Nested Structures

Consider two point or quasi-point (very small support) grades $Z({/boma x})$ and $Z({/boma x}+{/boma h})$ in a deposit separated by a distance vector ${/boma h}$. The variability between $Z({/boma x})$ and $Z({/boma x}+{/boma h})$, which is characterized by the variogram $E/{[Z({/boma x}+{/boma h})-Z({/boma x})]^2/}$, is due to many causes, which appear over a range of different scales, for example:

(i)

at the level of the support ( ${/boma h} = {/boma 0}$), there is a variability due to measurements, i.e., fluctuation in the rate of recovery of the core sample, sampling errors;

(ii)

at the petrographic level (e.g., $/vert{/boma h}/vert < 1 cm$) a second variability appears due to the transition from one mineralogical element to another;

(iii)

at the level of strata or mineralized lenses (e.g., $/vert{/boma h}/vert < 100 m$), a third variability may be due to the alternation of strata or of lenses with waste material;

(iv)

at the level of a metalliferous province (e.g., $/vert{/boma h}/vert < 100 km$), a fourth variability may appear, due to the distribution of the deposits related to the orogenesis of the province; etc.

All these sources or structures of variability, and possibly many more, come into play simultaneously and for all distances ${/boma h}$. They are called ``nested structures''.