geostatistics

Geostatistics is a set of tools that allow researchers to develop qualitative and quantitative insights into naturally occurring processes which are structured in space. It may be considered to be the sister field of time series analyses.

There are three fundamental elements which help determine the nature of the spatial data examined using geostatistics: grain size, interval and extent. The grain size refers to the size of the sampling unit, and is normally expressed as the surface area or volume sampled at each site. The sampling interval is the distance between sampling sites. Finally, the extent is the total area covered by the sampling design. These three concepts are critical to the design and execution of experiments.

The principal function, from which almost the entire field of study is derived, is the variogram. The variogram (or semi-variogram) is at once a graphical representation of how the data vary in space and a mathematical function which allows the researcher to predict values of the variable of interest. The value of the function is calculated at a number of lags (distances between observations) using the following formula:

gamma(d) = 1/2W sum_h=1sum_i=1w_hi(y_h-y_i)²

Here, y is the variable of interest in the study, h and i represent two observations in the data series, W represents the number of pairs of observations at a given lag d, and w is a weighting coefficient. Normally, w takes values of 0 if the pair of observations are not d units apart in space, and 1 otherwise.

After computing the values of this function for all the lags of interest (normally from grain size to one-half the extent), the researcher fits a theoretical function to the data in order to be able to predict values of y. The most commonly used functions that fit semi-variograms are cubic, Gaussian, spherical, or linear.