We use subscript *k* to represent the location of the trace,
i.e., . If *W*_{k} is predictable from , we have

(21) |

Determination of the coefficients 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

- Frequency-independent grids
- Prediction filter is estimated in the rectangular
`f-x`domain. - For each frequency slice, we need to solve an optimization problem separately. And the coefficients change from one slice to another.

- Prediction filter is estimated in the rectangular
- Frequency-dependent grids
- Prediction filter is estimated in the pyramid domain.
- We incorporate all the equations together and only solve one optimization problem. But the coefficients can be applied to all the frequencies within the pyramid.

11/11/1997