Processing sequence

Figure  shows the processing sequence applied to the data to alleviate the influence of noise and event-crossing in the velocity inversion. Although muting could be used to eliminate event-crossing, this would result in the discharge of useful information from a particularly important part of the reflections. Multiples and other coherent noise were attenuated by filtering techniques while the problem of interference between reflections was solved by a differential treatment of the shallow reflections.

 

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Figure 8 The processing sequence applied to the marine data shown in Figure a.

It is clear from Figure a that despite the application of predictive deconvolution and a dereverberation algorithm (described in Cunha and Muir, 1989), complex multiples and peg-legs are still dominant features in the data. More effective in the elimination of the multiples and linear noises was the application of a filter in the $\tau-p$ domain. The direct and inverse $\tau-p$ transform were performed by an algorithm developed by Kostov (1989); Figure a shows the shape of the cutoff curve. The high-slowness part of the shallow reflections is located inside the rejecting region to avoid the reflections interfering in the subsequent processing of the reflections below them. Figure b shows the filtered data transformed back to the x-t domain.

 

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Figure 9 (a) CMP gather from Brazil offshore after deconvolution and dereverberation. (b) The same data after filtering in the $\tau-p$ domain.

 

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Figure 10 (a) The shape of cutoff curve used in the $\tau-p$ domain filter. The bandpass region lies at the left side of the curve. (b) A surface slice of the filtered beam-stack cube along the 8th event. The overlaid curve corresponds to the mapping of the velocity-cutoff curve of Figureb into this domain. The transition between the pass (to the left of the curve) and cut (to the right of the curve) regions is actually smooth.

A comparison between the velocity spectra of the data before and after the $\tau-p$ filtering (Figure ) shows a good improvement in the resolution of primary events after the filtering. The times of the picks associated with primaries were used as the starting points for the event-detection algorithm. The dashed line in Figure b defines the cutoff velocity function for the velocity filter that was applied to the beam-stacked data. The application of this filter is essential to avoid the interference of multiples, not only in the event-picking algorithm, but also in the final inversion step.

A total of sixteen events were selected for the inversion. Their a priori nearest-offset times were selected from the velocity spectrum, but the event-picking algorithm had a pre-specified degree of freedom to reestimate them. The four initial events (which cross the reflections below) were selected with the help of a normal-moveout overlay program (Claerbout, 1987).

The last step before the velocity estimation algorithm selects the slices along the event-mapped surfaces in the beam-stack cube (Figure b). The slices corresponding to the shallow events are taken from a non-[$\tau-p$]filtered version of the beam-stack cube. To optimize the estimation, the beam-stack of the shallow events (1 to 9) was computed apart from the deep events (9 to 16), so that a lower slowness interval could be used for the latter.

 

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Figure 11 Velocity spectrum of (a) the deconvolved data, and (b) the same data after the $\tau-p$ filtering. The dashed line represents the cutoff curve used in the velocity-filter applied to the beam-stack.