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.
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References
Brötz, R., Marschall, R., and Knecht, M.: 1987, ‘Signal Adjustment of Vibroseis and Impulsive Source Data’,Geophys. Prosp. 35, 7, 739–766.
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.
Dash, B.P. and Obaidullah, K.A.: 1970, ‘Determination of Signal and Noise Statistics Using Correlation Theory’,Geophysics 35, 24–32.
Ellender, S.A.: 1986, ‘Considerations in Estimating the Minimum-Phase Properties of Sampled Data’,Geophys. Prosp. 34, 1200–1212.
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.
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.
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.
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.
Papoulis, A.: 1977,Signal Analysis, McGraw-Hill Book Company, Inc., New York.
Pieuchot, M.: 1984,Seismic Instrumentation, Geophys. Press, London-Amsterdam.
Rabiner, L. R. and Gold, B.: 1975,Theory and Application of Digital Signal Processing, Prentice Hall, Inc., Englewood Cliffs, New Jersey.
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.
Robinson, E. A.: 1983,Seismic Velocity Analysis and the Convolutional Model, IHRDC, Boston, U.S.A.
Robinson, E.A. and Treitel, S.: 1985,Geophysical Signal Analysis, Prentice-Hall, Inc., Englewood Cliffs, NJ 07632.
Waters, K.H.: 1978,Reflection Seismology, John Wiley & Sons, New York.
Wunsch, G.: 1962,Moderne Systemtheorie, Akademische Verlagsgesellschaft Geest & Portig KG, Leipzig.
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Marschall, R. Perfect zerophase sections, fact or fiction?. Surv Geophys 10, 225–304 (1989). https://doi.org/10.1007/BF01901492
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DOI: https://doi.org/10.1007/BF01901492