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As described in Lomask (1998), we use inversion to find the model () that when sampled into dataspace using linear interpolation () will have a derivative () that will equal the derivative of the data (). 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 :
 
(1) 
For the sparse tracks or missing bins, we add a regularization fitting goal to properly fill in the data. Our fitting goals are now:
 

 (2) 
Applying these goals on the dense data, we get the smooth result in Figure 3.
fulldenseNoRuf
Figure 3 Result of applying fitting goals (equation 2).
To make it look more interesting, we roughen the model by taking the first derivative in the eastwest direction as in Figure 4. This highlights alot of the minor northsouth oriented ridges. Similarly, we can roughen it in the northsouth direction as in Figure 5. This highlights the central main ridge. Applying the helical derivative, we get the results in Figure 6. Unlike the directional derivative operators, this highlights features with less directional bias. Lastly, we take the eastwest second derivative to get the very crisp image in Figure 7.
fulldense1
Figure 4 Results of fitting goals with eastwest derivative.
fulldenseNS1
Figure 5 Results of fitting goals with northsouth derivative.
helix
Figure 6 Results of fitting goals with helix derivative.
fulldense2nd1
Figure 7 Results of fitting goals with eastwest 2nd derivitive.
Next: Looking at dataspace
Up: Background
Previous: Background
Stanford Exploration Project
6/8/2002