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Estimating the spatial prediction filter

We use subscript k to represent the location of the trace, i.e., $W_{\rm k} = W(f,k\Delta x)$. If Wk is predictable from $(W_{\rm k-1}, 
W_{\rm k-2}, ..., W_{\rm k-N})$, we have
\begin{displaymath}
W_{\rm k} = \sum_{j=1}^N C_{\rm j} W_{\rm k-j}, \hspace*{0.2in}(k=2,3,...,N_2)\end{displaymath} (21)
where N2 is the length of the spatial axis.

Determination of the coefficients $C_{\rm j}$ can be treated as an optimization problem. Here we choose conjugate gradient code cgplus Claerbout (1994) as the solver. Originally, cgplus was used for real-valued optimization. We extend it to complex-valued optimization. Between the two gridding schemes, the most important difference is that

Hopefully, this difference will save computing resources in 3-D. Also, we can expect that the result from FDG will more stable.


previous up next print clean
Next: APPLICATION AND DISCUSSION Up: ESTIMATION OF SPATIAL PREDICTION Previous: Wavefield composed of two
Stanford Exploration Project
11/11/1997