Geoscience Reference
In-Depth Information
Fig. 3.7 Effect of β on the iso-
zero surface. With increasing
β , the surface expands; with
decreasing β the surface
contracts. (Munroe 2012 )
3.2.1.3 Distance Function Thresholds
Tonnages can be calculated from the uncertainty bandwidth,
the size of which is determined by the uncertainty constant
C and the minimum and maximum limits of the bandwidth
determined from both C and β . The inner limit of the uncer-
tainty band, DF min is calculated as;
1
2
DF
=− ⋅
C DS β
min
where DS is the drill spacing and is the lower limit defined as
one half the distance function of the portion inside the vein
structure.
The outer limit of the uncertainty band, DF max is calcu-
lated as:
Fig. 3.8 Schematic of uncertainty bandwidth between drillholes.
(Munroe 2012 )
1
2
C DS
DF
=
max
β
where z is the estimated DF value. The total tonnage for a
particular probability interval p i , is the total number of cells
where p  ≤  p i . Recall the zone of uncertainty is located be-
tween DF min and DF max . If z < DF min then z is certainly lo-
cated within the vein structure. If z > DF max then z is most
certainly located outside the vein structure. By dividing the
space between DF min and DF max into a [0,1] interval, we can
readily extract tonnages from a mapped distance function for
any probability interval.
In order to define those probabilities and vein geometries,
the DF is mapped using Simple Kriging on a regular 3D grid.
Although other options are available, simple kriging is the
preffered option because it allows more control over areas
with less or uneven drilling.
and is the maximum limit defined as one half the distance
function of the portion outside the vein structure (Fig. 3.8 ).
The probability thresholds within the bandwidth are de-
fined as a p —probability value. The bandwidth interval is
rescaled to [0,1] so that DF min = 0 and DF max = 1. The dashed
line is the p 50 and has a p value of 0.5.
The p values are used to define the possible vein geom-
etries and extract tonnages for defined probability intervals
by converting individual model cell values into p values. The
p value is calculated as:
z
DF
p
=
min
DF
DF
max
min
 
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