Skip to main content
Log in

Perfect zerophase sections, fact or fiction?

  • Published:
Surveys in Geophysics Aims and scope Submit manuscript

Abstract

The desired result of an optimum seismic data processing sequence, is a broad band zerophase section, i.e. a bandpassed version of the actual reflectivity function. However, a lot of socalled zerophase-sections still carry a significant phase-error, which is due to unrealistic assumptions in the processing stream in terms of the design of standard processes as for example deconvolution. The two major issues here are the color of the reflectivity series and the misuse of prewhitening. If not properly handled they lead to a phase- and amplitude spectrum bias in the final section, preventing it from being zerophase. Whereas the reflectivity bias leads to a phase error of 50 to 90 deg, the prewhitening bias results in a phase error, which is directly proportional to the logarithm of the actual prewhitening factor.

Therefore, if the spike deconvolution process is applied in a time-variant manner, as a consequence a time-variant and usually frequency dependent phase error is introduced! In this article we have made an effort to include sufficient detail to facilitate a clear understanding of the problems involved.

The standard processing flow should have a minimum-delay transform and spike deconvolution prestack, followed by a zerophase transform poststack, where the residual wavelet is assumed to be minimum phase.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Brötz, R., Marschall, R., and Knecht, M.: 1987, ‘Signal Adjustment of Vibroseis and Impulsive Source Data’,Geophys. Prosp. 35, 7, 739–766.

    Google Scholar 

  • Budny, M.: 1987, Personal communication.

  • Bunch, A.W.H. and White, R.E.: 1985, ‘Cross-Equalisation of Seismic Traces’,Geoexploration, V. 23, pp. 239–256, Elsevier Science Publ. B.V., Amsterdam.

    Google Scholar 

  • Dash, B.P. and Obaidullah, K.A.: 1970, ‘Determination of Signal and Noise Statistics Using Correlation Theory’,Geophysics 35, 24–32.

    Google Scholar 

  • Ellender, S.A.: 1986, ‘Considerations in Estimating the Minimum-Phase Properties of Sampled Data’,Geophys. Prosp. 34, 1200–1212.

    Google Scholar 

  • Fourman, J.M.: 1982,Minimum-Phase Decon of Band-Limited Data, 52nd SEG-convention, Dallas. Expanded Abstracts, paper S. 9.4.

  • Kets, F.B.: 1987,Deconvolution of Sampled Signals, paper presented at 49th EAEG meeting, Belgrade, Yugoslavia. Preprint, Shell Internationale Petroleum Maatschappij B.V., Exploration and Production Division, The Hague.

    Google Scholar 

  • Marschall, R.: 1978,Derivation of Two-Sided Recursive (TSR) Filters with Seismic Applications, paper presented at 48th SEG convention, San Francisco. Preprint Prakla-Seismos AG.

  • Marschall, R.: 1985,Ein- und zweidimensionale Rekursiv-Filter und ihre Anwendung in der Seismik, Habilitationsschrift, Ruhr-Universität Bochum.

  • Marschall, R.: 1986,Remarks on Vibroseis Phase Compensation, 39th Annual Midwest Regional Meeting of the SEG, March 23–26, Tulsa. Preprint, Prakla-Seismos AG, Hannover.

    Google Scholar 

  • Marschall, R.: 1988,How to Establish the Perfectly Repeatable Source; Bergbau im Wandel, Leobener Bergmannstag 1987. Akademische Druck-u. Verlagsanstalt, Graz. Verlag Glückauf GmbH, Essen.

    Google Scholar 

  • Marschall, R. and Knecht, M.: 1986, Reflectivity Corrected Deconvolution, and its Influence on Inversion; paper presented at: Research Workshop on Deconvolution and Inversion, Rome, Italy. Preprint, Prakla-Seismos AG.

  • Oldenburg, D.W., Levy, S., and Stinson, K.J.: 1986, ‘Inversion of Band-Limited Reflection Seismograms: Theory and Practice’, Proc. IEEE, special issue on seismic inversion,74, No. 3.

  • Papoulis, A.: 1962,The Fourier Integral and its Applications, McGraw-Hill Book Company, Inc., New York.

    Google Scholar 

  • Papoulis, A.: 1977,Signal Analysis, McGraw-Hill Book Company, Inc., New York.

    Google Scholar 

  • Pieuchot, M.: 1984,Seismic Instrumentation, Geophys. Press, London-Amsterdam.

    Google Scholar 

  • Rabiner, L. R. and Gold, B.: 1975,Theory and Application of Digital Signal Processing, Prentice Hall, Inc., Englewood Cliffs, New Jersey.

    Google Scholar 

  • Rietsch, E.: 1982, ‘Deconvolution in the Presence of Noise and a Higher than Nyquist signal Rate’,Geoexploration 20, pp. 61–73. Elsevier Scientific Publ. Co., Amsterdam.

    Google Scholar 

  • Robinson, E. A.: 1983,Seismic Velocity Analysis and the Convolutional Model, IHRDC, Boston, U.S.A.

    Google Scholar 

  • Robinson, E.A. and Treitel, S.: 1985,Geophysical Signal Analysis, Prentice-Hall, Inc., Englewood Cliffs, NJ 07632.

    Google Scholar 

  • Waters, K.H.: 1978,Reflection Seismology, John Wiley & Sons, New York.

    Google Scholar 

  • Wunsch, G.: 1962,Moderne Systemtheorie, Akademische Verlagsgesellschaft Geest & Portig KG, Leipzig.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Marschall, R. Perfect zerophase sections, fact or fiction?. Surv Geophys 10, 225–304 (1989). https://doi.org/10.1007/BF01901492

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01901492

Keywords

Navigation