Geostatistical

Geostatistical describes methods and theory in geostatistics, the field of statistics that analyzes and models spatial or spatiotemporal data. Geostatistical approaches aim to predict the value of a variable at unsampled locations by exploiting spatial autocorrelation captured through models of the variable's spatial structure, and to quantify the uncertainty of those predictions.

Key concepts include the variogram (or semivariogram), which characterizes how similarity between observations changes with distance; stationarity assumptions; and prediction methods such as kriging, a family of linear unbiased estimators that incorporate the variogram. Variants include ordinary, simple, universal, and indicator kriging, as well as co-kriging which uses secondary variables. Geostatistical simulation methods, such as sequential Gaussian simulation, generate multiple equally probable realizations to assess uncertainty and aid decision-making.

Typical workflow: data collection, exploratory spatial data analysis, variogram modeling, parameter fitting, kriging interpolation, and validation. History: geostatistics originated in the mining industry in the 1960s through Georges Matheron at the École des Mines de Paris. Applications include mining and mineral exploration, groundwater hydrology, environmental science, agriculture, meteorology, and petroleum geology. Limitations include assumptions of stationarity or local stationarity, dependence on data density and quality, and sensitivity to non-Gaussian distributions or anisotropy.

Software commonly used for geostatistical analysis includes SGeMS, GSLIB, the R packages gstat and geoR, Python tools such as PyKrige, and GIS packages with geostatistical modules.