Introduction to SuperGIS Spatial Statistical Analyst

Isotropy and Anisotropy

Geostatistics applies a variogram to present spatial variability and a variogram model is also a distance function. If the variogram of a spatial variable is only a distance function and does not vary along with different directions, this phenomenon is called “Isotropy.” If the variogram of a spatial variable varies along with different directions, this phenomenon is called “Anisotropy”. In other words, the variogram model of anisotropy is the function of distance and direction. Therefore, the equation could be revised as:

：angle along point “xi” and “xi+h”

N (h,θ)：pairs of samples with interval “h"” in the angles along point “xi” and “xi+h”.

If there are two regionalized variables “z” and “y”, the co-variogram could be obtained via:

General speaking, the procedures of distinguishing between isotropy and anisotropy are the same. We can fit a variogram model along all the directions and then obtain different variograms along different directions. Once we obtain the values of Sill, Range, Nugget Effect along all the directions, we can determine if the spatial data is isotropic or anisotropic. If the values of Sill, Range, Nugget Effect along all the directions are all the same, then it is isotropic; otherwise, it is anisotropic. Anisotropy, according to its different structures, could be divided into Geometric Anisotropy, Zonal Anisotropy, and Mixed Anisotropy.