Frequency-domain considerations

As pointed out by Prucha et al. (1999), the angle gathers can be conveniently formed in the frequency domain. This conclusion follows from the simple formula Fomel (1996a)  

$$\tan{\gamma} = \frac{\partial z}{\partial h}\;,$$ (15)

where z refers to the depth coordinate of the migrated image. In the frequency-wavenumber domain, formula (15) takes the trivial form  

$$\tan{\gamma} = \frac{k_h}{k_z}\;.$$ (16)

It indicates that angle gathers can be conveniently formed with the help of frequency-domain migration algorithms Stolt (1978). This interesting opportunity requires further research.