Example 4.3: Pure Nugget Effect at Adelaïda (Journel and Huijbregts, 1978[11])

The scheelite (WO$_4$Ca) of the Adelaïda (Spain) deposit is concentrated in veinlets and small nodules which are distributed more or less homogeneously in a network of quartz veins.

Drilling was carried out in a direction perpendicular to the plane of the greatest density of veins. The variable measured was the cumulative thickness of the quartz veins intersected by a drill core, the support of the variable being core samples of constant length $l = 5 m$. Thus, the variable measured, $Z_l({/boma x})$, is the regularization of the point variable ``density of quartz'' over the length of a core sample. The core samples can also be grouped in pairs to provide the variable $Z_{2l}({/boma x})$ regularized on core samples of length $2l = 10 m$.

Figure 4.4: Semi-variograms with Pure Nugget-effect.

Figure 4.4 shows the two regularized semi-variograms $/gamma_l(h)$ and $/gamma_{2l}(h)$, as well as the means and experimental dispersion variances of the data used in the calculations. Both these semi-variograms are flat up to around $h = 50 m$ (pure nugget effect), after which ($h > 50 m$) a slow increase indicates the presence of a macro-structure with a range that cannot be determined from the available data.

The respective nugget constants (sills of the flat semi-variograms) adopted are 60 and 30 $(cm/m)^2$, which verify the approximate rule of inverse proportionality to the support of the regularization.

The experimental dispersion variances, $s_l^2 =66.8$ and $s_{2l}^2 = 35.3 (cm/m)^2$, verify well enough the rule of inverse proportionality. These experimental variances are greater than the above nugget constants, the difference corresponding to the additional variability and nesting effect of the macro-structure observed at large distances ($h > 50 m$).

On the scale of observation, $h /in [5, 50 m]$, which is also the scale on which production is carried out, this pure nugget effect indicates that selective mining is not possible in this deposit, unless the size of the selection unit is of the order of the vein (5 to $40 cm$). In fact, the absence of spatial correlation makes impossible any local differentiation by estimation: at any location in the deposit, the best local estimator of the cumulative quartz thickness is the global mean, $m = 5 cm/m$ in the direction studied (approximately vertical).

This example is one of the rare examples of deposits in which the main variable exhibits no spatial auto-correlation at the scale on which the study is made. There is, however, a macro-structure which appears at greater distances.