Geoscience Reference
In-Depth Information
First: the goals of the study must be specified to deter-
mine the work effort required for the study, the variables to
be predicted, the scale relevant for evaluation and the spe-
cific estimation, simulation and post processing steps. A data
inventory must be taken to review all available measured
data from drillholes, other sampling and historical produc-
tion data. The numerical models should reproduce all of
these measured data within the scale and accuracy of the
data. Conceptual data must also be assembled including a
geological understanding of the spatial distribution and ana-
logue data. The conceptual model expressed in this first step
may include schematic pictures and illustrations of the fea-
tures that should be contained in the final model.
Second: the entire volume being modeled will not be
combined and modeled with one technique and set of param-
eters. There are logical subsets based on geological zones
and rock types. The estimation domains will define rock vol-
umes that genetically belong together. The domains must be
large enough to contain sufficient data for reliable statistics,
yet small enough to isolate geological features for local ac-
curacy. A hierarchical system may be used where large scale
zones are modeled first, then smaller scale geological units,
then continuous grades within the final domain definition.
Third: the mean value of each variable may depend on lo-
cation within the chosen estimation domains. There are often
significant trends in the distribution of rock types. These
trends are understood even with few data. Continuous grade
variables may also have local variations that are important.
The results of the second step (subsets of the volume for
geostatistical analysis) and third step (modeling the location
dependence of the mean) are collectively known as the deci-
sion of stationarity.
Fourth: infer all required statistical parameters. The re-
quired statistical parameters will depend on the chosen
technique that, in turn, depends on the conceptual model
chosen for each stationary subset of the domain. Almost al-
ways, there will be a need to infer the univariate proportions
and histograms of each grade variable within each domain.
These univariate distributions are computed from the data
and calculated to be representative of the entire subset. Some
measures of spatial variability must also be inferred. In tra-
ditional Matheronian geostatistics (Matheron
1971
), vario-
grams are the measures that quantify the spatial variability of
each category and rock property. In presence of sparse data,
these statistical parameters are considered uncertain and a
number of scenarios are documented.
Fifth: calculate an estimate of each variable at each un-
sampled location. These estimates are based on the data and
do not involve any random numbers. The estimation is com-
monly a form of kriging considering indicators, data transfor-
mation, cokriging, and/or locally varying means as required.
Whenever possible, the uncertainty is estimated directly with
indicators for categorical variables and normal scores in a
multivariate Gaussian context for continuous variables. This
provides a single best estimate at each unsampled location
together with a measure of uncertainty. This is based entirely
on the data and decisions taken in the first four steps. The
results are useful for resource assessment and checking.
Sixth: thorough validation of the estimated values is
necessary. Often, the effort involved in validating and even
calibrating a model is under-appreciated. Model calibration
implies running multiple iterations of the estimation pro-
cess, varying some specific parameters, in order to repro-
duce a certain reference (for example, a blast hole model).
Validations are done to ensure the internal consistency of
the model; that is, the estimated values are consistent with
all assumptions, data, and geologic model used to build it.
Comparisons with previous models are made also, and if
available, against a production or reference model deemed
to be a reasonably accurate representation of true grades and
tonnages in the deposit.
Seventh: multiple realizations of all surfaces, rock types
and grades could be obtained to quantify joint uncertainty
and to provide a model of variability suitable for the assess-
ment of dilution and recoverable reserves. The simulation
techniques are often closely linked to the estimation tech-
niques. The estimation results are used for checking the
realizations and for a first estimate of the resource/reserve.
Uncertainty over a large volume depends on the simultane-
ous uncertainty at many locations; simulating multiple re-
alizations is the only practical approach to quantify such
large-scale uncertainty. Also, the details of the geological
heterogeneity may have a large influence on recovery and
reserve calculations.
Eighth: post-process all of the model results. Sometimes,
the statistical parameters from Steps 3 and 4 are useful in
themselves; variogram ranges may be used to understand
data spacing and expected length scales of geological fea-
tures. The estimated model provides expected results at un-
sampled locations and measures of local uncertainty that are
useful for data collection and management. Models of differ-
ent grades must be combined and important resource vari-
ables calculated. The simulated models provide large scale
uncertainty and input to subsequent engineering design.
These eight steps provide an overview of the workflow
of resource estimation and geostatistics to address specific
study objectives. Some of the details have been explained
in preceding chapters; other details are inevitably learned
by tradecraft, other textbooks, technical papers and software
user's guides. Invariably, many assumptions are made during
the course of a resource estimation study. The consequenc-
es of these assumptions and the limitations of the resulting
models must be understood by the modeler and those using
the resulting estimates.
