Example 4.1: Nested Structure at Mazaugues (Journel and Huijbregts, 1978[11])

The bauxite deposit at Mazaugues aval (France) consists of subhorizontal stratiform lenses aligned principally in the North-South direction, cf. Figure 4.2a. These lenses are characterized by a regular hanging wall and a very irregular foot wall which consists of a dolomite karst. The mean dimensions of the lenses are between

and

in the N-S direction and

and

in the E-W direction.

The deposit was sampled by a network of vertical bore holes with a regular density; on average, each square

contains one bore hole.

Figure 4.2b shows the semi-variograms of the thickness of bauxite in the two main directions N-S and E-W. These semi-variograms reveal transition models, the ranges of which correspond to the observed mean dimensions of the lenses. Thus, the structure of the variability of the thickness observed on a hectometric scale is that of the lenticular beds.

If a spherical model of range $a_{NS} = 250 m$ is fitted to the experimental semi-variogram N-S in Fig. 4.2b, the nugget constant would be

. On the hectometric scale of this observation, it is not possible to specify the structures between 0 and 100 m to any greater degree of precision.

During the course of mining, the bauxite thickness at small sampling distances (2 and

) was measured within one particular lens. Figure 4.2c shows the semi-variogram calculated from these measurements. A transition with a range of approximately

can be noticed, which is characteristic of the karstic structure of the foot wall, cf. Figure 4.2a. Beyond this transition, the semi-variogram increases continuously in a way remarkably similar to the linear behavior at the origin of the previous transition model with range $a_{NS} = 250 m$ , which characterizes the macro-structure of the lenticular beds.

**Figure 4.2:** (a) Sampling a Bauxite Thickness. (b) Nested Structures at Mazaugues on a Hectometric Scale. (c) Nested Structures at Mazaugues on a Decametric Scale.
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Thus, what is seen on the hectometric scale as a nugget effect is, in fact, the micro-structure of the jagged outline of the karstic foot wall. The total variability of the bauxite thickness, up to

in the N-S direction, can, thus, be represented as a nested model which is the sum of two transition models (spherical, for example) with ranges

and