The basis for the computation of the 2D ADCIGs after migration is the equation

(1)

Sava and Fomel (2003) where k_{h} and k_{z} are the offset and
depth wavenumbers and is the aperture angle. In 3D the situation is
more complicated because the azimuth of the reflection plane at the reflection
point needs to be taken into account Biondi (2005) and the computation of
true 3D ADCIGs as a function of the aperture angle and the azimuth of the
reflection plane is not trivial Biondi (2005). We will explore this issue in
the next section. It is tempting to compute pseudo-3D ADCIGs by a direct
extension of equation 1, that is:

(2)

(3)

where x_{hx} and k_{hy} are the wavenumber components of the horizontal
wavenumber vector and k_{z}, as before, is the depth component of the
wavenumber vector. The angles and don't have an immediate
correspondence with the aperture angle or the azimuth, hence we will call the
ADCIGs obtained with equations 2 and 3 pseudo 3D
ADCIGs. Panel (a) of Figure shows the inline component of the
pseudo
ADCIG corresponding to the same SODCIG shown in Figure .
The primaries are flat and the multiples exhibit a similar residual
moveout as that seen in 2D ADCIGs Biondi and Symes (2004). Panel (b) of
Figure
shows the crossline component of the same pseudo 3D ADCIG. Since the
crossline aperture is small, there is very little discrimination between the
primaries and the multiples. This, of course means that using pseudo 3D ADCIGs
to attenuate the multiples relies entirely on the inline direction and is
therefore essentially a 2D process.

adcigs
Figure 15 Inline component (a) and crossline component (b)
of the pseudo 3D ADCIG corresponding to the SODCIG shown in
Figure .