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

$$\bold S \eq \bold F' \,\bold N \, \bold F$$ (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

$$\bold S' \eq \bold F' \, \bold N'\, \bold F$$ (33)

We see then that the transpose to Stolt modeling is Stolt migration. (There are a few more details with Stolt's Jacobian.)