Transformation to pseudo 3D ADCIGs

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

$$k_h=-k_z\tan\gamma,$$ (1)

Sava and Fomel (2003) where k_h and k_z are the offset and depth wavenumbers and $\gamma$ 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:

$$\begin{eqnarray} k_{h_x}&=&-k_z\tan\gamma_x\ k_{h_y}&=&-k_z\tan\gamma_y\end{eqnarray}$$ (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 $\gamma_x$ and $\gamma_y$ 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 .