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Two methods that attenuate coherent noise present in the data are
derived from the need to have IID residual components. In the presence
of noise, having IID residual guarantees the inversion to converge
toward a model that will be consistent with the signal only. One method
weights the residual with a PEF estimated from a noise model.
The PEF (squared) plays the role of the data covariance operator. The
second method introduces a noise modeling part such that the data
covariance operator is not needed anymore. This method can be
interpreted as a weighting of the data residual
with projection operators. On a velocity analysis problem, both
techniques perform similarly. In terms of convergence properties,
the modeling approach gives better results with less energy left
in the residual. Added to the fact that projection operators have
excellent filtering abilities, the modeling approach should be the
method of choice when possible. The next Chapter illustrates on
an interpolation problem of noisy data failures of the filtering
method and successes of the modeling one.

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Stanford Exploration Project

5/5/2005