Discussion

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.