ALIASING OF THE OPERATOR

Applying DMO in time slices assures that the operator will not introduce spatial aliasing in the data. However, the spatial spreading from a time slice to the next must never exceed the bin spacing in order to avoid temporal aliasing Hale (1991). The previous condition is not verified for the gentle dips of the operator.

A technique described by Claerbout 1992 prevents operator aliasing. The method consists of the convolution of the operator with triangles whose width depends on the dip of the operator. The convolution is applied horizontally in the time slices. Figure  shows the DMO response of several impulses corrected with anti-aliasing triangles.

 

res Figure 6 Impulse responses of DMO applied to time slices. The anti aliasing triangles are wide at gentle dips and shrink towards the steepest dips.

In three dimensions, the triangles cannot be obtained by Clearbout's double integration technique and thus, they are pre-computed and convolved explicitly.