Sage Journals: Discover world-class research

Abstract

Geochemical data from soils in mineralised areas commonly have skewed and non-normal distributions. As such, raw soil geochemical data cannot be used for direct geostatistical analysis of spatial variability and interpolation without introducing additional uncertainties to any interpretation. The non-normal distributions will influence the robustness and fitting of variograms to the data, and negatively influence the accuracy of any interpolations produced from these data. Therefore, prior to assessment, the dataset must be transformed to ensure that it has a normal distribution. Three transformations, namely the logarithmic, Box–Cox and Johnson transformations, were applied to As, Cd, Hg, Pb and Zn soil geochemical data from the Tongling metallogenic district, part of the Yangtze metallogenic belt, Anhui Province, China. The results of these transformations were analysed to determine the skewness of the data; and, using a Kolmogorov–Smirnov test, how closely the transformed data approximate a normal distribution. A comparison of the differing normalisation approaches indicates that: the logarithmic transformation could not transform the data to approximate a normal distribution; the Box–Cox transformation removed the skewness of the data but the results were still non-normally distributed; and the Johnson transformation proved to be the optimal method, with the results, including outliers, passing the Kolmogorov–Smirnov test. Both the Johnson and Box–Cox transformations also improved the shape of variograms produced from the data. However, compared to Box–Cox, more of the Johnson transformed data fit within 95% confidence intervals for the Kolmogorov–Smirnov test; this improved data distribution means that this transformation should be considered the preferred geostatistical normalisation tool for soil geochemical data. The application of the Johnson transformation to soil geochemical data may improve the robustness of predictive targeting and mineral exploration in areas of known mineralisation that have non-normal spatially variable data.

Keywords

GEOSTATISTICS DATA TRANSFORMATION SOIL GEOCHEMISTRY TONGLING METALLOGENIC DISTRICT

Get full access to this article

View all access options for this article.

References

Box

and Cox

. 1964. An analysis of transformations, J. Royal Stat. Soc., Ser. B (Methodological), 26, 211–252.

Cerioli

and Riani

. 2002. Robust methods for the analysis of spatially autocorrelated data, Stat. Meth. Appl., 11, 335–358.

Chang

. 1991. The Cu, Fe metallogenic belt in the middle-lower reaches of Yangtze River, 379, Beijing, Geological Publish House.

Chou

, Polansky

and Mason

. 1998. Transforming non-normal data to normality in statistical process control, J. QuaL Technot, 30, 133–141.

Corbett

C. J

. and Pan

J.-N.

2002. Evaluating environmental performance using statistical process control techniques, Eur. J. Oper. Res., 139, 68–83.

Cressie

and Hawkins

. 1980. Robust estimation of the variogram: I, Math. Geol., 12, 115–125.

, Tunney

and Zhang

. 2010. Spatial variation of soil nutrients in a dairy farm and its implications for site-specific fertilizer application, Soil Tillage Res., 106, 185–193.

Gaus

, Kinniburgh

D. G.

, Talbot

J. C.

and Webster

. 2003. Geostatistical analysis of arsenic concentration in groundwater in Bangladesh using disjunctive kriging, Environ. Geol., 44, 939–948.

Genton

. 1998. Highly robust variogram estimation, Math. Geol., 30, 213–221.

10.

Hawkins

and Cressie

. 1984. Robust kriging—a proposal, Math. Geol., 16, 3–18.

11.

Hill

, Hill

and Holder

. 1976. Algorithm AS 99: fitting Johnson curves by moments, Appl. Stat., 25, 180–189.

12.

Jobson

. 1991. Applied multivariate data analysis: regression and experimental design categorical and multivariate methods, 621, New York, Springer.

13.

Johnson

. 1949. Systems of frequency curves generated by methods of translation, Biometrika, 36, 149–176.

14.

Journel

and Huijbregts

. 1978. Mining geostatistics, 600, New York, Academic San Diego.

15.

Juan

, Mateu

, Jordan

M. M

., Mataix-Solera

, Meléndez-Pastor

and Navarro-Pedrefio

2010. Geostatistical methods to identify and map spatial variations of soil salinity, J. Geochem. Explor., 108, 62–72.

16.

Kerry

and Oliver

. 2007. Determining the effect of asymmetric data on the variogram. I. Underlying asymmetry, Comput. Geosci., 33, 1212–1232.

17.

Krige

and Magri

. 1982. Studies of the effects of outliers and data transformation on variogram estimates for a base metal and a gold ore body, Math. Geol., 14, 557–564.

18.

M. W.

, Zhan

M. G.

, Zhao

C. S.

, Li

, Zhao

H. F.

, Yao

F. J.

, Cheng

and Wang

L. L

. 2006. Application of robust estimation methods to anomaly appraisal of stream sediment survey in Xinhure area, Inner Mongolia, Miner. Depos., 25, 27–35.

19.

Lilliefors

. 1967. On the Kolmogorov-Smirnov test for normality with mean and variance unknown, J. Am. Stat. Assoc., 62, 399–402.

20.

