Extracting image perturbations

The upper panel of Figure shows the optimal image perturbation, found by subtracting the image obtained by prestack depth migration with the constant (2000 m/s) background velocity from that obtained with the correct velocity. While the absolute values of the amplitudes in the FEAVO anomalies are stronger than the background as expected, the polarities change every time the seismic wavelet alternates sign. Vlad (2002) proposed an extraction approach that would involve sweeping the image space with summations along the analytically computable shapes of the FEAVO effects. To do that, we would have to use absolute or squared values to prevent the polarity alternation from cancelling the summed values. However, discarding the information stored in the sign of the anomaly forfeits the ability to distinguish between positive and negative velocity anomalies.

There are several ways of circumventing this problem. They can be simple and cheap, but case-specific (a priori knowledge whether the lenses are faster or slower than the background). They can be more general, but also more complex and expensive (do WEMVA iterations assuming a single sign until all anomalies of that sign are eliminated, allowing anomalies of the other sign to increase; then when only increases in the image perturbations are noticed, switch the sign and start again). Even with the polarity problem, more consideration will be given in the future to the focus-filter-spread approach as envisaged by Vlad (2002) because of its potential power of eliminating the non-FEAVO noise and of exploiting the entirety of the FEAVO morphological characteristics.

The polarity conundrum mentioned above can be eliminated by identifying anomalies by their local, rather than global, characteristics. The middle panel of Figure shows the image perturbation for the TIF WEMVA obtained by eliminating the DC component and by performing several other small adjustements (correcting with a cosine of the angle factor for amplitude decay, windowing away irrelevant energy at higher angles, etc). The lower panel in Figure presents the velocity update obtained after one WEMVA iteration. Additional iterations did not change the result too much. The results may have improved had we used a weighting operator to mask the unresolved anomalies at higher angles (so they would not be fitted when inverting).

 

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Figure 6 Top: ideal image perturbation for TIF WEMVA obtained by subtracting the image produced with the correct velocity and the image produced with the background velocity; Middle: image perturbation for TIF WEMVA obtained by processing the background velocity image in a DSO manner; Bottom: Velocity model obtained after one WEMVA iteration taking as input the image perturbation shown in the middle panel