Geoscience Reference
In-Depth Information
might consider 1-D vertical trends and 2-D areal trends that
are then merged into a 3-D trend model. There is no unique
way to merge 1-D and 2-D trends into a 3-D trend model,
but a simple approach is to merge these trends by assuming
conditional independence of vertical and areal trends:
There is also the uncertainty carried over from the geo-
logic interpretation and modeling which is more significant
in sparsely drilled areas. The geologic model can be another
important source of uncertainty that, when combined into es-
timation domains, can result in serious flaws in the resource
model.
All these sources of uncertainty combine with the fact
that mineralization will be naturally varying from one loca-
tion to another. This natural variability within the estimation
domains exists at different scales and should be considered
at the time of estimation.
( )
(
)
m z m
⋅
xy
,
(
)
z
xy
,
mxyz
,,
=
m
global
Where
m
z
(z) =
mean from vertical trend,
m
x, y
(x, y) =
mean
from areal trend,
m
global
=
global mean from histogram, and
m(x,y,z) =
mean at location
(x,y,z).
This equation effectively
rescales the vertical trend curve by the areal trend. Other
probability combination schemes such as permanence of ra-
tios could be used in situations where assuming conditional
independence leads to extreme mean values too close to zero
or too high.
4.6
Summary of Minimum, Good and Best
Practices
At a minimum, the methodology used to define estimation
domains should consider the most evident mineralization
controls, and include the basic tools needed to demonstrate
the relationships between geologic attributes and grade. The
main mineralization controls can often be described through
mapped geology and a working hypothesis of the genesis
of the deposit. Basic exploratory data analyses characterize
mineralization controls.
Good practice considers all available geologic informa-
tion and the relationship between grades and each geologic
variable. This process involves a first phase, in which the in-
dividual mapped geology, such as mineralization, lithology,
alteration, or others, is grouped in part by applying geologic
knowledge and common sense, in part applying numeric and
statistical constraints.
A new set of descriptive statistics is then developed in a
second phase of the study, from which an initial set of esti-
mation domains may be proposed. An iterative process that
includes further statistical analysis supported by geologic
knowledge results in the final definition of the estimation
domains.
The definition of estimation domains is an imperfect pro-
cess, characterized by compromises between the estimation
domains that should be defined (according to geology and
statistical analysis) and the amount of data available to de-
fine them. Sometimes, limitations in the coding of the origi-
nal database may also affect the definition of the estimation
domains.
Best practice is to define the estimation domains and
accompany it by an assessment of its uncertainty and the
limitations and assumptions used to define it. The defini-
tion should include limitations related to data quality and
quantity, geologic information used, and the type of statisti-
cal analysis used to assess whether the domains contacts are
hard or soft. The better tool to assess geologic uncertainty is
simulation.
4.5
Uncertainties Related to Estimation
Domain Definition
The definition of estimation domains is an important prereq-
uisite in the application of most geostatistical tools used in
resource modeling. The domains determine the mineralized
volume available, and thus is a major factor in the estimated
tonnage above economic cutoffs.
The definition of estimation domains is subjective and
limited by data and practical considerations. There are many
sources of uncertainty contributing to the uncertainty in the
definitions of contacts and volumes.
Some of the more typical sources of uncertainty include
geologic data: errors, omissions, or imprecise mapping and
logging are common. For example, in highly altered rock,
the precise description of lithology types can be difficult,
more so if diamond drilling is not used. Porphyries of dif-
ferent kinds are difficult to differentiate and different litholo-
gies may not be easy to distinguish. Human perceptions and
errors are important since many geologic attributes are sub-
ject to visual estimations and interpretations in the field. For
example, the alteration intensity or the percentage of sulfides
may have to be estimated by the geologist.
Limited data also may be a significant source of uncer-
tainty. It is common that two domains with clearly different
mineralization controls have to be combined into one do-
main because one of them does not have enough drill hole
information. This results in a mixture of populations that
cannot be resolved until more data are collected. The domain
with more data will influence the statistics, the variogram
models, and the kriging plans applied to estimate the grades
of the combined units.
