Conclusions

The application of weighted least squares using the first derivative effectively removes the shifts from one track to the next to create a realistic looking map of the ocean floor in the dense data. The use of PEFs to fill in the missing data looks promising as the test cases indicate.

When PEFs are applied to the sparse tracks, the calculated $\epsilon$ proposed by Jon Claerbout seems to return values close to those that I arrived at through trial and error. However, it does not seem to work well when applied to the entire merged data set when the southern region is sampled much more than the northern region. Nontheless, the calculated $\epsilon$ may provide a good starting point for choosing $\epsilon$.