Geoscience Reference
In-Depth Information
4
Deinition of Estimation Domains
Abstract
Estimation of grades proceeds within domains defined on the basis of geological and sta-
tistical considerations. The definition and modeling of these domains is an important step
in mineral resource estimation. This Chapter presents practical aspects of the development
of estimation domains, the limitations faced when defining these domains, details of the
modeling of estimation domains, and the most commonly used methods to assign estima-
tion domains to a resource block model.
4.1
Estimation Domains
have some spatial predictability and not be overly mixed
with other domains.
A good definition of estimation domains is very impor-
tant. The consequences of defining inadequate estimation
domains are rarely evaluated. It is common to confuse the
concepts of geologic and estimation domains. Geologic do-
mains are commonly described by a single geologic variable.
Estimation domains are defined by a set of mineralization
controls and may contain more than one geological domain.
In multi-element deposits it is common to assume that the
estimation domains defined for the main element/mineral of
interest applies to all secondary elements that may be pres-
ent. In practice, different grades are controlled by different
geologic variables, and thus they may be predicted using dif-
ferent estimation domains.
For example, porphyry deposits with copper and gold
mineralization may exhibit an inverse spatial relationship,
that is, gold may not leach through weathering as copper
does. Gold may form a cap on the upper part of the deposit.
In such cases, copper and gold should be modeled using
different estimation domains. In epithermal deposits, gold
and silver mineralization may exhibit little correlation since
they are deposited differently. Estimating gold and silver
using the same estimation domains would lead to suboptimal
results.
Estimation domains must make spatial and geologic
sense (Coombes
2008
). The combination of geologic vari-
ables used to define the domains must have spatial and geo-
logic characteristics that are recognizable in drilling and/or
production data. The estimation domain must be sufficiently
Estimation domains are the geological equivalent to geosta-
tistical stationary zones and are defined as a volume of rock
with mineralization controls that result in approximately ho-
mogeneous distributions of mineralization. The spatial dis-
tributions of grade exhibit consistent statistical properties.
This does not mean that the grades are constant within the
domains; however, the geological and statistical properties
of the grades facilitate its prediction.
The concept of statistically homogeneous populations is
termed stationarity. Stationarity is a two-fold decision. First,
there is a choice of the data to pool together for common
analysis. Second, there is a choice of how statistics such
as the mean vary by location within the domain. Stationar-
ity is a property of the random function model (Isaaks and
Srivastava
1989
) and is not an intrinsic characteristic of the
variable. It is a decision made by the resource estimator and
is necessary to make inferences. Stationarity was formally
defined by Matheron (1962-1963) in the context of geosta-
tistics and is also discussed in Chap. 6.
Exploratory data analysis (EDA) may indicate the ex-
istence of several populations with significantly different
summary statistics. The understanding of the statistical
characteristics of the data, coupled with geologic knowl-
edge, leads to subdividing the deposit into domains for esti-
mation. This is considered more reasonable than taking the
entire deposit at one time. Domain definition depends on
the availability of enough data to reliably infer statistical pa-
rameters within each domain. Moreover, the domains must
