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CONCLUSIONS

Using the IRLS method showed definite improvement in the interpolation of both test cases presented in this paper. However, there are problems with using the IRLS method. One of them is that it adds to an already large parameter space, requiring a significant amount of trial and error to set the parameters, especially when using IRLS on the second stage of the interpolation. Next, this method does not deal with the underlying problems that are caused by noise in the data, such as errors in the operator in the first step, and the fixing of the bad values in the second step. More sophisticated approaches, such as total least squares Brown (2002) that can account for errors in the operator, could be used to further reduce these issues.

We have also seen that the multi-scale PEF estimation appears to be much less susceptible to the noise than a single-scale estimation. This is attributed to some noise attenuation that happens during the rescaling of the data. This benefit of the multi-scale method could be further enhanced by using a more sophisticated rescaling operator than the current linear-interpolation based method, so that the rescaled copies of the data (d_i) would provide more reliable information.

Another approach of dealing with bursty noise could be in pre-processing, where the noise is identified and removed prior to the interpolation or the rescaling. This would then avoid the need for overly robust optimization methods, or more sophisticated rescaling methods. Problems arise with this avenue of research, since most signal-noise separation methods require regularly-sampled data.


next up previous print clean
Next: REFERENCES Up: Curry: Iteratively re-weighted least-squares Previous: CASC93 Data Set
Stanford Exploration Project
7/8/2003