Application of the filter

In this section I test the approach described in the previous section on a simple synthetic and a real dataset. Figure  shows the result of applying this filter to a velocity stack of a synthetic data.

 

spike_comp
Figure 3 Spike after 5 iterations of conjugate gradient and after removing ``butterfly wings.''

Figure  shows that the filter does remove the strongest artifacts and the result spatially looks more like the original spike.

Figure  shows the result of filtering the velocity stack panel of one CMP gather of the Mobile AVO dataset. As we can see, strong individual events on the right panel are much easier to identify. Water-bottom multiples are clearly separated from other events and easy to identify.

 

mob_comp_500
Figure 4 Velocity stack of a CMP from Mobile AVO dataset before and after filtering

Unfortunately, the filtering removes some of the energy from the model, limiting the application of the simple filtering described above. In the next section I discuss the possibilities and problems of incorporating the filtering approach as described above in a solution of the least-squares problem [equation ()].