Prestack or poststack?

I have been very careful not to make a distinction between prestack and poststack algorithms: all of the above applies to both domains. The prestack version use the dispersion relation in a form that solves for $k_z = F(\omega,k_x)$.Sources and receivers are downward continued in depth by calculating

$$k_z = k_{z,s} + k_{z,g} = F(\omega,k_{x,s}) + F(\omega,k_{x,g}) ,$$ (2)

where k_x,s and k_x,g are spatial frequencies in shot-geophone coordinates. Again F depends on the exact anisotropic dispersion relation or its double elliptic approximation.