Mandraccia

, Halverson

and Chou

. 1996. Control chart design strategies for skewed data, in Process, equipment, and materials control in integrated circuit manufacturing II, 196–205, Austin, SPIE.

21.

Mao

, Wang

, Lehmann

, Yu

, Du

, Mei

, Li

, Zang

, Stein

and Zhou

. 2006. Molybdenite Re-Os and albite 40Ar/39Ar dating of Cu-Au-Mo and magnetite porphyry systems in the Yangtze River valley and metallogenic implications, Ore Geol. Rev., 29, 307–324.

22.

Marchant

and Lark

. 2007. Robust estimation of the variogram by residual maximum likelihood, Geoderma, 140, 62–72.

23.

McGrath

, Zhang

and Carton

O. T

. 2004. Geostatistical analyses and hazard assessment on soil lead in Silvermines area, Ireland, Environ. Pollut., 127, 239–248.

24.

Mulla

and McBratney

. 2002. Soil spatial variability, in Soil physics companion, 343–373, Boca Raton, FL, CRC Press.

25.

Pannatier

1996. Variowin: software for spatial data analysis in 2D, 91, New York, Springer.

26.

Park

J.-J.

, Shin

K. -I.

and Cho

2004. Evaluation of data transformations and validation of a spatial model for spatial dependency of trialeurodes vaporariorum populations in a cherry tomato greenhouse, J. Asia-Pacific Entomol, 7, 289–295.

27.

Perez-Valdivia

and Sauchyn

. 2010. Tree-ring reconstruction of groundwater levels in Alberta, Canada, Long term hydroclimatic variability, Dendrochronologia, 29, 41–47.

28.

Sørlie Heier

, Meland

, Ljones

, Salbu

and Stromseng

A. E

. 2010. Short-term temporal variations in speciation of Pb, Cu, Zn and Sb in a shooting range runoff stream, Sci. Total Environ., 408, 2409–2417.

29.

Shi

R. G.

, Zhao

Y. J.

, Zhou

Q. X.

, Li

, Liu

F. Z.

and Sun

2008. Spatial variability analysis of soil arsenic content in predominant agricultural area in the north of Jiangsu Province, Trans. Chin. Soc. Agric. Eng., 24, 80–84.

30.

Slifker

and Shapiro

. 1980. The Johnson system: selection and parameter estimation, Technometrics, 22, 239–246.

31.

Stanley

. 2006. Numerical transformation of geochemical data: 1. Maximizing geochemical contrast to facilitate information extraction and improve data presentation„ Geochem. Explor., Environ., Anal, 6, 69–78.

32.

Sun

H. Q

. 1990. Geostatistics and its application, 282, Xuzhou, China University of Mining & Technology Press.

33.

Wang

S. X.

and Jia

X. Z

. 2007. Model of non-normal process capability indices to semiconductor quality control, Chin. J. Semicond., 28, 227–231.

34.

Wang

W. J.

and Ye

J. Y

. 2000. A brief history of ancient mining in Anhui, Geol. Anhui, 1, 74–77.

35.

Wang

Z. Q

. 1999. Geostat. AppL Ecol, 195, Beijing, Science Press.

36.

Wei

F. Y.

and Cao

H. X.

2002. Geostatistics and its application to meteorological studies, Meteorol Mon., 28, 3–5.

37.

Yue

W. Z.

, Xu

J. H.

and Xu

L. H

. 2005. A study on spatial interpolation methods for climate variables based on geostatistics, Plateau MeteoroL, 24, 974–980.

38.

Zhai

, Yao

and Lin

. 1992. The metallogeny of the Fe-Cu(Au)deposits in the middle-lower Yangtze region, 235, Beijing, Geological Publishing House.

39.

Zhang

, Selinus

and Schedin

. 1998. Statistical analyses for heavy metal contents in till and root samples in an area of southeastern Sweden, Sci. Total Environ., 212, 217–232.

40.

Zhang

and Zhang

. 1996. A robust-symmetric mean: a new way of mean calculation for environmental data, Geofournal, 40, 209–212.

41.

Zhang

C. B.

, Li

Z. B.

, Yao

C. X.

, Yi

L. H.

, Wu

L. H.

, Song

, Teng

and Luo

Y. M.

2006. Characteristics of spatial variability of soil heavy metal contents in contaminated sites and their implications for source identification, Soils, 38, 526–533.

42.

Zhang

. 2005. The theory and application of spatial variation, 188, Beijing, Science Press.

43.

Zhou

T. F.

, Yuan

, Fan

, Xie

J. C.

and Zhang

. 2009. Mineral deposits practice tutorial of Tongling ore concentration area, 139, Beijing, Geological Publishing House.

44.

Zhou

Y. Q.

, Tian

and Tian

Z. Y

. 2004. Estimation of non-normal process capability index based on Johnson system of transforma-tions, Syst. Eng., 22, 98–102.

Comparison of normalisation methods for non-normal distributed soil geochemical data: A case study from the Tongling metallogenic district,Yangtze belt,Anhui Province,China

Abstract

Keywords

Get full access to this article

References