The interpolation method is used to determine how values should be interpolated among a group of objects. Interpolation can only be used for 2D data sets. Only one of the PHAST data sets, Initial_Water_Table, is a 2D data set. However, the user can define his or her own 2D data sets and use interpolation in it. One appropriate use of such 2D data sets would be to define the tops and bottoms of geologic units. Three interpolation algorithms are available in GoPhast: Nearest, Inv. Dist. Sq. (Inverse Distance Squared), and Nearest Point.
The Nearest interpolation method (fig. 14A) works by determining the object that is closest to the location where the data set in question is being evaluated. Then the formula of that object is evaluated at that location.
The Nearest Point interpolation method (fig. 14B) is similar to the Nearest interpolation method except that only the vertices of objects are considered rather than the lines connecting the vertices. If only point objects are being used, the results are identical. However, the Nearest Point interpolation method uses an algorithm that is faster than the Nearest interpolation method when the number of points is greater than several hundred.
With the Inv. Dist. Sq. interpolation method (fig. 14C), the formula for each object is evaluated at the location under consideration. The final value is a weighted average of these values. The weights are the inverse of the distance from the location to the closest point on each respective object. The Inv. Dist. Sq. interpolation method may only be used with data sets containing real numbers.
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Figure 14. Interpolation methods. A. Nearest interpolation method. B. Nearest Point interpolation method. C. Inv. Dist. Sq. interpolation method. |
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