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Model-space weighting functions have shown to be robust in the
presence of noise. However, for the examples in this chapter
data-space weighting functions have tended to amplify poorly-modeled
coherent noise. The question remains: why is this the case?
This is especially unclear since Figure
suggests that a data-space weighting function is exactly what would be
required to compensate for the illumination problems in that example.
A possible answer to this question comes from considering the relative
sizes of model and data spaces for the example in this chapter
and the example in Chapter .
For the prestack Amoco dataset,
the data space is many times larger than the model space, leaving an
overdetermined problem.
However, the formulation for the data-space weighting functions
[equation ()] is based on the underdetermined
problem [equation ()].
In contrast, model spaces and data spaces for the zero-offset example
in Chapter are approximately of equal size.
Therefore the data-space weights may be more appropriate for that
example.

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Stanford Exploration Project

5/27/2001