In many instances the variogram is not of constant form in all directions. This feature is known as anisotropy, and the example shown in Figure 6‑39 is of an isotropic variogram, i.e. one in which any directional variations are ignored. An alternative approach to the calculation of the semivariance would be to divide the lag band into a series of discrete segments, say at 45 degree intervals, and then calculate separate variograms for each direction. Since the directions are not oriented (i.e. directions such as 0 and 180 degrees are treated as equivalent) there would be four such variograms in this case at 0, 45, 90 and 135 degrees. More generally the variogram can be thought of as a function of two variables or surface, γ(q,h), that may or may not be radially symmetric.

The semivariance surface may be plotted as a 2D map (Figure 6‑42) or 3D surface representation. The center of the map is the origin of the semivariogram, with a radially symmetric structure indicting that there is little or no anisotropy. If there is a strong directional bias, this can be regarded as the major axis of a directional ellipse, with a major axis providing the range in the primary direction, and the minor axis providing the range in the orthogonal direction. A single anisotropic model may be fitted to such datasets, or a series of separate models fitted to the data grouped into distinct directional bins. Note that the practical range may vary with direction in anisotropic modeling.

Figure 6‑42 Anisotropy 2D map, zinc data

Not all software packages use radial sectors — some (including ArcGIS) use approximations to this form based on a grid structure. Other packages, such as Isatis, support more complex directional models and 3D variograms and anisotropy (e.g. for mineral deposit applications). They take into account the problem that simple directional sectors, which can be seen as cone-like regions in 2D and 3D, widen as distance from the selected point increases. To ensure that only points from a narrower band of directions are selected they provide for cylindrical and block-like anisotropic modeling.