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STOLT MIGRATION

NMO is based on the quadratic equation v2 t2 = z2 + x2 (as explained in IEI). Stolt migration is based on the quadratic equation

$ \omega^2 / v^2 = k_z^2 + k_x^2$,which is the dispersion relation of the scalar wave equation. Stolt migration is NMO in the Fourier domain (see IEI). Denote the Fourier transform operator by $\bold F$and the Stolt operator by ${\bf S}$, where
\begin{displaymath}
\bold S \eq \bold F' \,\bold N \, \bold F \end{displaymath} (32)

A property of matrix adjoints is $ ( \bold A \, \bold B \, \bold C )' \ =\ \bold C' \, \bold B' \, \bold A' $.We know the transpose of NMO, and we know that the adjoint of Fourier transformation is inverse Fourier transformation. So
\begin{displaymath}
\bold S' \eq \bold F' \, \bold N'\, \bold F\end{displaymath} (33)
We see then that the transpose to Stolt modeling is Stolt migration. (There are a few more details with Stolt's Jacobian.)


next up previous print clean
Next: References Up: Adjoint operators Previous: Units
Stanford Exploration Project
10/21/1998