Angle-gather time migration

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.