Dix conversion

Seismic Data Analysis

Series	Investigations in Geophysics
Author	Öz Yilmaz
DOI	http://dx.doi.org/10.1190/1.9781560801580
ISBN	ISBN 978-1-56080-094-1
Store	SEG Online Store

The horizon-consistent stacking velocity profiles (Figure 9.1-3) at each of the layer boundaries are used to perform Dix conversion to derive the interval velocity profiles for each of the layers. Dix conversion is based on the formula

$v_{n}={\sqrt {\frac {V_{n}^{2}\tau _{n}-V_{n-1}^{2}\tau _{n-1}}{\tau _{n}-\tau _{n-1}}}},$

(1)

where v_n is the isotropic interval velocity within the layer bounded by the (n − 1)st layer boundary above and the nth layer boundary below, τ_n and τ_n−1 are the corresponding two-way zero-offset times, and V_n and V_n−1 are the corresponding rms velocities. Derivation of equation (1) is provided in Section J.4.

Equation (1) is based on the assumptions that the layer boundaries are flat and the offset range used in estimating the rms velocities V_n and V_n−1 corresponds to a small spread.

The procedure for estimating the layer velocities and reflector depths using Dix conversion of stacking velocities includes the following steps:

1. For each of the layers in the model, pick the time of horizon on the unmigrated CMP-stacked data that corresponds to the base-layer boundary (Figure 9.1-2a). These times are used in lieu of the two-way zero-offset times in equation (1).
2. Extract the rms velocities at horizon times (Figure 9.1-3).
3. Use equation (1) to compute the interval velocities for each of the layers from the known quantities — rms velocities and times at top- and base-layer boundaries.
4. Use interval velocities and times at layer boundaries to compute depths at layer boundaries. If the input times are from an unmigrated stacked section as in Figure 9.1-2a, use normal-incidence rays for depth conversion. If the input times are from a migrated stacked section, use image rays for depth conversion.

Interval velocity profiles derived from Dix conversion are shown in Figure 9.1-4a. The earth model can be constructed by combining the estimated interval velocity profiles and depth horizons (Figure 9.1-4b). Comparison with the true model shown in Figure 9.1-1b clearly demonstrates that the interval velocity estimation based on Dix conversion is not completely accurate. The interval velocity profiles derived from Dix conversion (Figure 9.1-4a) exhibit the sinusoidal oscillations caused by the swings in the stacking velocity profiles themselves (Figure 9.1-3).

The fundamental problem is that the stacking velocity estimation is based on fitting a hyperbola to CMP traveltimes associated with a laterally homogeneous earth model. If there are lateral velocity variations in layers above the layer under consideration, and if these variations are within a cable length, then stacking velocities would oscillate in a physically implausable manner . As a consequence, the resulting interval velocity estimation based on Dix conversion is adversely affected. In the present case, Dix conversion has produced fairly accurate estimates for the interval velocities of the top three layers — H1, H2, and H3 as shown in Figure 9.1-4a. But the interval velocity estimates for layers H4 and H5 have been adversely affected by the laterally varying velocities within the layer above, H3.

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  Figure 9.1-1  An earth model that comprises six flat layers: (a) the interval velocity profiles for the six horizons H1-H6; (b) true velocity-depth model created from the profiles in (a).

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  Figure 9.1-2  (a) The CMP-stacked section derived from the modeled common-shot gathers using the earth model shown in Figure 9.1-1b; (b) the stacking velocity section.

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  Figure 9.1-3  Horizon-consistent stacking velocity semblance spectra computed from the CMP gathers of the synthetic data as in Figure 9.1-2a along the time horizons H1-H6.

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  Figure 9.1-4  (a) The interval velocity profiles derived from Dix conversion of the horizon-consistent stacking velocity profiles picked from the semblance spectra shown in Figure 9.1-3; (b) estimated velocity-depth model. Compare with the true velocity-depth model shown in Figure 9.1-1b.

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  Figure 9.1-5  (a) The interval velocity profiles as in Figure 9.1-4a displayed by the thick curves and smoothed interval velocity profiles displayed by the thin curves; (b) estimated velocity-depth model using the smoothed interval velocity profiles in (a). Compare with the true velocity-depth model shown in Figure 9.1-1b and the model derived from the unsmoothed interval velocities shown in Figure 9.1-4b.

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  Figure 9.1-6  Central portions of (a) the true velocity-depth model shown in Figure 9.1-1b, (b) the velocity-depth model shown in Figure 9.1-4b estimated using the unsmoothed interval velocity profiles shown in Figure 9.1-4a, and (c) the velocity-depth model shown in Figure 9.1-5b estimated using the smoothed interval velocity profiles shown in Figure 9.1-5a.

The pragmatic approach would be to smooth out the oscillations in the stacking velocities before Dix conversion and smooth out the oscillations in the velocity profiles after Dix conversion (Figure 9.1-5a). Then, the resulting earth model is expected to be free of the adverse effects of stacking velocity anomalies (Figure 9.1-5b). A closer look at the central portions of the estimated models using Dix conversion is shown in Figure 9.1-6. Note that the model derived from the smoothed interval velocities is closer to the true model. We shall make an attempt in model updating to update this result by using tomography.

See also

• Dictionary:Dix_formula
• Models with horizontal layers
• Coherency inversion
• Near-surface layer with laterally varying velocities

External links

find literature about Dix conversion