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The next question is how to choose
?
We have three general requirements:
- it produces relatively smooth (by some criteria) results;
- it spreads information quickly;
- and it is computationally inexpensive.
By defining our operators via the helix method
Claerbout (1997) we can meet all of these
requirements.
The helix concept is to transform N-Dimensional
operators into 1-D operators to take
advantage of the well developed 1-D theory.
In this case we utilize our ability to construct
stable inverses from simple, causal filters.
We can set
, from equation (4) to
|  |
(5) |
where
is the roughening operator from fitting
goal (1), and
is simulated using
polynomial division.
If
is a small roughening
operator,
is a large smoothing operator without the
heavy costs usually associated with larger operators.
Next: Steering Filters
Up: THEORY/MOTIVATION
Previous: Preconditioning
Stanford Exploration Project
9/12/2000