Control

The number of adjustable parameters in the filter construction is both a curse and a blessing. Whenever you add parameters to your problem, the model space that you have to search increases exponentially. With two adjustable parameters, taken to the extreme, at every model point, the task can seem daunting. Generally, the smartest course is to keep these two parameters constant throughout the whole model space. But, this freedom also opens up interesting possibilities. In certain regions of the data you might feel that the radial assumption is not quite is valid, or that dips aren't changing quite as fast. In this region you could consider making your triangle bigger, smoothing you filter coefficients over a wider angle range, while keeping it small in areas where dip changes quickly. The sum of the non-zero lag coefficients opens up another intriguing freedom. As Figure 8 shows, when the sum of the non-zero lag coefficients gets close to -1, the area over which the smoother operates increases greatly. This is similar to increasing the $\epsilon$ value over only a portion of your model space. This gives you the freedom to easily smooth regions where filter stability is questionable, while allowing high frequency changes in areas of good data.

 

width
Figure 7 The impulse response of the smoothing filter as function of the triangle base. Note the wider the base, the less precise the dip smoothing.

 

distance
Figure 8 The impulse response of the smoothing filter as the sum of the non-zero lag coefficients get closer to 1.