Sampling variogram

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In mathematical statistics, a sampling variogram is a graph that shows where a significant degree of spatial dependence in a sample space or a sampling unit dissipates into randomness. A sampling variogram is obtained by plotting the statisticallly significant variance terms of a temporally or in situ ordered set of measured values against the variance of the set and the lower limits of its asymmetric 95% and 99% confidence range. Corrected sampling variograms derive from uncorrected ones when extraneous measurement variances are subtracted before spatial dependence is verified. Bre-X's bogus gold grades for crushed, salted and in situ ordered core samples of Borehole BSSE198 in Busang's South-East zone give the following uncorrected sampling variogram.

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The corrected sampling variogram for Bre-X's bonanza borehole, its primary data set and test statistics are posted on this website. A temporally ordered set of on-stream data for mill feed to a mineral processing plant, its test statistics and sampling variogram are given in Appendix D of Sampling in Mineral Processing. The variogram or semi-variogram, unlike the above sampling variogram, does not show where spatial dependence in a sample space dissipates into randomness simply because the kriging variance of a set of kriged estimates is an invalid measure for variability, precision and risk.

[edit] References

1. Armstrong, M and Champigny, N, 1988, A Study on Kriging Small Blocks, CIM Bulletin, Vol 82, No 923
2. Clark, I, 1979, Practical Geostatistics, Applied Science Publishers, London
3. David, M, 1977, Geostatistical Ore Reserve Estimation, Elsevier Scientific Publishing Company, Amsterdam
4. Hald, A, 1952, Statistical Theory with Engineering Applications, John Wiley & Sons, New York
5. ISO/DIS 11648, Statistical aspects of sampling from bulk materials, Part 1: General Principles
6. Journel, A G and Huijbregts, C J, 1978, Mining Geostatistics, Academic Press Inc, London 1978
7. Philip, G M and Watson, D F, 1986, Matheronian Geostatistics; Quo Vadis?, Mathematical Geology, Vol 18, No 1

[edit] External Link

• This website explains how to design uncorrected and corrected sampling variograms, and how to verify where spatial dependence in sample spaces or sampling units dissipates into randomness