**JOURNAL PAPER**

**Statistics or geostatistics? Sampling error or nugget effect?**

**I. Clark**

Geostokos Ltd, Scotland

**SYNOPSIS**

Arguments were put forward that 'sampling errors' actually exist at zero distance. Some geostatistical schools actually maintain that the '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 semivariogram 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 semivariogram 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 interval

^{3}

• Christensen

^{4}has shown that the 'nugget effect', or nonzero 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 semivariogram is ambiguous as the formulae for semivariogram models is not actually specified at zero distance

^{6,7,8}.

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**References**

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5.** **CHAMBERS, R.L., YARUS, J.M., and HIRD, K.B. Petroleum geostatistics for nongeostatisticians, Part 1, *The Leading Edge*, May 2000, vol. 19, no. 5, pp. 474-479; [ Links ]

6.** **SINCLAIR, A.J. and BLACKWELL, H. *Applied Mineral Inventory Estimation*, Cambridge University Press, 2002. 381 pp. [ Links ]

7.** **http://www.bioss.ac.uk/smart/unix/mvariog/slides/sl07.htm, Biomathematics & Statistics Scotland, Edinburgh. [ Links ]

8.** **SAMAL, A. Basics of Variogram Analysis, *Pincock Perspectives, *Issue No. 84, May 2007, Pincock, Allen & Holt, Lakewood, Colorado. [ Links ]