Geoscience Reference
In-Depth Information
represented in the database and in the deposit. These condi-
tions provide constraints on what can realistically be mod-
eled in practice.
regardless of whether they represent a strong mineralization
control or not. A rule of thumb threshold is 1 % of the total
number of intervals in the database, although this is depen-
dent on the total size of database.
Next, statistical comparisons between the initial domains
accepted will often lead to grouping. Statistical tools such
as histograms, probability plots, box plots, scatterplots,
quantile-quantile (Q-Q) plots, proportional effect plots, and
variograms are used. They allow comparisons of grade dis-
tributions within each of the domains proposed. Analysis of
the statistics requires a degree of subjectivity, since an ac-
ceptable degree of similarity needs to be defined. Once two
variables are shown to provide a similar degree of mineral-
ization control, and assuming it makes geologic sense, they
are grouped, and the statistical analysis repeated.
This iterative process can be labor-intensive, and is
usually repeated until a group of geologic variables and
elements have been defined that clearly separates differ-
ent types of mineralization. Some of the variables will be
grouped even though there are clear differences in the spa-
tial characteristics of the mineralization. This is often done
because of practical limitations, including data quantity,
metallurgical considerations, and other economic and tech-
nical factors.
4.2
Defining the Estimation Domains
A thorough stepwise approach is suggested here. It is based
on a combination of geological and statistical analyses. This
approach is more detailed and time-consuming, but it pro-
vides better support for estimation. The concept is based on
decomposing the problem by describing and modeling the
relationships between each geologic variable. The combina-
tion of variables results in a matrix that ranks the most criti-
cal grade controls as identified by the data. These should be
explained in terms of plausible natural processes, to ensure
that the controls derived from the data are consistent with
known geology.
Development of the grade domains begins and ends with
geologic knowledge. The first step is to define the geologic
variables that are used as the building blocks for the estima-
tion domains definition. Typical variables mapped from drill
hole data include lithology, alteration, mineralogy, weather-
ing (oxide/sulfide, for example), and structures or structural
domains. Not all these variables are always mapped; some
may not be relevant for a particular deposit type.
The second step is to decide the specific geologic vari-
ables that are the most important. This is based on geologic
considerations, overall abundance within the deposit, and
drill hole information.
Third, estimation domains based on all reasonable com-
binations of the geologic attributes are defined. Consider, for
example, 3 geologic attributes each with 4 variables, and thus
a total of 64 theoretically possible estimation domains. For
example, porphyry, andesites, breccias, and dacites could be
the 4 variables of lithology in a porphyry copper-type de-
posit. Data abundance will filter out a number of these. Con-
sideration of practical aspects will further reduce the number
of theoretical domains, such as existing or planned mineral
processing facilities. In copper, gold, and many other pre-
cious and base metal deposits, for example, it is not advis-
able to mix oxide and sulfide mineralization, since they are
frequently treated at separate processing plants, or, if one of
the two metallurgical types is small in volume or low grade,
it may be simply stockpiled. Another criterion often used is
proximity: certain units may be at the periphery of the de-
posit, and therefore should not be mixed with units at the
central portion of the deposit.
The fourth step involves a statistical description of the
initial domains. The main purpose is to remove or group do-
mains according to geologic considerations. Variables that
have little representation in the database should be removed,
Alternative Statistical Techniques
Other multivariate sta-
tistical techniques could be used to describe the relationships
between geology and grade. For example, some practitioners
have proposed the use of Classification and Regression Tree
analysis (CART, Breiman et al.
1984
) to determine and cat-
egorize relationships between geology and grade distribu-
tions. Techniques such as Principal Component Analysis and
Cluster Analysis have also been proposed. A common prob-
lem, however, is that these techniques are often used to clas-
sify the relationships based on statistical parameters without
geological consideration.
The proportional effect may also be used to define do-
mains. The proportional effect appears in the presence of
positively skewed distributions. It indicates that, as the aver-
age of the variable increases, so does its variability. These
plots, when comparing means and standard deviations of
groups of data defined according to geologic variables, may
show clusters of data. The assumption is that data within
each cluster belong to a quasi-stationary population, thus
defining estimation domains. These data clusters should be
correlated to specific geologic controls.
The iterative process using simple statistics described
is recommended. An important by-product is that the more
labor-intensive process leads to a more thorough understand-
ing of the geology. It ensures that the estimation domains are
a group of quasi-stationary domains that make spatial and
geologic sense, as opposed to only statistical groupings.
