GNGTS 2013 - Atti del 32° Convegno Nazionale

The singular value decomposition (SVD) is then applied to each of these matrices and from the 1 st eigenvalue the reflected waveform can be separated from interfering events and random noise. Finally, an average across the columns is computed to obtain the estimated wavelet. The short-offset window is then shifted by a predetermined time amount, which ranges between 50% and 80% of the window’s time length, and the whole estimation procedure is repeated. Thus, we end up with an estimation of the offset variant wavelets for each 4 th order traveltime curve derived from the velocity analysis spectrum. These time and offset variant wavelets will constitute our desired output in the successive deconvolution steps that will be carried out in an iterative fashion after the application of each partial NMO correction. It is worth noting that in order to avoid edge effects on the representative wavelets, all the adjacent estimation windows are both time and offset overlapped, typically this overlap is between 20% and 50% of the considered dimension. The short-offset window time length is approximately equal to the wavelet duration, while the offset width depends on whether the waveform variations along the offset are strong or mild. The second phase of our method is the NMO partial correction. The purpose of this operation is to limit the waveform distortions, which would be greater if the corrections were performed in a single step. We regulate the amount of NMO correction by means of the NMO percentage parameter that is defined as follow: (1) where t 1 is the traveltime at the maximum offset for the uncorrected trajectory, t 1new is the traveltime at the same offset for the partially corrected trajectory and t 0 is the final correction time. Once α has been set, it is possible to move the original traveltime curve t old to the partially NMO corrected trajectory t new using the following equations: (2) (3) where c 2old and c 3old are the coefficients of the fourth order equation, X is the maximum offset and x is the offset. The result of the partial correction is a CMP where the reflections have been only partly moved to their final horizontal alignment so that they have been subjected to only a minimal stretch. The limited distortions introduced by the partial correction can be removed by shaping the stretched wavelets to their original (unstretched) status by the application of Wiener shaping filters. In fact, knowing the relations between the old and the new traveltime curves (equation 3) and using the estimated wavelets, it is possible to build the partially corrected unstretched CMP gather which constitutes the desired output. To enhance the coherent reflections and to attenuate the influence of the noise we may weigh the samples of the desired output CMP with the semblance values computed from the velocity analysis. To create the unstretched CMP gather, that is our desired output, the estimated wavelets are inserted into an empty CMP panel centered along the corresponding partially corrected 4 th order curves. We employ the same time and offset overlaps we used in the wavelet estimation. Then we apply a trace by trace shaping deconvolution to the partially corrected and stretched CMP gather having as the desired output the partially corrected unstretched CMP. The procedure of partial NMO correction and shaping deconvolution is then reiterated until a complete NMO correction is achieved. 18 GNGTS 2013 S essione 3.1