Geoscience Reference
In-Depth Information
10
Recoverable Resources: Simulation
Abstract
Local uncertainty estimates do not account for the variability from one location to another.
The idea of simulation is to assess the joint uncertainty between multiple realizations allow-
ing a more complete representation of block uncertainty and the uncertainty between mul-
tiple block locations. The tools described in this Chapter allow transferring uncertainty of
the resource estimates into risk in downstream studies. These studies are mine design, mine
planning, or operational optimization studies; the risk assessment is achieved after applying
transfer functions to the conditional simulation models.
10.1
Simulation versus Estimation
control tools in daily operations (Rossi
1999
), to analyze
risk related to resource classifications (Rossi and Camacho
2001
), to assess the uncertainty of minable reserves at the
project's feasibility stage (Guardiano et al.
1995
; Glacken
1996
; Van Brunt and Rossi
1999
; Journel and Kyriakidis
2004
; Leuangthong et al.
2006
; Badenhorst and Rossi
2012
),
and to assess mineralization potential in certain settings.
Other applications include assessment of recoverable re-
serves and drill hole spacing optimization studies.
Geostatistical conditional simulations are used to build
models that reproduce the full histogram and modeled mea-
sures of spatial continuity of the original, conditioning data.
They honor the characteristics of the spatial variable of inter-
est as represented by the conditioning data.
The simulation model should correctly represent the pro-
portion of high and low values, the mean, the variance, and
other univariate statistical characteristics of the data, as repre-
sented by the histogram. It should also correctly reproduce the
spatial continuity of the variable, including the connectivity of
low and high contaminant zones, anisotropies, relative nugget
effect, and other characteristics of the variogram model.
Conditional simulations are built on fine grids, fine
enough to provide a sufficient number of nodes within the
block size of interest. The vertical resolution of the grid
should be a function of the support data, for example the size
of the mining bench, if modeling a variable mined by open
pit. Larger grid sizes may be used sometimes because of the
amount of computer time and hard disk space involved.
Simulated models provide the same information that an es-
timated block model does, but, in addition, it also provides
a joint model of uncertainty. A “complete” resource model
should not only include an estimated grade, or even an es-
timated distribution, but also a more detailed assessment of
uncertainty and the consequences of that uncertainty (Dimi-
trakopoulos
1997
).
Estimation provides a value that is, on average, as close
as possible to the actual (unknown) value, based on some
definition of goodness or quality. It is unbiased, has mini-
mal quadratic error, uses linear combinations of the available
data, and has an unavoidable smoothing effect. Simulations
reproduce the original variability observed in the data and
allow an assessment of uncertainty. This implies that the ex-
treme values of the original distribution are preserved, see
Fig.
10.1
. The uncertainty model also provide the tools for
risk analysis when applying to it a transfer function
Estimation honors local data, is locally more accurate, and
has a smoothing effect appropriate for visualizing trends, but is
inappropriate for simulating extreme values and provides no as-
sessment of local uncertainty. Simulation also honors the local
data, but additionally reproduces the histogram, honors spatial
variability, and is able to provide an assessment of uncertainty.
Geostatistical conditional simulations have become popu-
lar as tools that provide models of uncertainty at different
stages of a mining project. They have been used as grade
