Near-surface layer with laterally varying velocities
We now examine the accuracy of Dix conversion and coherency inversion for the model with horizontal layers (Table 9-2) but with a near-surface layer H1 with laterally varying velocities between 800 m/s and 1500 m/s. The interval velocity profiles are shown in Figure 9.1-18a and the velocity-depth model is shown in Figure 9.1-18b.
|Layer||Velocity (m/s)||Depth (m)|
|H3||2400 – 2700||1500|
|H4||3000 – 3500||1800|
As for the model with a constant-velocity near-surface layer (Table 9-2), a total of 384 shot records was modeled using the two-way acoustic wave equation with identical line geometry. Figure 9.1-19a shows the CMP-stacked section with the picked time horizons that correspond to the layer boundaries H1 through H6 in Figure 9.1-18b. The stacking velocity section is shown in Figure 9.1-19b with the color bar on the right-hand margin.
The stacking velocity section was derived from the horizon-consistent stacking velocity profiles shown in Figure 9.1-20. As a direct consequence of the lateral velocity variations in the near-surface layer H1, the stacking velocities oscillate violently for the layers below. If Dix conversion is done using the unedited stacking velocity profiles, the resulting interval velocity profiles exhibit geologically implausable variations (Figure 9.1-21a). It is imperative in practice to remove the oscillations from the stacking velocity profiles before Dix conversion. The resulting interval velocity profiles shown in Figure 9.1-21b are closer to the true profiles shown in Figure 9.1-18a.
By using the interval velocity profiles, convert the time horizons shown in Figure 9.1-19a to depth horizons. Then, combine the interval velocity profiles with the depth horizons to compose the velocity-depth model shown in Figure 9.1-21c. A comparison with the true model shown in Figure 9.1-19b, once again, clearly demonstrates that the interval velocity estimation based on Dix conversion is not completely accurate. We shall make an attempt in model updating to update the model in Figure 9.1-21c by using tomography.
Figure 9.1-21 (a) The interval velocity profiles derived from Dix conversion of the horizon-consistent stacking velocity profiles picked from the semblance spectra shown in Figure 9.1-20, (b) the interval velocity profiles of (a) after lateral smoothing, (c) estimated velocity-depth model. Compare with the true velocity-depth model shown in Figure 9.1-18b.
Figure 9.1-23 Horizon-consistent coherency inversion semblance spectra computed from the CMP gathers associated with the stacked data in Figure 9.1-19a. When computing the semblance spectrum for a given layer, smoothing has been applied to the velocity profiles picked from the semblance spectra associated with the layers above.
Figure 9.1-24 (a) The interval velocity profiles derived from coherency inversion semblance spectra shown in Figure 9.1-23; (b) estimated velocity-depth model. Compare with the true velocity-depth model shown in Figure 9.1-18b.
Figure 9.1-23 shows the semblance spectra derived from coherency inversion for layers H2 through H6 of the model shown in Figure 9.1-18. The analysis was conducted layer by layer starting from the top. Based on the lessons learned from the model experiments shown in Figures 9.1-13 and 9.1-15, the oscillations in the semblance spectra were rejected while tracking the interval velocity profile from the semblance spectrum for the layer under consideration before moving down to the next layer. Despite the rejection of the oscillations, the semblance spectra still exhibit the influence of the near-surface layer with lateral velocity variations (Figure 9.1-23).
Shown in Figure 9.1-24b is the velocity-depth model using the interval velocity profiles (Figure 9.1-24a) derived from coherency inversion. A closer look at the central portion of the estimated model using coherency inversion is shown in Figure 9.1-25. As long as the oscillations shorter than a cable length are eliminated from the interval velocity profiles, coherency inversion seems to produce a better estimate of the velocity-depth model compared to Dix conversion (Figure 9.1-22). The difference between the two estimates is in the reflector geometries. Dix conversion has introduced spurious structures into the model (Figure 9.1-22), while coherency inversion has introduced a bulk shift in the reflector depths (Figure 9.1-25). In earth modeling, an error in the form of a distorted reflector geometry is worse than an error in the form of a bulk shift in the reflector depth. While the error in the form of a bulk shift can be corrected for by calibrating the estimated model to well tops, the error in the form of a distorted reflector geometry may require a serious revision of the estimated model.