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There is a simple trick that modifies the fitting goals in equation ().
We can pose the following preconditioning transformations:
where 348#348 and 347#347 are new variables.
Now we can derive a new system of fitting goals as follows:
This system is almost equivalent to what I introduced in
(), except for the regularization
that I omitted. With 374#374
the noise-modeling operator and 375#375 the signal-modeling
operator, the least-squares inverse of
equations () without the regularization terms is then given by
with
I showed in () that 378#378 and
379#379 can also be interpreted in term of projection
filters.
The estimated noise and signal are then computed as follows
Because of the relationship that exists between the filtering and
subtraction methods, the estimated noise or signal should be equivalent
for both. This has been observed in a multiple attenuation problem by
().
Next: Discussion
Up: From the filtering to
Previous: The filtering method
Stanford Exploration Project
6/7/2002