Conclusion

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.