Geoscience Reference
In-Depth Information
Fig. 9.3
Transformation of the panel grades (
left
) and the SMU grades (
right
) to Gaussian units
the panel grade is known, the distribution of the SMUs within
that panel can be calculated. The average of the SMUs is the
estimated panel grade; the variance in Gaussian units is based
on the change of support coefficients. For a panel grade,
y
(
V
),
the SMUs within that panel will have a mean and variance of
2
†‡
r
'
r
'
{
}
{
}
E yv
()
= ⋅
yV
( );
Var yv
()
=−
ˆ
Š‹
1
r
r
The recoverable resources are easily calculated using the bi-
variate Gaussian assumption and the anamorphosis function.
Consider Fig.
9.4
, where a panel estimate and SMU distribu-
tion are shown. The recoverable resources are evaluated as a
truncated statistic, the SMU cutoff
Y
c
(
v
).
The tonnage (or proportion) above cutoff can be calcu-
lated as:
P z
( )
=
P z v
()
≥
z
| ( )
zV
=
P yv
()
≥
y
| ( )
yV
=
c
c
c
†
‡
ˆ
†‡
r
‰
y
−
ˆ‰
yV
()
Fig. 9.4
Transformation of the panel grades (
left
) and the SMU grades
(
right
) to Gaussian units. This figure is adapted from the Isatis User's
Manual
ˆ
‰
c
Š‹
r
1
−
G
ˆ
‰
ˆ
2
‰
'
†‡
r
r
ˆ
‰
1
−
ˆ‰
Step 4 is to transform the estimated panel grades to Gauss-
ian units using the panel anamorphosis equation.
Step 5 is to transform the cutoff grades to Gaussian values
using the modeled SMU anamorphosis. Under the bivariate
normal assumption, knowing the Gaussian panel grade al-
lows us to calculate the mean and variance of the conditional
SMU distribution. For this transformation the SMU anamor-
phosis is used.
Finally, the proportion and the grade above cutoff for the
conditional SMU distribution can be calculated. Given that
ˆ
‰
Š‹
Š
‹
The quantity of metal and the mean grade can be calculated
in two different ways, which give very similar results: (1) by
integrating the conditional distribution above cutoff (Rivoi-
rard
1994
):
∞
=Φ ⋅
∫
Qz
(
)
(
yv
( ))
gY v YV
(
( ) |
(
))
⋅
d yv
(
( ))
c
v
y
c