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Finite differences

Each of Equations (10) or (11) can be split in two parts:
      \begin{eqnarray}
\frac{\partial P}{\partial z } &=&
\pm ik_zP \\ 
\frac{\partial...
 ...
\frac{1}{1+\frac{v^2}{\omega^2}\frac{\partial^2}{\partial^2 x}}P.\end{eqnarray} (20)
(21)
Equation (20) can be written in the general form of the 45 equation Claerbout (1999) in which $\alpha$ and $\beta$ are two coefficients to be set:  
 \begin{displaymath}
\frac{\partial P}{\partial z} =
\pm \frac{i\omega}{v}
\frac{...
 ...1+\beta \frac{v^2}{\omega^2}\frac{\partial^2}{\partial^2 x}} P.\end{displaymath} (22)
Equation (21) resembles (22) enough for us to use the same scheme to solve it. We present some details of the implementation in Appendix A.
next up previous print clean
Next: Mixed domain Up: Implementing the operator Previous: Implementing the operator
Stanford Exploration Project
7/8/2003