Results

Figure a shows the picked reflection-events overlaid with the data shown in Figure a. For clarity, the same estimated events are plotted without the data in Figure b. The detection of these events (which cross the trend of multiples and linear noise) was feasible because of the filters that were applied in the $\tau-p$ and beam-stack domains.

A sonic log from a well drilled 1 Km away from the location of the CMP gather was used to generate an interval velocity profile. This well-velocity profile was smoothed with a high-cut Walsh-spectrum filtering, to emphasize its "blockiness" and allow a better comparison with the result of the inversion. The basic lithology includes calcilutite in the top 1.5 kilometers, followed by shale in the next half kilometer, then shale-sand from 2 to 3.5 Km, shale again to a depth of 4.65 Km, and finally a calcarenite-calcilutite sequence. The low velocity interval around 1.5 Km corresponds to a highly porous sand-calcilutite transitional formation with occurrences of shale and salt lenses.

Figure  compares the well-velocity profile with the velocity profile estimated from a Dix's least-squares fitting of the picked events (a), the result from the picking-based algorithm (b), and the result from hybrid method (c). The results from the three inversions are reasonably similar for the shallow layers, but the Dix-based as well as the picked-based inversions completely fail at the deeper layers, while the hybrid scheme maintains the same resolution at all depths. Surprisingly, the deep, high-velocity, carbonate sequence was almost perfectly resolved by the hybrid method. Although [for the real data case] the errors are large in comparison to the synthetic case, they are smaller than we should expect given the low signal-to-noise ratio of the real data.

 

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Figure 12 (a) Final estimation of the reflected wavefronts overlaid with the data shown in Figure a. (b) The same wavefronts of a.

 

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Figure 13 The continuous lines are the sonic-derived velocity from a well located 1 Km away from the CMP position. The dotted lines are the results of (a) the least-squares Dix-hyperbola fitting of the picked events, (b) the picking-based algorithm, and (c) the hybrid algorithm.