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As described above, a non-stationary filter can have a different
impulse response for each point in the input/output space.
For the non-stationary shaping filter estimation procedure, we need to
define which coefficients are adjustable for every individual impulse
response.
For simplicity, we characterize each impulse response with the same
set of adjustable coefficients: for the examples, shown here, they
were one-dimensional non-causal symmetric filters about 180 ms long.
Tests indicated that if the filters were shorter than the seismic
wavelength, the quality of the results decreased. Increasing filter
length beyond this length, however, did not alter results
significantly, even in cases when the kinematics of the multiples
were not accurately predicted.
When implementing the non-stationary filters, it is not strictly
necessary to force each point of the input/output space to keep a
unique impulse response. Rather, we apply the concept of
``micropatches'' Crawley (2000), in which points within a small
neighbourhood share a single impulse response.
This cuts computational memory requirements significantly, and
provides an alternative method of controling spatial and temporal
variabilty of impulse responses.

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Stanford Exploration Project

4/29/2001