Conditioning

There are an infinite number of possible realizations $z_s({/boma x}), s = 1,/ldots,/infty,$ of a random function $Z({/boma x})$. From among this infinity of realizations, the simulations $z_{sc}({/boma x})$ that are chosen are those that meet the experimental data values at the actual data locations ${/boma x_i}$, i.e., those simulations for which

This is known as conditioning the simulation to the experimental data: the simulated deposits and the real one have the same clusters of rich and poor data at the same locations. This conditioning confers a certain robustness to the simulation ${z_{sc}({/boma x})}$ with respect to the characteristics of the real data ${z_0({/boma x})}$ which are not explicitly modelled by the random function $Z({/boma x})$. If, for example, a sufficient number of data show a local drift, then the conditional simulations, even though based on a stationary model, will reflect the local drift in the same zone. These conditional simulations can be further improved by adding all sorts of qualitative information available from the real deposit, such as geometry of the main faults, intercalated waste seams, etc.

Figure 7.1 illustrates a simulation along a profile. The small circles represent the conditioning data values, the thick curve is for the true values and the small dashed curve stands for the simulated ones.

Figure 7.1: Comparison: Simulation - Kriging.

The right-hand side of the profiles on Figure 7.1 also illustrates the fact that a simulation cannot be used to replace sampling, which is always necessary for a good local estimation of the deposit. In any case, the better the deposit is known, the better the structure of variability can be modelled and the denser the grid of conditional data will be, all of which will result in a simulation closer to, and more representative of, reality.