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Abma (1995) solved a
constrained leastsquares problem to separate signal from
spatially uncorrelated noise:
 

 (2) 
 
The first equation defines mathematically the annihilation filter
whereas the second equation defines the annihilation filter
.
Minimizing in a leastsquares sense the
fitting goals in equation (2) with respect
to leads to the following expression for the estimated signal:
 
(3) 
is a projection filter. I call it
the filtering method because the noise components are filtered out
by the PEF in equation (3).
Next: Preconditioning the filtering method
Up: From the filtering to
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Stanford Exploration Project
6/7/2002