Applications of Wavelet Transforms to the Suppression of Coherent Noise from Seismic Data in the Pre-Stack Domain

Deighan, Andrew J (1997) Applications of Wavelet Transforms to the Suppression of Coherent Noise from Seismic Data in the Pre-Stack Domain. PhD thesis, University of Glasgow.

Abstract

The wavelet transform, a relatively new mathematical technique, allows the analysis of non-stationary signals by using basis functions which are compact in time and frequency. The variables in the wavelet domain, scale (a frequency range), and translation (a temporal increment) can be associated with time-frequency, and so in the wavelet transform we have the potential to filter seismic signals in a pseudo time-frequency sense. The one dimensional discrete multiresolution form of the wavelet transform can be effectively used to suppress low frequency coherent noise on seismic shot records. This process, achieved by the muting or weighting of coefficients in the wavelet transform domain, is demonstrated by suppressing low velocity, low frequency ground roll from land- based seismic data, the benefits of which are visible at both the shot and stack stages of the seismic processing stream. The extension of this technique to the suppression of higher frequency coherent noise is limited by the octave band splitting of frequency space by the transform. The wavelet packet transform, an extension of the wavelet transform, allows a more adaptable tiling of the time frequency domain which in turn allows the suppression of noise containing high frequencies whilst minimising signal distortion. This technique is demonstrated to be effective in suppressing airblast from land based common receiver gathers, whilst minimising the distortion of reflected signals. These filtering techniques can be extended to two dimensions, filtering data in the two dimensional wavelet and wavelet packet domains. This technique involves muting the transform coefficients in the wavelet/wavelet packet transform space which has four variables: temporal translation, offset translation, frequency scale and wavenumber scale. As for the one-dimensional case the two dimensional wavelet transform suffers from poor resolution due to the octave splitting of f-k space, but when used in combination with a velocity based shift such as normal moveout, can be used to filter data with minimal distortion to the residual signal. Extending the process to using the two-dimensional wavelet packet transform eliminates the shift requirement and leads to more effective filtering in the four variable transform space. The wavelet packet filtering technique is effective in suppressing low velocity noise from land based seismic records showing visible improvement in both the common shot records and resultant stack. The non-stationary properties of the wavelet transform allows the filtering across geophone arrays (that is, the common shot record) by the application of the transform in the offset domain. Filtering of the wavelet coefficients, in combination with a linear or hyperbolic shift applied before and removed after filtering, allows discrimination against linear noise on common shot records associated with first breaks and hyperbolic events on common midpoint records such as multiples. The use of a simple muting technique in the wavelet domain effectively suppresses these forms of coherent noise. Where the velocity contrast between signal and noise is high, noise suppression is possible whilst preserving reflector amplitudes. Where the velocity contrast is smaller, weighting of the wavelet coefficients (based on transforms of the input signal after translation) allows noise suppression whilst preserving the amplitude versus offset relationships of the primary signal. This is shown to be effective on synthetic, marine and land based data, with improvements observed on common shot records and resultant stacks. The results of all these wavelet transform based filtering techniques are sensitive to the choice of wavelet transform kernel wavelet. The suitability of a kernel wavelet for filtering can be related to the frequency spectra of the kernel wavelet. A fast rate of frequency amplitude fall-off at the edge of a given scale of basis wavelet minimises frequency overlap between neighbouring kernel wavelet scales and so minimises contamination by noise associated with aliasing in the filtered signal, a process that is inherent in the transform process. A flat amplitude response across the frequency range of a given scale also leads to improved filtering results.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Additional Information: Adviser: R Watts
• Keywords: Geophysical engineering
• Date of Award: 1997
• Depositing User: Enlighten Team
• Unique ID: glathesis:1997-74737
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 27 Sep 2019 16:44
• Last Modified: 27 Sep 2019 16:44
• URI: https://theses.gla.ac.uk/id/eprint/74737