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We show that by using helicon enabled inverse
operators built from small steering filters we can quickly obtain esthetically
pleasing models.
Tests on smooth models, with a single dip at each location proved
successful. The methodology does not adequately handle models with
multiple dips at each location and presupposes some knowledge of the
desired final model.
A different approach would be to estimate
the steering filters () from the experimental data ().
Generally, this leads to a
system of non-linear equations
| |
(24) |

which need to be solved with respect to . One way of solving
system (24) is to apply the general Newton's method,
which leads to the iteration
| |
(25) |

where the derivative can be computed analytically.
It is interesting to note that if we start with and apply
the first-order filter (8), then the first iteration of
scheme (25) will be exactly equivalent to the
slope-estimation method of Claerbout (1992a), used by
Bednar (1997) for calculating coherency attributes.
Finally, the steering filter
regularization methodology needs to be tried in
conjunction with a variety of operators and
applied to real data problems.

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Stanford Exploration Project

10/9/1997