Example 3.1: Deposit of Copper

A deposit of copper was explored through a series of vertical drill holes. The grade of copper decreases systematically with increasing depth, which indicates a certain trend (non-stationarity) in the vertical direction. The estimated (computed) (semi-) variogram in vertical direction ${/boma h}$ over all drill holes is presented in Figure 3.1.

Figure 3.1: Variogram of a Deposit of Copper.

The properties of this experimental variogram may be summarized as follows (special expressions will be explained in the following chapters):

(i)

a nugget-effect of about .4 $[/%Cu]^{2};$

(ii)

a transition phenomenon between 0 and about 100 feet with a sill of 1 and a range of about 50 feet;

(iii)

beyond about 100 feet the variogram suddenly tends to increase, which indicates the mentioned trend.

In words we summarize that in this example, in a vertical range of 100 feet the intrinsic hypothesis of a mineralization may be accepted. The semi-variogram shows a (finite) range (of influence) of about 50 feet. In this range we also may fit a theoretical variogram, the so-called spherical model which is specified by

with

The value for the quasi-stationarity is about $b = 100$ feet.