Monte Carlo velocity picks

Next I ran the Monte Carlo automatic velocity fitting algorithm on all 300 velocity semblance scans. The total CPU time requires an average of 10 CPU seconds per velocity scan on an IBM RS/6000 Model 530 with the following search parameters. For the initial parametric interval velocity estimate, I searched over the surface velocity range v_o = 1.4-1.6 km/s in 0.5 km/s increments, the velocity gradient parameter range $\alpha$ = 0.1-0.5 km/s/s in 0.1 km/s/s increments, and the time exponent range $\beta$ = 0.1-1.0 in 0.1 unit increments.

For the subsequent Monte Carlo search, I used the following parameters: 20 interval velocity layers per second, a maximum adjacent vertical velocity increment of 0.2 km/s, a random walk velocity search corridor bound of 0.8 and 1.2 times the best current interval velocity model, a surface velocity of 1.525 km/s constant from 0.0-0.2 seconds, a global minimum and maximum interval velocity of 1.525 and 3.0 km/s, a standard deviation of 10% of the best current v_i value for the random velocity perturbations drawn from a uniform distribution, a convergence error tolerance of 0.1% of the peak maximum semblance integral value, a ``stale'' convergence criterion of 10 unchanged consecutive random walks, and a maximum of 100 random walks each consisting of 100 random steps, resulting in a maximum of 10,000 random trial interval velocity models. These parameters were discussed in the previous section explaining the Monte Carlo method.

Figures - show velocity scans and their Monte Carlo picks, as selected at every 30 CMPs (1.0 km) along the line from the entire survey velocity cube. One can see that the quality and shape of the semblance peak trajectories varies along the line, and that the Monte Carlo picks are very good in most circumstances. Note that to the east, the dipping events are caused by the uprise of the flanks of a salt dome (which peaks just east of 17 km at about 2 seconds depth). Some interval velocity picks show a deep high velocity zone which may be due to the presence of salt and/or steep dip (remember these are NMO stacking, not migration, velocities).

 

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Figure 6 Velocity semblance scans at (a) 7.0 km, and (b) 8.0 km, overlain with Monte Carlo automatic rms and interval velocity picks.

 

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Figure 7 Velocity semblance scans at (a) 9.0 km, and (b) 10.0 km, overlain with Monte Carlo automatic rms and interval velocity picks.

 

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Figure 8 Velocity semblance scans at (a) 11.0 km, and (b) 12.0 km, overlain with Monte Carlo automatic rms and interval velocity picks.

 

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Figure 9 Velocity semblance scans at (a) 13.0 km, and (b) 14.0 km, overlain with Monte Carlo automatic rms and interval velocity picks.

 

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Figure 10 Velocity semblance scans at (a) 15.0 km, and (b) 16.0 km, overlain with Monte Carlo automatic rms and interval velocity picks.

Figure shows the unsmoothed contour plot of all 300 Monte Carlo rms velocity picks in the upper panel, and the smoothed rms velocities (a triangle of 330 m half-width) in the lower panel. It is evident that the automatic picks exhibit a large degree of lateral consistency, even though they are not constrained to do so. This gives some reassurance that the Monte Carlo algorithm is somewhat robust, at least for these 300 CMP gathers. The smoothed velocities in Figure b are used for the subsequent Kirchhoff prestack time migration. Note that the velocity varies laterally, and sags in velocity toward the east where the shallow low velocity sediments have been downthrown by the slump faults activated by the salt dome.

Figure shows the unsmoothed raster plot of all 300 Monte Carlo interval velocity picks, and the smoothed v_i contours below. In general, the interval velocities are much more noisy than the rms velocities, as is to be expected. However, there is a definite low frequency trend that parallels the rms trends and the downthrown low velocities. This seems rather promising that there really is some low frequency information in the interval velocities. For example, Figure b could be used directly as a first estimate of depth migration velocity, after a vertical time-to-depth conversion. In fact, it would be interesting to use the smoothed interval velocity model to convert the time migration to depth.

Figure is a useful byproduct of the Monte Carlo velocity fitting procedure. It is a plot of the relative misfit error of the velocity picks. Since the maximum possible integrated semblance value S_max can be calculated from each velocity scan, the relative misfit error E measure is also available:

 

$$E = 1 - S_{mc} / S_{max} \;,$$ (5)

where S_mc is the optimal integrated semblance value that the Monte Carlo algorithm converged to for a given velocity scan. Figure shows that the fits are fairly consistent at about 20% relative misfit error, which is rather good. Figure could also be extremely useful as a Quality Control tool, since bad velocity picks will cause the error to spike in the plot. For example, one can quickly decide that the velocity picks around midpoints at 11 km are not as favorable as the contiguous CMP velocity picks. For an interpreter, a quick look at this plot can tell you (a) how good the overall picks are quantitatively, and (b) which areas might need to be edited and repicked manually to produce the final velocity field estimate.

 

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Figure 11 (a) Upper panel: unsmoothed Monte Carlo rms velocity picks, (b) Lower panel: laterally smoothed Monte Carlo rms velocities using a triangle of 330 m half-width.

 

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Figure 12 (a) Upper panel: unsmoothed Monte Carlo interval velocity picks, (b) Lower panel: laterally smoothed Monte Carlo interval velocities using a triangle of 330 m half-width.

 

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Figure 13 A plot of the Monte Carlo velocity fit error as a function of surface midpoint coordinate. A perfect fit would maximize semblance and represent 0.00 fit error on the plot. A very poor fit would achieve a low semblance integral value and represent a value near 1.00 in the fit error.