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Mixed domain

In a homogeneous media, $-i\Lambda=k_z=k_{z0}$. Hence the $\Lambda^{-1}$ correction is simply a division by kz0 of the source wavefield at the surface. If a split-step formulation of $k_z = k_{z0} + \omega \left(\frac{1}{v}-\frac{1}{v_0}\right)$ is considered, then the corrections must be carried out both in the space and wavenumber domain. One solution consists of doing the following expansion:
\begin{displaymath}
\frac{1}{k_z} = \frac{1}{k_{z0} + \omega
 \left(\frac{1}{v}-...
 ...c{\omega}{k_{z0}}\left(\frac{1}{v}-\frac{1}{v_0}\right)\right].\end{displaymath} (19)
It is now possible to perform the correction in a few stages in the space and wavenumber domain.
next up previous print clean
Next: Implementing the operator Up: Implementing the operator Previous: Finite differences
Stanford Exploration Project
7/8/2003