FEAVO migration and modeling

Since velocity heterogeneities of the size of those which cause FEAVO break the high-frequency assumption of the ray theory Woodward (1990), wavefield extrapolation methods should be used to migrate and model FEAVO-affected data. Vlad (2005) has demonstrated qualitatively that one-way migration methods with the correct velocity model (containing the FEAVO-causing velocity lenses) eliminate all FEAVA effects from the image. The same publication shows in the same way that: (1) only FEAVO effects modeled with two-way schemes have a microstructure (i.e., width of the bordering shadows) identical to that of real data, but (2) the errors introduced by one-way modeling schemes are removed when migrating with one-way schemes and the correct velocity model. Thus the numerical experiments from Vlad et al. (2003a), which show that migration with the correct velocity model removes FEAVA, keep their validity.

Needed: Mathematical proof of the conclusions of Vlad (2005), and further investigation for cases involving absorption.

Figure shows the output of modeling FEAVO with a one-way scheme.

 

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Figure 8 Top: Velocity model with 2000m/s background and anomalies with peak values, from left to right, of -153m/s, -188m/s and +231 m/s. Middle: Prestack data generated with one-way source-receiver upward continuation with two reference velocities. Bottom: ``Kjartansson V's''. From Vlad et al. (2003a).

While the synthetic dataset does feature the small traveltime anomalies associated with FEAVO, it does not exhibit the several-fold increase in amplitudes noticed in the real data and which got FEAVO discovered in the first place Kjartansson (1979); White et al. (1988). The magnitude of the velocity ``lenses'' (10% of the background) should have been sufficient to have caused it. It is unclear to what extent the lack of strong amplitude effects is caused by modeling with a one-way scheme in general (as discussed above) or by the amplitude characteristics of the particular one-way scheme employed. FEAVA effects obtained by modeling with a one-way scheme followed by migrating with the background velocity (Figure have neither border shadows/highs as real data does (Figure ), nor extremely high amplitudes. Modifications of the downward propagation operators designed to take into account vertical gradients in velocity Vlad et al. (2003b) will not result in improvements in this case because the background velocity is constant. Having correct amplitudes of FEAVA effects, including their microstructure, is paramount to the success of any inversion-based removal procedure that inverts FEAVA into velocity/absorption anomalies, and any such procedure would need to be tested on a synthetic while being prototyped.

 

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Figure 9 ``Pure'' FEAVA. Obtained by: (1) migrating the dataset shown in Figure with the correct velocity; (2) migrating it with the background velocity; (3) subtracting the ADCIGs. From Vlad et al. (2003a).

Needed: Extraction of ``pure'', correct FEAVA effects by two-way modeling of FEAVA effects followed by two-way migration with the correct velocity, with the background velocity, and subtraction in ADCIGs. A comparison with the result of the equivalent one-way flow (Figure ) will allow then to assess whether the errors introduced by the one-way problem are negligible or not.

Not only primaries are focused by the heterogeneities that caused FEAVO. Multiples are too. Vlad (2004a) uses numerical experiments on highly realistic data to present evidence towards the idea that, unlike FEAVO from primaries, FEAVO from multiples is not eliminated through simple migration that does not take multiples into account. It is easy to understand this intuitively: during a migration designed for primaries, the multiples wavefields do not pass through the focusing heterogeneities enough times for the focusing to be undone by the extrapolation operators. Another type of FEAVO that may not be eliminated by migration is the one caused by absorption. An absorption compensating-scheme, such as Lu et al. (2004), would need to be employed to eliminate FEAVO after an absorption model has been obtained through inversion.