variogrammeja

A variogrammeja, often shortened to variogram, is a fundamental tool in geostatistics used to describe the spatial dependence of a variable. It quantifies how the difference between values of a variable increases as the distance between the locations at which those values are measured increases. Essentially, it measures dissimilarity in relation to separation.

The empirical variogram is calculated from observed data points. For a set of data points scattered across a region, pairs of points are grouped based on their separation distance and direction. The average squared difference between the values of the variable at these paired locations is then computed for each distance. This results in a set of points (distance, semivariance) that form the empirical variogram.

A theoretical variogram model is then fitted to the empirical variogram. Common models include the spherical, exponential, and Gaussian models. These models have parameters like the sill (the maximum semivariance), the range (the distance at which the semivariance reaches the sill), and the nugget effect (the semivariance at zero distance, often representing measurement error or micro-scale variability).

The variogram is crucial for kriging, a geostatistical interpolation technique that estimates values at unobserved locations. By understanding the spatial structure captured by the variogram, kriging can assign optimal weights to surrounding observed data, producing the best linear unbiased estimates. It is widely used in fields such as mining, environmental science, hydrology, and soil science for spatial analysis and prediction.