so that noise effects can be reduced. We then show that an infinite number of Kunetz‐type equations exist for the lossless wave equation in layered media. Finally, we show that it is indeed valid to formulate and solve the inverse problem using filtered signals.


Article metrics loading...

Loading full text...

Full text loading...


  1. AshrafiF‐H.1978, Estimation of parameters in lossless layered media systems, Ph.D. dissertation, Univ. of Southern California, Dept. of Electrical Engineering.
  2. ClaerboutJ.1976, Fundamentals of geophysical data processing, McGraw‐Hill, New York .
    [Google Scholar]
  3. KunetzG. and D'ErcevilleI.1962, Sur certaines propriétés d'une onde acoustique plane de compression dans un milieu stratifié, Annales de Geophysique18, 351–359.
    [Google Scholar]
  4. MendelJ.M.1979, Suboptimal estimation of reflection coefficients, for lossless layered systems, from noisy data, presented at 49th SEG Meeting, New Orleans, La.
  5. MendelJ.M., NahiN.E. and ChanM.1979, Synthetic seismograms using the state space approach, Geophysics44, 880–895.
    [Google Scholar]
  6. MiuraR.M.1976, The Kortewig‐de Vries equation: a survey of results, SIAM Review18, 412–459.
    [Google Scholar]
  7. NahiN.E., MendelJ.M. and SilvermanL.M.1978, Recursive derivation of reflection coefficients from noisy seismic data, presented at 1978 IEEE International Conference on Acoustics, Speech and Signal Processing, Tulsa, Oklahoma.
  8. RobinsonE.A.1967, Multichannel time series analysis with digital computer programs, Holden Day, San Francisco .
    [Google Scholar]
  9. RobinsonE.A. and TreitelS.1977, The spectral function of a layered system and the determination of the waveforms at depth, Geophysical Prospecting25, 434–460.
    [Google Scholar]
  • Article Type: Research Article
This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error