Anisotropies and Zone of Influence

In a given direction $/alpha$, the variogram may become stable beyond some distance $/vert /boma{h} /vert = a$ called the range, cf. Figure 1.3. Beyond this distance $a$, the mean square deviation between two quantities $Z(/boma{x})$ and $Z(/boma{x}+/boma{h})$ no longer depends on the distance $/vert /boma{h} /vert = a$ between them and the two quantities are no longer correlated. The range $a$ gives a precise meaning to the intuitive concept of the zone of influence of a sample $z(/boma{x})$. However, there is no reason for the range to be the same in all directions $/alpha$ of the space. In Figure 1.3, for instance, the vertical range characterizing the mean vertical dimension of the mineralized lenses differs from the horizontal ranges. For a given distance $/vert /boma{h} /vert = a$, the horizontal variogram presents a weaker variability than the vertical variogram: this expresses the horizontal sedimentary character of the phenomenon considered.

Figure 1.3: Structural Anisotropy Expressed by the Variogram.