Fitting goals

As described in (), we use inversion to find the model (10#10) that when sampled into data-space using linear interpolation (11#11) will have a derivative (637#637) that will equal the derivative of the data (9#9). 638#638 is a weighting operator that merely throws out fitting equations that are contaminated with noise or track ends. Expressed as a fitting goal, this is :

   639#639 (262)

For the sparse tracks or missing bins, we add a regularization fitting goal to properly fill in the data. Our fitting goals are now: Applying these goals on the dense data, we get the smooth result in Figure .

 

fulldenseNoRuf
Figure 3 Result of applying fitting goals (equation ).

To make it look more interesting, we roughen the model by taking the first derivative in the east-west direction as in Figure . This highlights alot of the minor north-south oriented ridges. Similarly, we can roughen it in the north-south direction as in Figure . This highlights the central main ridge. Applying the helical derivative, we get the results in Figure . Unlike the directional derivative operators, this highlights features with less directional bias. Lastly, we take the east-west second derivative to get the very crisp image in Figure .

 

fulldense1
Figure 4 Results of fitting goals with east-west derivative.

 

fulldenseNS1
Figure 5 Results of fitting goals with north-south derivative.

 

helix
Figure 6 Results of fitting goals with helix derivative.

 

fulldense2nd1
Figure 7 Results of fitting goals with east-west 2nd derivitive.