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UBC Theses and Dissertations

Developments in minimum entropy deconvolution Nickerson, William Alexander


Minimum entropy deconvolution (MED) is investigated in light of recent work, and reports of poor performance in the deconvolution of real reflection seismograms. The problems with MED fall into two catagories. The first contains problems related to operator design such as avoiding local extrema in the simplicity criterion, problems with bandwidth, and the selection of filter length and preprocessing parameters. The second is the determination of model validity for the data at hand. MED is based on the iterative maximization of a data simplicity criterion which exhibits multiple extrema. A geometrical interpretation of this algorithm leads to an intuitive alternative algorithm, the projection method, and to the conclusion that iteration starting filter governs which extremum is reached and hence output wavelet delay. Choice of starting filter is therefore tantamount to a wavelet phase assumption and there is no basis for choosing the standard, centred impulse, starting filter if the global extremum is desired. An optimum lag MED algorithm is proposed to achieve the global maximum. Bandlimiting, data tapering and other aspects of MED operator design are discussed. No criterion exists for assessing MED model validity. Studies with various synthetic reflectivity statistics reveal that "sparseness" and "simplicity" are poor descriptors of the minimum entropy assumption. Preliminary attempts to quantify MED applicability are made but fail and indicate that any successful measure must include both underlying reflectivity and wavelet characteristics. Examples using synthetic data show the advantages of the bandlimited optimum lag MED algorithm over a conventional starting filter method.

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