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When running datasets that have duplicate points through a suface interpolator operation (IDW, Spline, Kriging) in Spatial Analyst, the points that are removed are not always the best choices.
When a point coverage contains more than one point with the same XY coordinate, the Spatial Analyst surface interpolators will process them out. The first point encountered at a particular location is retained, and all other subsequent ones are removed from consideration.
This poises a question on the validity of the final result, as the criteria for deciding which value to use for surface interpolation is the order encountered.