130
approximately 0.75 (blue line), hard data (Cu_DDH) with soft data (Cu_Chip) is close to
0.80 (red line), soft data (Cu_Chip), with data (Cu_XRF) is near to 0.75 (black line). In general, the variables have a moderate correlation. It indicates the soft and uncertain data can
improve the models obtained by stochastic simulation.
The variogram model was fitted to the experimental variogram of the normal score of the
primary variable. Equation 1 defines the variogram model of the primary variable (normal
score):
γ Cu ( )
.
.
. ,
.
Sph(1)
m
m
=
⋅
⋅
Sph(1)
⎛
⎝ ⎜
⎛ ⎛
⎝ ⎝
⎞
⎠ ⎟
⎞ ⎞
⎠ ⎠
0 1
. . 0 0
+ 90
157 5
66
67 5
40
(1)
3.2 Validations
To validate the simulated datasets obtained with Bayesian Updating, their spatial covariance and histogram were compared with the histogram and variogram of the original data.
These simulated values are at the locations where the secondary data had been sampled.
Figure 4 shows the experimental variograms along the major and minor directions, where the
red line represents the variogram model (Eq. 1) and the black lines represent the experimental
variograms of the data simulated by Bayesian Updating. The models are similar; meaning
the inferred data have the same spatial continuity of the hard data.
Figure 5 compares the histogram of original (red line) and simulated (by Bayesian updating) data (black lines). The simulated values reproduced the histogram of the original data.
Figure 4. Experimental (black line) data inferred by Bayesian Updating and modeled variograms of
the hard data (red line) a) Major direction, b) Minor direction.
Figure 5. Histogram reproduction hard data (red line) and Bayesian Updating data (black lines).
a)
1.20
0.80
0.40
b)
Variogram major direction( 157.5)
Variogram major direclion{67.5)
1.20
0.80
0.40
0.
20.
4 0.
60.
80.
100.
20.
40.
60.
80.
Di:otance
Oist<~nce
Histograr11~eproduction_Cu (%)inferred by Bayesian Updating
>2! 0.8
Q)
:::l
0'
~ 0.6
LL..
Q)
· .5 0.4
~
:::l
§ 0.2
u
-2
n real =so
m real = - 0.006
Oreal = 1.050
n ret= 195
m,., = 0 .000
Oret= 0.997
100
approximately 0.75 (blue line), hard data (Cu_DDH) with soft data (Cu_Chip) is close to
0.80 (red line), soft data (Cu_Chip), with data (Cu_XRF) is near to 0.75 (black line). In general, the variables have a moderate correlation. It indicates the soft and uncertain data can
improve the models obtained by stochastic simulation.
The variogram model was fitted to the experimental variogram of the normal score of the
primary variable. Equation 1 defines the variogram model of the primary variable (normal
score):
γ Cu ( )
.
.
. ,
.
Sph(1)
m
m
=
⋅
⋅
Sph(1)
⎛
⎝ ⎜
⎛ ⎛
⎝ ⎝
⎞
⎠ ⎟
⎞ ⎞
⎠ ⎠
0 1
. . 0 0
+ 90
157 5
66
67 5
40
(1)
3.2 Validations
To validate the simulated datasets obtained with Bayesian Updating, their spatial covariance and histogram were compared with the histogram and variogram of the original data.
These simulated values are at the locations where the secondary data had been sampled.
Figure 4 shows the experimental variograms along the major and minor directions, where the
red line represents the variogram model (Eq. 1) and the black lines represent the experimental
variograms of the data simulated by Bayesian Updating. The models are similar; meaning
the inferred data have the same spatial continuity of the hard data.
Figure 5 compares the histogram of original (red line) and simulated (by Bayesian updating) data (black lines). The simulated values reproduced the histogram of the original data.
Figure 4. Experimental (black line) data inferred by Bayesian Updating and modeled variograms of
the hard data (red line) a) Major direction, b) Minor direction.
Figure 5. Histogram reproduction hard data (red line) and Bayesian Updating data (black lines).
a)
1.20
0.80
0.40
b)
Variogram major direction( 157.5)
Variogram major direclion{67.5)
1.20
0.80
0.40
0.
20.
4 0.
60.
80.
100.
20.
40.
60.
80.
Di:otance
Oist<~nce
Histograr11~eproduction_Cu (%)inferred by Bayesian Updating
>2! 0.8
Q)
:::l
0'
~ 0.6
LL..
Q)
· .5 0.4
~
:::l
§ 0.2
u
-2
n real =so
m real = - 0.006
Oreal = 1.050
n ret= 195
m,., = 0 .000
Oret= 0.997
100