Semivariogram
A semivariogram is a graphical and mathematical tool that depicts how spatial dependence changes as a function of distance between sample locations. It is the foundation of geostatistical interpolation methods, particularly kriging, and is essential for characterizing spatial continuity.
A semivariogram (or simply variogram) plots the semivariance of paired observations against the distance (lag) separating them. Semivariance measures half the average squared difference between values at pairs of locations separated by a given distance. As distance increases, semivariance typically rises from a low value (indicating high similarity between nearby points) to a plateau (indicating that distant points are statistically independent).
Key Components
The semivariogram has several characteristic parameters. The nugget is the semivariance at zero distance, representing measurement error or microscale variation. The sill is the plateau value at which semivariance stabilizes, representing the total variance of the data. The range is the distance at which the sill is reached, indicating the maximum distance over which spatial autocorrelationSpatial AutocorrelationSpatial autocorrelation measures the degree to which values at nearby locations are similar (positive) or dissimilar ... exists. An empirical semivariogram is computed from observed data, then a mathematical model (spherical, exponential, Gaussian, or others) is fitted to provide a continuous function for use in krigingKrigingKriging is an advanced geostatistical interpolation method that uses the spatial covariance structure of sample data ....
Role in Kriging
KrigingKrigingKriging is an advanced geostatistical interpolation method that uses the spatial covariance structure of sample data ... uses the fitted semivariogram model to determine the optimal weights for interpolation at unsampled locations. The semivariogram provides the spatial structure needed to calculate both predicted values and prediction uncertainties. Different semivariogram models lead to different interpolation results, making variogram modeling a critical step in geostatistical analysis.
Applications
Semivariograms are used in mining to model ore grade continuity for resource estimation, in soil science to characterize spatial variability of nutrients and contaminants, in environmental monitoringEnvironmental MonitoringEnvironmental Monitoring is the systematic collection and analysis of data about environmental conditions, including ... to plan optimal sampling networks, and in meteorology to interpolate weather station observations. Anisotropic semivariograms account for directional variation in spatial structure.
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