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UBC Theses and Dissertations

Wavelet estimation and debubbling using minimum entropy deconvolution and time domain linear inverse methods Levy, Shlomo


A new and different approach to the solution of the normal equations of minimum entropy deconvolution (MED) is developed. This approach which uses singular value decomposition in the iterative solution of the MED equations increases the signal-to-noise ratio of the deconvolved output and enhances the resolution of MEC. The problem of deconvolution, and in particular wavelet estimation, is formulated as a linear inverse problem. Both generalized linear inverse methods and Backus-Gilbert inversion are considered. The proposed wavelet estimation algorithm uses the MED output as a first approximation to the earth response. The approximated response and the observed seismograms serve as an input to the inversion schemes and the outputs are the estimated wavelets. The remarkable performance of the linear inverse schemes for cases of highly noisy data is demonstrated. A debubbling example is used to show the completeness of the linear inverse schemes. First the wavelet estimation part was carried out and then the debubbling problem was formulated as a generalized linear inverse problem which was solved using the estimated wavelet. This work demonstrates the power of the linear inverse schemes when dealing with highly noisy data.

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