Test on Solid elastic model data

We apply the above direct velocity transform method to map between the space-time domain and the Abelian group (g1',g2') domain. Figure 4 displays the synthetic data as in Figure 1, and the data after velocity transform to (g1',g2') and back to the space-time domain. The far offset data are attenuated by the velocity transform. For all the mappings here, we use one-pass conjugate mapping. Conjugate gradient iteration gives a better result, but is the last resort. Figure 5 is the data in (g1',g2') domain before and after gapped predictive decon. On the gapped predictive deconned (g1',g2'), we apply a cosine muting on the left of g2'=0. Figure 6 shows the space-time data after conjugate velocity transforming the deconned (g1',g2') data in Figure 5b and the original water-related reverberations-free data. The reverberations attenuated section shows that at near offset the first waterbottom multiple remains strong; because the hyperbola curvature is large at near offset, it maps to a large area in velocity space. Its amplitude relationship in velocity space thus deteriorates. The gapped predictive deconvolution does not work well here. The remedy to this problem lies in further improved velocity transform.

 

SynMM
Figure 4 (a) is the input synthetic data as in Figure 1; (b) is the data after conjugate velocity transforming back from (g1',g2') in Figure 5a. The far offset data are attenuated by the velocity transform.

 

SynMMAbelian
Figure 5 (a) is the Abelian group data (g1',g2'); (b) is the (g1',g2') data after gapped predictive decon, gap=550ms, filter length=550ms.

 

SynMultAtten
Figure 6 (a) is the water related reverberations attenuated section; (b) is the Solid elastic modeling section free of water related reverberations.