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It may seem difficult to estimate the plane slope *p*_{x} for a
Lax-Wendroff filter of the form (10) because *p*_{x} appears
non-linearly in the filter coefficients. However, using the analytical
form of the filter, we can easily linearize it with respect to the
plane slope and set up a simple iterative scheme:

| |
(11) |

where *k* stands for the iteration count, and is found
from the linearized equation
| |
(12) |

where is the derivative of with respect to
*p*_{x}. To avoid unstable division by zero when solving equation
(12) for , Adding a regularization equation
| |
(13) |

where is a small scalar regularization parameter, I solve
system (12-13) in the least-square sense to
obtain a smooth slope variation at each iteration. In
practice, iteration process (11) quickly converges to a
stable estimate of *p*_{x}.

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** Previous:** Factorizing plane waves
Stanford Exploration Project

10/25/1999