Semivariogram

Semivariograms (short: variograms ) are important tools in geostatistics . They represent the spatial relationship between a point ( regionalization ) and neighboring points. B. used in kriging .

For a semivariogram, pairs of points are formed at different distance levels (  lags ). The squared differences of the pairs are summed up and divided by the number of points (see also variance ). The result is the semivariance , which is shown in a two-dimensional diagram as a function of the distance to the reference point.

Ideally, there are basic shapes that can be described by mathematical functions (theoretical variograms). The most common are:

• spherical
• exponential
• linear
• Gaussian variograms.

Usually (exception: linear variogram) a semivariogram runs towards a limit value ( sill ). The distance between the first value (x = 0) and the value x at which the y values reach the sill is called the range . If y (x = 0)> 0, y is called a nugget , a measure of the noise .

Standard literature

• H. Wackernagel: Multivariate Geostatistics . Springer, Berlin / Heidelberg / New York 1995.
• JP Chiles, P. Delfiner: Geostatistics: Modeling Spatial Uncertainty . Wiley, New York 1999.

Web links

• Variogram on Geographic Information Technology Training Alliance