Stratigraphic filtering

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An elastic pulse propagating down through a sedimentary section, with the different strata having differing elastic impedances, experiences a partial reflection at every such interface. This upcoming reflected energy is, in turn, reflected back down from a shallower interface; this double reflection constitutes a peg-leg multiple. The same process occurs with an upcoming primary. A cartoon representation of this process, in terms of rays, is shown in the left figure below.

The peg-leg:
* reduces the amplitude of the primary;
* typically has the same polarity as the primary, with its amplitude reduced by the product of two reflection coefficients (see Friendly multiples).
* is delayed in time, thus extending the length of the pulse, and leading to "apparent attenuation"; this is stratigraphic filtering [1] [2] [3]

An example of this process, in data from a downgoing wave as measured in a VSP is given in the center figure below. The corresponding spectra are shown in the right figure below.

References

  1. Banik, N.C., Lerche, I., & Shuey, R.T. 1985. Stratigraphic Filtering, Part I: Derivation of the O'Doherty-Anstey Formula. Geophysics, 50, 2768.
  2. Banik, N. C. , I. Lerche, J. R. Resnick, and R. T. Shuey, 1985. Stratigraphic filtering, Part II: Model spectra. GEOPHYSICS. VOL. 50(12) P. 2775-2783.
  3. Shapiro, S. and P.Hubral, 1999. Elastic Waves in Random Media: Fundamentals of Seismic Stratigraphic Filtering. Springer Verlag, Berlin. 191 pp.