1887
Volume 19 Number 3
  • E-ISSN: 1365-2478

Abstract

A

A review of the most significant mathematical properties of digital operators and an introduction to their important applications to seismic digital filtering is given.

Basic definitions in the time‐series field and the principles of digital filtering are introduced starting from the ‐transform domain.

Predictive decomposition for stationary stochastic processes and inverse operators are also discussed.

Applications of digital filtering to seismic signal concern the predictive deconvolution, characteristics of dispersive and recursive operators, matched filters, and multichannel operators.

A brief discussion on frequency, wave number, and velocity filtering phylosophy is given at the end of the paper.

Loading

Article metrics loading...

/content/journals/10.1111/j.1365-2478.1971.tb00601.x
2006-04-27
2024-04-19
Loading full text...

Full text loading...

References

  1. Backus, M. M., 1959, Water reverberations—their nature and eliminations. Geophysics24, 233–261.
    [Google Scholar]
  2. Bendat, J. S., 1958, Principles and applications of random noise theory. John Wiley & Sons. Inc., New York .
    [Google Scholar]
  3. Blackman, R. B., Tukey, J. W., 1958, The measurement of power spectra. Dover Publications, New York .
    [Google Scholar]
  4. Claerbout, J. F., Robinson, E. A., 1964, The error in least squares inverse filtering. Geophysics29, 118–120.
    [Google Scholar]
  5. Darby, E. K., Norman, N. S., 1966, Application of dynamic programming to the problem of wave propagation in a layered medium. Geophysics31, 1037–1048.
    [Google Scholar]
  6. Doob, J. L., 1953, Stochastic Processes. John Wiley & Sons. Inc., New York .
    [Google Scholar]
  7. Embree, P., Burg, J. P., Backus, M. M., 1963, Wide Band Velocity Filtering—The Pie‐Slice Process. Geophysics28, 948–975.
    [Google Scholar]
  8. Fail, F., Grau, G., 1963, Les filtres en eventail. Geophysical Prospecting11, 131–163.
    [Google Scholar]
  9. Fail, F., 1965, Le Filtrage en Sismique. Publications de l'Institut Français du Pétrole, No. 1.
  10. Ford, T. W., Hearne, J. H., 1966, Least squares inverse filtering. Geophysics31, 917–926.
    [Google Scholar]
  11. Levinson, N., 1947, The Wiener R.M.S. error criterion in filter design and prediction. J. Math. Phys.25, 261–278.
    [Google Scholar]
  12. Lindsey, G. P., 1960, Elimination of seismic ghost reflections by means of a linear filter. Geophysics25, 130–140.
    [Google Scholar]
  13. Papoulis, A., 1965, Probability, Random Variables and Stochastic Processes. McGraw‐Hill Book Co., New York .
    [Google Scholar]
  14. Rice, R. B., 1962, Inverse convolution filters. Geophysics27, 4–18.
    [Google Scholar]
  15. Richer, N., 1940, The form and nature of seismic waves and the structure of seismograms. Geophysics5, 348–366.
    [Google Scholar]
  16. Ricker, N., 1953a, Wavelet contraction, wavelet expansion and the control of seismic resolution. Geophysics18, 769–792.
    [Google Scholar]
  17. Ricker, N., 1953b, The form and laws of propagation of seismic wavelets. Geophysics18, 10–40.
    [Google Scholar]
  18. Robinson, E. A., 1957, Predictive decomposition of seismic traces. Geophysics22, 767.
    [Google Scholar]
  19. Robinson, E. A., 1964a, Wavelet composition of time‐series. H. Wold, North Holland Pub. Comp., Amsterdam , 37–106.
    [Google Scholar]
  20. Robinson, E. A., Treitel, S., 1964b, Principles of digital filtering. Geophysics29, 395–404.
    [Google Scholar]
  21. Robinson, E. A., Treitel, S., 1964c, The stability of Digital filters. I.E.E.E. Transactions of Geoscience Electronics G.E.‐2, No. 1.
  22. Robinson, E. A., Treitel, S., 1965, Dispersive digital filters. Geophysics30, 433–461.
    [Google Scholar]
  23. Robinson, E. A., 1966a, Recursive Solution of the multichannel normal equation. Annual summary report No. 1 (report No. 46) Seismological Institute, Uppsala University.
  24. Robinson, E. A., 1966b, Wave propagation in Layered Media. Annual summary report No. 1 (report No. 46) Seismological Institute, Uppsala University.
  25. Robinson, E. A., 1966c, Multichannel Z‐transform and minimum‐delay. Geophysics31, 482–500.
    [Google Scholar]
  26. Robinson, E. A., 1967a, Multichannel Time‐series Analysis with Digital Computer Programs. Holden‐Day, San Francisco .
    [Google Scholar]
  27. Robinson, E. A., 1967b, Predictive decomposition of time‐series with applications to Seismic exploration. Geophysics32, 418–484.
    [Google Scholar]
  28. Robinson, E. A., 1967c, Statistical communication and detection, with special reference to digital data processing of radar and seismic signals. Griffin, London .
    [Google Scholar]
  29. Schneider, W. A., 1964, A new data processing technique for elimination of ghost arrivals on reflection seismograms. Geophysics29, 783–805.
    [Google Scholar]
  30. Shanks, J. L., 1967, Recursion filters for digital processing. Geophysics32, 33–51.
    [Google Scholar]
  31. Swartz, C. A., Sokoloff, V. M., 1954, Filtering associated with selective sampling of geophysical data. Geophysics14, 402–419.
    [Google Scholar]
  32. Treitel, S., Robinson, E. A., 1966a, The design of high resolution digital filters. I.E.E.E. Transactions on Geoscience Electronics G.E.‐4, No. 1.
  33. Treitel, S., Robinson, E. A., 1966b, Seismic wave propagation in layered media in terms of communication theory. Geophysics31, 17–32.
    [Google Scholar]
  34. Treitel, S., Shanks, J., Fraisier, C. W., 1967, Some aspects of fan‐filtering. Geophysics32, 789–800.
    [Google Scholar]
  35. Wadsworth, G. P., Robinson, E. A., 1953, Detection of reflections on seismic records by linear operators. Geophysics16, 539–586.
    [Google Scholar]
  36. Wiener, N., 1949, The extrapolation, interpolation and smoothing of stationary time series with engineering applications. John Wiley & Sons Inc., New York .
    [Google Scholar]
  37. Wiggins, R. A., Robinson, E. A., 1965, Recursive solution to the multichannel filtering problem. J. Geoph. Res.70, 1885–1891.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/j.1365-2478.1971.tb00601.x
Loading
  • Article Type: Research Article

Most Cited This Month Most Cited RSS feed

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