ALIASING IN THE SLANT STACK DOMAIN

The $p-\omega$ domain can be viewed as a mapping of the f-k domain along lines of constant slowness (radial lines). It should come as no surprise that aliasing in the $p-\omega$ has features in common with aliasing in the f-k domain. Figure  shows the amplitude spectrum of a single dipping event in the and $p-\omega$domain. The most important point to note is that in the $p-\omega$domain all the unaliased energy for a single dip lies along a single trace of constant slowness. The aliased energy lies along trajectories given by,

$$p_{alias} = p_{true} + n { 2 \pi \over \omega \Delta x }.$$

Where $\Delta x$ is the spatial sampling of the data and p_true is the true dip.

 

single-pw Figure 1 Amplitude spectrum of a single dipping event in the $p-\omega$ domain. The unaliased energy lies along a single ``p trace.'' The aliased energy is along curved lines that are the $p-\omega$ equivalent of the ``wrapped lines'' in the f-k domain.