Controlling the angle

It is possible to perform a dip filter with our phase-shift migration algorithm; because we calculate $R^{\prime}$ with the Muir recursion (4,8), we can use the recursion starting with R₀=r₀s, in order to have control on the desire dip.

 

$$R^{\prime}_{0}=s(r_{0} - 1),$$ (14)

where r₀ defines the cosine of the angle that starts the Muir recurrence, often $0^{\circ}$ or $45^{\circ}$; following the recursion (8) we find

 

$$R^{\prime}_{1} = \frac{v^{2} k_{x}^{2}}{s(1+r_{0})}$$ (15)

and subsequently:

 

$$R^{\prime}_{2} = \frac{v^{2} k_{x}^{2}}{2s + \frac{v^{2} k_{x}^{2}}{s(1+r_{0})}}$$ (16)

The expressions (14), (15), and (16) are the relations for a $5^{\circ}$, $15^{\circ}$, and $45^{\circ}$ dip migration in the Fourier-domain, respectively.