Variogram surface

Algorithm

The Variogram surface operation uses a point map or a raster map as input and calculates a surface of semi-variogram values where each cell (pixel) in the surface represents a directional distance class. The output surface, a raster map with a special kind of georeference, may help you to visualize possible anisotropy of your data and to determine the direction of the anisotropy axis.

Subsequently, you can calculate directional semi-variograms by using the bidirectional method in the Spatial correlation operation. From the output table of Spatial correlation, you can prepare a semi-variogram model and you can investigate the range of the variable in the semi-variogram model both in the direction of anisotropy as well as in the direction perpendicular to it. Then, you are ready to perform Anisotropic Kriging.

Process:

The 'separation vectors' between all input point pairs are determined, i.e. the distances and the directions between individual points in point pairs.
All separation vectors are 'transferred' to the framework of the output semi-variogram surface: all vectors start in the origin. For more information, see Variogram surface : functionality.
For each cell in the output surface, a semi-variogram value is then calculated from the values of all point pairs whose separation vectors end up in that cell/pixel. For the calculation of semi-variogram values, see Spatial correlation : functionality and Spatial correlation : algorithm.

The formula to calculate experimental semi-variogram values reads:

S (z_i - z_j)² / 2n

where:

	experimental semi-variogram value of points that have a certain distance (h) towards each other
z_i	the value of point i
z_j	the value of point j
S (z_i - z_j)²	the sum of the squared differences between point values of all point pairs within a certain distance class
n	the number of point pairs within a distance class