Geostatistical method

Geostatistical methods can be used for different reasons. Often the main objective is  

Geostatistical methods are comprehensively described in literature by Chiles (1999), Sandilands Swan (1995), Davis (1986), Srivastava (1989) and Goo-vaerts (1997). 

In common, geological variables are not stationary, which means that the mean value and variance vary in space (Gorelick, 1996). By determining the trend within the data it is possible to take into account this spatial variation of the mean and variance. A trend analysis divides conditional (measured) data in two components the regional trend and the deviation from the trend. An example of a method for trend analysis is polynominal regression. The theory of trend analysis is described by Davis (1986). 

The value at which a variogram levels of is called the sill value. The distance at which the variogram approaches the sill value is called the range. 

The nugget-value reflects the differences found between neighbouring samples and/or sampling errors. 

A further problem concerning the sampling location must be discussed. Many environmental queries include the question of the depth at which the sample must be taken. For example, it is of essential importance to know the depth or, better, the depth interval in the studies of soil, river, or groundwater pollution. The sampling depth must be adapted to the specific purpose of the investigation. Often this aim depends on the planned use of the soil area or water body. 

Geostatistical methods are also termed random field sampling as opposed to random sampling [BORGMAN and QUIMBY, 1988], The spatial dependence of data and their mutual correlation can be analyzed by use of semivariograms. Statements on the anisotropy of the spatial distribution are also possible. Kriging, a geostatistical method of 

---

Terrado M, Kuster M, Raldua D, Lopez de Alda M, Barcelo D, Tauler R (2007) Use of chemometric and geostatistical methods to evaluate pesticide pollution in the irrigation and drainage channels of the Ebro river delta during the rice-growing season. Anal Bioanal Chem 387(4) 1479-1488... 

Rendu, J. M. "An Introduction to Geostatistical Methods of Mineral Evaluation" South African Institute of Mining and Metallurgy Johannesburg, 1978. 

Reis, A.P., Sousa, A.J., Da Silva, E.F. and Fonseca, E.C. (2005) Application of geostatistical methods to arsenic data from soil samples of the Cova dos Mouros mine (Vila Verde-Portugal). Environmental Geochemistry and Health, 27(3), 259-70. 

Under these suppositions, the application of linear geostatistical methods, like point kriging, is possible on the basis of the semivariogram. 

An important advantage of geostatistical methods is that the sampling points do not necessarily have to be regularly distributed. For environmental investigation, this point is of particular importance because sometimes certain locations in the area cannot be sampled. 

If the purpose of sampling is the detailed description of the composition of an object, the character of the internal correlation has to be investigated. The methods of autocorrelation and/or semivariogram analysis, as described in Sections 6.6 and 4.4.2, may be useful for clarification of the internal spatial and/or temporal relationships existing within the parent population to be sampled. Geostatistical methods, e.g. kriging, enable undistorted estimation of the composition of unsampled locations in the area of investigation. 

The whole sampling process may be subdivided into two practical steps primary and secondary sampling. This division is described by FLATMAN et al. [1988] for the application of geostatistical methods in particular. These authors differentiate between primary sampling to obtain the internal correlation of the sampling locations in space and the secondary step for map-making. 

The state of pollution of the soil can be more objectively described by means of geostatistical methods. The computation of semivariograms and the use of kriging uncover spatial structures which are not discernible by means of simple univariate statistical tests. 

One problem encountered when assessing exposure of human populations to contaminated land is spatial heterogeneity of pollution. To overcome this problem, Gay and Korre (2006) propose the combinations of spatial statistical methods for mapping soil concentrations, and probabilistic human health risk assessment methods. They applied geostatistical methods to map As concentrations in soil. Subsequently, an age-stratified human population was mapped across the contaminated area, and the intake of As by individuals was calculated using a modified version of the Contaminated Land Exposure Assessment (CLEA) model. This approach allowed a... 

Erickson, T. A. Development and Application of Geostatistical Methods to Modeling Spatial Variation in Snowpack Properties, Front Range, Colorado. Ph.D. Dissertation, University of Colorado, Boulder, CO, 2004. 

---