1887
  1. Home
  2. A-Z Publications
  3. Geophysical Prospecting
  4. Volume 15, Issue 3
  5. Article
Volume 15 Number 3
  • E-ISSN: 1365-2478

Abstract

ABSTRACT

The theory of statistical communication provides an invaluable framework within which it is possible to formulate design criteria and actually obtain solutions for digital filters. These are then applicable in a wide range of geophysical problems. The basic model for the filtering process considered here consists of an input signal, a desired output signal, and an actual output signal. If one minimizes the energy or power existing in the difference between desired and actual filter outputs, it becomes possible to solve for the so‐called optimum, or least squares filter, commonly known as the “Wiener” filter. In this paper we derive from basic principles the theory leading to such filters. The analysis is carried out in the time domain in discrete form. We propose a model of a seismic trace in terms of a statistical communication system. This model trace is the sum of a signal time series plus a noise time series. If we assume that estimates of the signal shape and of the noise autocorrelation are available, we may calculate Wiener filters which will attenuate the noise and sharpen the signal. The net result of these operations can then in general be expected to increase seismic resolution. We show a few numerical examples to illustrate the model's applicability to situations one might find in practice.

Loading

Article metrics loading...

/content/journals/10.1111/j.1365-2478.1967.tb01793.x
2006-04-27
2024-04-23

  • From This Site

    /content/journals/10.1111/j.1365-2478.1967.tb01793.x
    dcterms_title,dcterms_subject,pub_keyword
    -contentType:Journal -contentType:Contributor -contentType:Concept -contentType:Institution
    10
    5
Loading full text...

Full text loading...

References

  1. Claerbout, J. F. and Robinson, E. A., 1964, The error in least squares inverse filtering: Geophysics, v. 29, p. 118–120.
    [Google Scholar]
  2. Foster, M. R., Sengbush, R. L., and Watson, R. J., 1964, Design of sub‐optimum filters for multi‐trace seismic data processing: Geophysical Prospecting, v. 12, p. 173–191.
    [Google Scholar]
  3. Lee, Y. W., 1960, Statistical theory of communication: New York , John Wiley & Sons, Inc.
    [Google Scholar]
  4. Levinson, N., 1947, The Wiener RMS (Root mean square) error criterion in filter design and prediction: Jl. of Mathematics and Physics, v. 25, p. 261–278.
    [Google Scholar]
  5. MIT Geophysical Analysis Group
    MIT Geophysical Analysis Group , 1952–1957, GAG Reports No. 1 through No. 11: Massachusetts Institute of Technology, Cambridge , Mass .
    [Google Scholar]
  6. Robinson, E. A., 1954, Predictive decomposition of time series with application to seismic exploration: PhD thesis, MIT, Cambridge, Mass.
  7. Schneider, W. A., Larner, K. L., Burg, J. P., and Backus, M. M., 1964, A new data‐processing technique for the elimination of ghost arrivals on reflection seismograms: Geophysics, v. 29, p. 783–805.
    [Google Scholar]
  8. Simpson, S. M.Jr., et al, 1960–1964, Advanced Research Projects Agency, Project VELA UNIFORM, Reports No. 1 through No. 8, Contract No. AF (604) 7378. Treitel, S., and Robinson, E. A., 1964, The stability of digital filters: IEEE Trans. Geoscience Electronics, v. 2, p. 6–18.
    [Google Scholar]
  9. Treitel, S., and Robinson, E. A., 1966a, The design of high resolution digital filters: IEEE Trans. Geoscience Electronics, v. 4, p. 25–38.
    [Google Scholar]
  10. Treitel, S., and Robinson, E. A., 1966b, Seismic wave propagation in layered media in terms of communication theory: Geophysics, v. 31, p. 17–32.
    [Google Scholar]
  11. Wiener, N., 1949, Extrapolation, interpolation, and smoothing of stationary time series: Cambidge, Mass., The Technology Press and New York , John Wiley & Sons, Inc.
    [Google Scholar]
  12. Wiggins, R. A., and Robinson, E. A., 1965, Recursive solution to the multichannel filtering problem: J. Geophys. Res., v. 70, p. 1885–1891.
    [Google Scholar]
  13. Wuenschel, P. C., 1960, Seismogiam synthesis including multiples and transmission coefficients: Geophysics, v. 25, p. 106–129.
    [Google Scholar]
http://instance.metastore.ingenta.com/content/journals/10.1111/j.1365-2478.1967.tb01793.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