Geostatistics

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Geostatistics is a branch of statistics focusing on spatiotemporal datasets. Developed originally to predict probable distributions for mining operations, it is currently applied in diverse disciplines including petroleum geology, hydrogeology, hydrology, meteorology, oceanography, geochemistry, geometallurgy, geography, forestry, environmental control, landscape ecology, and agriculture (esp. in precision farming). Geostatistics is applied in varied branches of geography, particularly those involving the spread of disease (epidemiology), the practice of commerce and military planning (logistics), and the development of efficient spatial networks. Geostatistics are incorporated in tools such as geographic information systems (GIS) and digital elevation models.

Background

Devil's Punchbowl Waterfall, New Zealand may be studied using geostatistics

When any phenomena is measured, the observation methodology will dictate the accuracy of subsequent analysis; in geography, this issue is complicated by unique variables and spatial patterns such as geospatial topology. An interesting feature in geostatistics is that every location displays some form of spatial pattern, whether in the form of the environment, climate, pollution, urbanization or human health. This is not to state that all variables are spatially dependent, simply that variables are incapable of measurement separate from their surroundings, such that there can be no perfect control population. Whether the study is concerned with the nature of traffic patterns in an urban core, or with the analysis of weather patterns over the Pacific, there are always variables which escape measurement; this is determined directly by the scale and distribution of the data collection, or survey, and its methodology. Limitations in data collection make it impossible to make a direct measure of continuous spatial data without inferring probabilities, some of these probability functions are applied to create an interpolation surface - predicting unmeasured variables at innumerable locations.

Computational Geometry

See main article Computational Geometry

Topography

This section requires expansion with: connection to the main topic.

See main article Topography

Sampling methodology

This section requires expansion with: details.

• Statistical sampling

See Statistics

• Geospatial sampling

Criticism

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Jan W Merks, a mineral sampling expert consultant from Canada, has strongly criticized^[1] geostatistics since 1992. Referring to it as "voodoo science"^[2] and "scientific fraud", he claims that geostatistics is an invalid branch of statistics. Merks submits^[2] that geostatistics

• ignores the variance of Agterberg's distance-weighted average point grade,
• ignores the concept of degrees of freedom of a data set when testing for spatial dependence by applying Fisher's F-test to the variance of a set and the first variance term of the ordered set,
• abuses statistics by not using analysis of variance properly,
• replaced genuine variances of single distance-weighted average point grades with pseudo-variances of sets of distance-weighted average point grades, violating the one-to-one correspondence between variances and functions such as Agterberg's distance-weighted average point grade.

Furthermore, Merks claims geostatistics inflates mineral reserve and resources such as in the case of Bre-X's fraud. Merks's expertise and credibility are supported by several company executives, who regularly hire his consulting services^[3].

Philip and Watson have also criticized geostatistics in the past ^[4].

There is a consensus that inappropriate use of geostatistics makes the method susceptible to erroneous reading of results^[3][5].

Related software

• gslib is a set of fortran 77 routines (open source) implementing most of the classical geostatistics estimation and simulation algorithms
• sgems is a cross-platform (windows, unix), open-source software that implements most of the classical geostatistics algorithms (kriging, Gaussian and indicator simulation, etc) as well as new developments (multiple-points geostatistics). It also provides an interactive 3D visualization and offers the scripting capabilities of python.
• gstat is an open source computer code for multivariable geostatistical modelling, prediction and simulation. The gstat functionality is also available as an S extension, either as R package or S-Plus library.
• besides gstat, R has at least six other packages dedicated to geostatistics and other areas in spatial statistics.

Notes

References

1. Armstrong, M and Champigny, N, 1988, A Study on Kriging Small Blocks, CIM Bulletin, Vol 82, No 923
2. Armstrong, M, 1992, Freedom of Speech? De Geeostatisticis, July, No 14
3. Champigny, N, 1992, Geostatistics: A tool that works, The Northern Miner, May 18
4. Clark I, 1979, Practical Geostatistics, Applied Science Publishers, London
5. David, M, 1977, Geostatistical Ore Reserve Estimation, Elsevier Scientific Publishing Company, Amsterdam
6. Hald, A, 1952, Statistical Theory with Engineering Applications, John Wiley & Sons, New York
7. Chilès, J.P., Delfiner, P. 1999. Geostatistics: modelling spatial uncertainty, Wiley Series in Probability and Mathematical Statistics, 695 pp.
8. Deutsch, C.V., Journel, A.G, 1997. GSLIB: Geostatistical Software Library and User's Guide (Applied Geostatistics Series), Second Edition, Oxford University Press, 369 pp., http://www.gslib.com/
9. Deutsch, C.V., 2002. Geostatistical Reservoir Modeling, Oxford University Press, 384 pp., http://www.statios.com/WinGslib/index.html
10. Isaaks, E.H., Srivastava R.M.: Applied Geostatistics. 1989.
11. ISO/DIS 11648-1 Statistical aspects of sampling from bulk materials-Part1: General principles
12. Journel, A G and Huijbregts, 1978, Mining Geostatistics, Academic Press
13. Kitanidis, P.K.: Introduction to Geostatistics: Applications in Hydrogeology, Cambridge University Press. 1997.
14. Lantuéjoul, C. 2002. Geostatistical simulation: models and algorithms. Springer, 256 pp.
15. Lipschutz, S, 1968, Theory and Problems of Probability, McCraw-Hill Book Company, New York.
16. Matheron, G. 1962. Traité de géostatistique appliquée. Tome 1, Editions Technip, Paris, 334 pp.
17. Matheron, G. 1989. Estimating and choosing, Springer-Verlag, Berlin.
18. McGrew, J. Chapman, & Monroe, Charles B., 2000. An introduction to statistical problem solving in geography, second edition, McGraw-Hill, New York.
19. Merks, J W, 1992, Geostatistics or voodoo science, The Northern Miner, May 18
20. Merks, J W, Abuse of statistics, CIM Bulletin, January 1993, Vol 86, No 966
21. Myers, Donald E.; "What Is Geostatistics?
22. Philip, G M and Watson, D F, 1986, Matheronian Geostatistics; Quo Vadis?, Mathematical Geology, Vol 18, No 1
23. Sharov, A: Quantitative Population Ecology, 1996, http://www.ento.vt.edu/~sharov/PopEcol/popecol.html
24. Shine, J.A., Wakefield, G.I.: A comparison of supervised imagery classification using analyst-chosen and geostatistically-chosen training sets, 1999, http://www.geovista.psu.edu/sites/geocomp99/Gc99/044/gc_044.htm
25. Strahler, A. H., and Strahler A., 2006, Introducing Physical Geography, 4th Ed., Wiley.
26. Volk, W, 1980, Applied Statistics for Engineers, Krieger Publishing Company, Huntington, New York.
27. Wackernagel, H. 2003. Multivariate geostatistics, Third edition, Springer-Verlag, Berlin, 387 pp.
28. Yang, X. S., 2009, Introductory Mathematics for Earth Scientists, Dunedin Academic Press, 240pp.
29. Youden, W J, 1951, Statistical Methods for Chemists: John Wiley & Sons, New York.

See also

• Statistics
• Geology
• Geodemographic segmentation
• Geographic information system (GIS)
• Remote sensing
• Kriging
• Pedometrics

External links

• Kriging link, contains explanations of variance in geostats
• Arizona university geostats page
• A resource on the internet about geostatistics and spatial statistics
• On-Line Library that chronicles Matheron's journey from classical statistics to the new science of geostatistics