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- W82010248 abstract "Nonstationary filter theory and its application in single-trace deconvolution are reviewed. The wavelet estimation methods used in nonstationary deconvolution (NSD) are examined. As an alternative, the homomorphic method gives a good estimation of the propagating wavelet when the noise level is low and a proper low pass filter in the quefrency domain is applied. A reformulation of nonstationary deconvolution using homomorphic wavelet estimation gives promising results. Most conventional single-trace deconvolution techniques are based on the assumption of a stationary wavelet. The wavelet is assumed stationary so that it can be removed by from the seismic trace by applying a single stationary inverse filter. Such an assumption leads to unacceptable errors when serious wavelet distortion occurs due to anelastic attenuation or nonstationary effects. We use 'propagating wavelet' to describe a model of nonstationary seismic wavelet. Low seismic quality factor (Q) and strong stratigraphic filtering effects cause serious nonstationary wavelet distortion. This can only be handled well by a proper nonstationary inverse filter. With the assumption of local minimum phase, nonstationary deconvolution (NSD) (Schoepp, 1998) handled this problem well. The propagating wavelet is estimated from the time-variant-spectrum (TVS) of a seismic trace. The inverse filter is applied in the frequency domain in the manner of nonstationary convolution. The success of nonstationary deconvolution is dependent on how well the propagating wavelet is estimated. Following the traditional way of estimating a minimum-phase wavelet from a smoothed version of seismic trace amplitude spectrum, NSD smoothes the TVS by convolving the amplitude spectra with a 2-D boxcar smoother and then calculates the corresponding minimum-phase spectrum. The inverse filter is then calculated and applied through nonstationary filtering. As in traditional techniques, the idea behind the smoothing is to remove both the primary and multiple reflections from the amplitude spectrum, leaving only the wavelet signature. A closer examination of NSD shows that simple spectrum smoothing may not be the best method. Another approach, homomorphic method, which is capable of separating a rapidly varying component (reflectivity) from a slowly varying component (wavelet), can be a good option for wavelet estimation." @default.
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- W82010248 title "Application of homomorphic theory in nonstationary deconvolution" @default.
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