Primaries and multiples can also be discriminated on the basis of their residual moveouts in 3D ADCIGs. Furthermore, in 3D ADCIGs there is the additional advantage of the multiples and the primaries behaving differently as a function of azimuth for a given aperture angle and as a function of aperture angle for a different azimuth. This differential azimuth dependency can be exploited to compute a three-dimensional Radon transform that is a function of aperture angle and azimuth similar to the apex-shifted Radon transform of chapter 2. For the sake of computer time, in Chapter I will take the simpler route of attenuating the multiples as a function of aperture only by first stacking the data over azimuths. I use a slight modification of the methodology presented in Chapters and .
In this chapter I make no attempt to actually compute a multiple model, and thereby estimate the primaries, for two reasons: first, the model is so simple that the multiples and the primaries separate completely as a function of depth in the Radon domain, defeating the purpose of separating them as a function of curvature. Second, a full application of the ideas presented in this chapter will be applied in Chapter with all the challenges of real data and therefore it would be redundant to present it here. The value of this chapter is that the simple model allows a relatively straight forward interpretation of the mapping of the multiples in the five-dimensional image spaces of SODCIGs and ADCIGs, which would have been difficult with real data. The lessons learned in this chapter will prove useful in interpreting the less straight forward results of Chapter .
Another important result of this chapter is the realization that, despite its theoretical appeal, source-receiver migration is not an ideal imaging tool for these kinds of sparse geometry (even without feathering). For the imaging of the real dataset, therefore, I will use shot profile migration. The main advantage is that each shot can be migrated separately, feathering is easier to handle and, more importantly, there is no need to create a gigantic, regular, five-dimensional dataset.