Polynomial Filter and its Application to Seismic Data

Claudia Steiner-Luckabauer

Research output: ThesisDoctoral Thesis


One of the main problems in land seismic datasets is that primary energy, which are reflections, are covered by ground roll. It is a non trivial task to separate primaries from ground roll, when the amplitudes of the reflections should stay unaffected. This is important, because for reservoir geophysics, the inversion of amplitudes play a key role when inferring petrophysical properties, like porosity, permeability, pore pressure and fluid saturation. Until now, simple bandpass filter or frequency - wavenumber filter (f-k) are applied to remove the ground roll from a seismic section. One of the main difficulties involved in applying those Fourier techniques to the processing of seismic data is the energy associated with the Gibbs error. This work introduces the concept of discrete polynomial basis functions to filter seismic data as global polynomial approximation and local polynomial approximation as an alternative to convential Fourier techniques. Gram polynomials were chosen, as their properties support polynomial preserving filtering, ringing free filtering and offer an ideal noise behaviour. The derivation of the Gram basis is shown and that the principle of superposition holds. For discrete local polynomial approximation, the concept of Savitzky-Golay smoothing was extended to the application to seismic data. Wavelength selective filters were implemented and tested on a 2D-3C seismic dataset. It is demonstrated, that the ground roll can be suppressed as a 1D trace by trace algorithm and as a 2D approach. For the 1D approach, the new concept of ringing free polynomial preserving filtering introduces a powerful tool for proper ground roll removal in the time domain. In the past, undersampled or highly unequally spaced seismic data was difficult to process. With this new approach, a ringing free and relative amplitude preserving filtering is possible, also for undersampled or unequally spaced data. The application of Savitzky-Golay smoothing in 2D introduces this new technique in detecting and removing waveforms in both time and spacial domain. The separation of reflective energy from ground roll was shown. The principle of discrete local polynomial smoothing was extended to high frequency noise removal and, that the method can be modified to other approaches than ground roll removal.
Translated title of the contributionPolynomfilter und ihre Anwendung auf reflexionsseismische Daten
Original languageEnglish
  • O'Leary, Paul, Assessor B (internal)
  • Millahn, Karl, Assessor A (internal)
Publication statusPublished - 2011

Bibliographical note

no embargo


  • seismic
  • ground roll
  • discrete polynomial filtering
  • Gibbs error
  • reservoir characterization
  • amplitude preserving

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