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3-D Residual Stolt Migration

The RPrSM equations in three dimensions can be written similarly to those in two dimensions if we consider the relationship between source-geophone and midpoint-offset coordinates as follows:

\begin{displaymath}
\vec{k_g}= \vec{k_y}+ \vec{k_h}\end{displaymath}

\begin{displaymath}
\vec{k_s}= \vec{k_y}- \vec{k_h}. \end{displaymath}

The equivalent prestack residual migration equation in source-geophone coordinates thus becomes
\begin{displaymath}
\begin{array}
{r}
k_{z_m}=\frac{1}{2}
\sqrt{ \frac{v_0^2}{v_...
 ...t)^2\right]} 
{16k_{z_0}^2}-\vert\vec{k_s}\vert^2} .\end{array}\end{displaymath} (7)
In midpoint-offset coordinates, the same equation becomes
\begin{displaymath}
\begin{array}
{r}
k_{z_m}=\frac{1}{2}
\sqrt{ \frac{v_0^2}{v_...
 ...]} 
{16k_{z_0}^2}-\vert\vec{k_y}-\vec{k_h}\vert^2} ,\end{array}\end{displaymath} (8)
which, for the post-stack case, takes the form
\begin{displaymath}
k_{z_m}= \sqrt{ \frac{v_0^2}{v_m^2}\left[k_{z_0}^2+ \vert\vec{k_y}\vert^2\right]-\vert\vec{k_y}\vert^2}.\end{displaymath} (9)

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Next: Examples Up: Sava: Residual migration Previous: 2-D Residual Stolt Migration
Stanford Exploration Project
6/30/1999