Statistics or geostatistics? Sampling error or nugget effect?

What is a nugget effect? In the early development of geostatistics, the term ‘nugget effect’ was coined for the apparent discontinuity at the beginning of many semi-variogram graphs. This name was chosen to reflect the large differences found between neighbouring samples in ‘nuggety’ mineralizations such as Wits gold reefs. Geostatistical theory assumes that the difference between a sampled value and a potential repeat sample at the same location is actually zero. Included in this ‘nugget effect’would be true variation between contiguous samples due to the nature of the mineralization, microfracturing, nugget or crystal size and so on. Also included in the nugget effect would be any ‘random’ sampling variation which might occur due to the method in which the sample was taken, the adequacy of the sample size, the assaying process, etc. Arguments were put forward that ‘sampling errors’ actually exist at zero distance. Some geostatistical schools actually maintain that ‘nugget effect’ is all sampling error. This would imply that ‘perfect’ sampling would eliminate the nugget effect entirely. There is now a dichotomy both in the geostatistical world and in the software packages provided for geostatistical analyses. It may seem academic to argue over whether the semi-variogram model should take a value of zero, a value equal to the nugget effect or a partial value at distance zero. However, the decision can have a profound effect on both the estimated resource and in our confidence on that resource. Whereas most geostatistical texts define the semi-variogram model as taking the value of zero at zero distance, others imply that the full nugget effect should be used at zero distance. For example: • The nugget effect refers to the nonzero intercept of the variogram and is an overall estimate of error caused by measurement inaccuracy and environmental variability occurring at fine enough scales to be unresolved by the sampling interval3. • Christensen4 has shown that the ‘nugget effect’, or non-zero variance at the origin of the sernivariogram, can be reproduced by a measurement error model. • The nugget effect is considered random noise and may represent short-scale variability, measurement error, sample rate, etc.5. In many training texts and web courses, the definition of the semi-variogram is ambiguous as the formulae for semi-variogram models is not actually specified at zero distance6,7,8.