Sampling of Offsets in SODCIGs

In order for the migration-demigration process to yield useful results, the offset sampling of the CMPs, as well as the subsurface offset sampling of the SODCIGs must satisfy the well-known aliasing condition: $\vert p\vert\le\frac{K_N}{\omega_d}$ with $K_N=\frac{\pi}{\Delta x}$. This condition is easy to satisfy for the CMPs but is much more difficult for the SODCIGs, in particular for the water-bottom multiple which has a steep moveout as shown in Figure . Therefore, if we want to attenuate the water-bottom multiples we may need to interpolate the subsurface-offsets before the adjoint migration. This will obviously increase the cost of the adjoint migration. It may be better to attenuate the water-bottom multiples in the time domain since there moveout is predictable and apply the procedure described here to the data without the water-bottom multiples.