A variogram plots the variance of the difference between sample pairs on a field (any dimensionality) against spatial separation (the "lag") of those samples.
The extrapolation from observed small-lag variances to a zero-lag variogram value is generally termed the "nugget" value.
Variograms I've come across before (geostatistics) always had positive "nuggets", and these values were generally interpreted as arising from (and being some sort of guide to the magnitude of) a combination of measurement error and sub-observation-scale variation in the observed field.
However, I'm just now looking at variograms of some imaging data and any reasonable extrapolation of the low-lag variogram clearly results in a negative "nugget" value. Of course it's always possible to "force" a non-negative nugget by, say, fitting an exponential model... but this doesn't look very convincing when plotted.
Is there any simple interpretation of negative nugget values (or a simple explanation of how they arise) as there is for positive ones ?