Geoscience Reference
In-Depth Information
However, the basic problems to be solved remain the same. The five principal
sources of uncertainty are:
1. The first major source of uncertainty is provided by the probability of occurrence
itself. Any point in a study area on a map has probabilities associated with it that
a small unit area surrounding it contains mineral deposits of different types.
(If depth can be considered as a third dimension, unit volumes can be used in
addition to unit areas.)
2. The estimated probabilities have variances to express their uncertainty. Suppose
that one is concerned with a single deposit type or commodity in 2-D. For small
unit areas, the probabilities of occurrence then are very small. For example,
suppose the 10 % largest probabilities are approximately 0.01. This does not
only mean that a unit area with probability 0.01 would contain a deposit but also
that the variance of this probability is 0.01. This intrinsic variance normally
exceeds the estimation variance of the probability itself.
3. Intensity of exploration is a third source of uncertainty. This is a largely
unknown variable that is difficult to quantify. Fortunately, uncertainty associated
with variable intensity of exploration is much less than the uncertainty intrinsic
in the probability itself. However, it should be kept in mind that, from an
economic point of view, intensity of exploration can be regarded as the most
important variable because it principally determines number of undiscovered ore
deposits.
4. A second major source of uncertainty in mineral resource estimation is size
distribution of the deposits for which the probabilities of occurrence are being
estimated. In general, size of mineral deposits as a random variable covers
several orders of magnitude with the largest deposits (supergiants; cf . Agterberg
1995 ) being exceedingly rare but of utmost economic importance. It also should
be kept in mind that it is possible that deposit size is positively correlated with
probability of occurrence.
5. Metal grades including cut-off grades are to be considered as well although these
can often be incorporated in the definition of deposit type. In general, economic
data on past production, various types of reserves and grades are of highest
quality for the largest deposits with amount of information diminishing and
tending to become unavailable for smaller and lower-grade deposits. Two
factors to be considered are that mineral deposits for the same metal may
occur in different geological settings and that usually more than a single metal
is mined from the same deposit suggesting that total amount of ore also is useful
as a variable for estimating probabilities of occurrence together with size
frequency distribution modeling.
In order to further illustrate uncertainties (1) and (2), let us take a typical
weights-of-evidence ( cf . Bonham-Carter 1994 ; also see Chap. 5 ) result for example.
The output map with posterior probabilities in weights-of-evidence usually is
accompanied by a t -value map. Suppose that the t -value associated with a posterior
probability of 0.01 is equal to 4. This would mean that the estimation variance of
the probability of 0.01 amounts to (the square of 0.04
) 0.0016, and this is less
than 0.01 representing the intrinsic variance associated with the probability itself.
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