Geoscience Reference
In-Depth Information
Fig. 3.5
Schematic of distance
function. Numbers indicate the
distance assigned by the DF.
(Taken from Munroe
2012
)
3.2.1.2 Modified Distance Function (DF
mod
)
The DF is modified in a second step by applying a bias pa-
rameter,
β
, used to center the distribution of estimates. The
bias parameter is applied to the original DF:
(
dist
+
C
) /
β
β
∀
VI = 0
=
DF
mod
(
dist
+⋅ ∀
C
)
VI = 1
The fairness parameter
β
divides or multiples the original DF
depending whether VI indicates non-vein or vein, respec-
tively. A value of
β
= 1 returns the original DF value.
The iso-zero surface is the contact between vein and non-
vein. This zero point is known and honoured by the data. But
at locations away from sampled locations, however, there will
be uncertainty as to where the actual position of the contact
surface is located. The shape and size of the iso-zero surface
is controlled by
β
; it has the effect of dilating it for the larger
values of
β
(outer dashed ellipse in Fig.
3.7
), or eroding it for
decreasing values of
β
(corresponding inner dotted line).
The
β
parameter is a number typically between 0.1 and
2 and is dependent on drill hole spacing. For example, if
the drill hole spacing tends to inflate the vein geometry and
overestimate tonnage, then
β
values greater than 1 are used
to decrease it. The parameter
β
imposes a control on the final
surface and makes it possible to adjust the iso-zero surface
so that fair and unbiased estimates can be obtained. The cali-
bration of
β
needs careful consideration.
Fig. 3.6
Schematic of the uncertainty bandwidth defined by C, from
Munroe (
2012
)
nage uncertainty. The contrary would be true for closely
spaced drill holes. A symmetric variation on a constant
C
(a traditional “plus or minus”) could possibly lead to biases,
since it does not incorporate geologic knowledge. A second
parameter is defined to center the uncertainty width, beta
(
β
), providing more flexibility in the modeling of the vein
geometry.
