Zonal Anisotropy

The model of zonal anisotropy is the one most currently used in practice, since any observed anisotropy which cannot be reduced by a simple linear transformation of coordinates will call for this model.

Let $/gamma({/boma h})$ be a nested model characterizing a variability in the three-dimensional space $/gamma({/boma h}) = /sum_i/gamma_i({/boma h})$, where ${/boma h}$ is a vector with coordinates $(h_u,h_v,h_w)$. Each of the components $/gamma_i({/boma h})$ of this nested model can be anisotropic in ${/boma h}$, i.e., $/gamma_i({/boma h})$ is a function of the three coordinates $(h_u,h_v,h_w)$ rather than of just the modulus $/vert{/boma h}/vert$. Moreover, the anisotropy of $/gamma_i({/boma h})$ may be completely different to that of $/gamma_j({/boma h})$. Thus, the structure $/gamma_1({/boma h})$ may have a geometric anisotropy, while $/gamma_2({/boma h})$ is a function of the vertical distance $h_w$ only:

A third structure may be isotropic in three dimensions: $/gamma_3({/boma h}) = /gamma_3(/vert{/boma h}/vert)$.

The model of zonal anisotropy can thus be defined as a nested structure in which each component structure may have its own anisotropy. An obvious anisotropy of the structural function $/gamma({/boma h})$ will most often correspond to a genetic anisotropy known beforehand, so that any preferential direction is well known and, thus, can be differentiated when modeling the three-dimensional structural function $/gamma({/boma h})$.